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Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais

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Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais
Computer Simulation A Foundational Approach Using Python
CHAPMAN & HALL/CRC COMPUTER and INFORMATION SCIENCE SERIES Series Editor: Sartaj Sahni ADVERSARIAL REASONING: COMPUTATIONAL APPROACHES TO READING THE OPPONENT’S MIND Alexander Kott and William M. McEneaney COMPUTER-AIDED GRAPHING AND SIMULATION TOOLS FOR AUTOCAD USERS P. A. Simionescu COMPUTER SIMULATION: A FOUNDATIONAL APPROACH USING PYTHON Yahya E. Osais DELAUNAY MESH GENERATION Siu-Wing Cheng, Tamal Krishna Dey, and Jonathan Richard Shewchuk DISTRIBUTED SENSOR NETWORKS, SECOND EDITION S. Sitharama Iyengar and Richard R. Brooks DISTRIBUTED SYSTEMS: AN ALGORITHMIC APPROACH, SECOND EDITION Sukumar Ghosh ENERGY-AWARE MEMORY MANAGEMENT FOR EMBEDDED MULTIMEDIA SYSTEMS: A COMPUTER-AIDED DESIGN APPROACH Florin Balasa and Dhiraj K. Pradhan ENERGY EFFICIENT HARDWARE-SOFTWARE CO-SYNTHESIS USING RECONFIGURABLE HARDWARE Jingzhao Ou and Viktor K. Prasanna EVOLUTIONARY MULTI-OBJECTIVE SYSTEM DESIGN: THEORY AND APPLICATIONS Nadia Nedjah, Luiza De Macedo Mourelle, and Heitor Silverio Lopes FROM ACTION SYSTEMS TO DISTRIBUTED SYSTEMS: THE REFINEMENT APPROACH Luigia Petre and Emil Sekerinski FROM INTERNET OF THINGS TO SMART CITIES: ENABLING TECHNOLOGIES Hongjian Sun, Chao Wang, and Bashar I. Ahmad FUNDAMENTALS OF NATURAL COMPUTING: BASIC CONCEPTS, ALGORITHMS, AND APPLICATIONS Leandro Nunes de Castro HANDBOOK OF ALGORITHMS FOR WIRELESS NETWORKING AND MOBILE COMPUTING Azzedine Boukerche PUBLISHED TITLES
HANDBOOK OF APPROXIMATION ALGORITHMS AND METAHEURISTICS Teofilo F. Gonzalez HANDBOOK OF BIOINSPIRED ALGORITHMS AND APPLICATIONS Stephan Olariu and Albert Y. Zomaya HANDBOOK OF COMPUTATIONAL MOLECULAR BIOLOGY Srinivas Aluru HANDBOOK OF DATA STRUCTURES AND APPLICATIONS Dinesh P. Mehta and Sartaj Sahni HANDBOOK OF DYNAMIC SYSTEM MODELING Paul A. Fishwick HANDBOOK OF ENERGY-AWARE AND GREEN COMPUTING Ishfaq Ahmad and Sanjay Ranka HANDBOOK OF GRAPH THEORY, COMBINATORIAL OPTIMIZATION, AND ALGORITHMS Krishnaiyan “KT” Thulasiraman, Subramanian Arumugam, Andreas Brandstädt, and Takao Nishizeki HANDBOOK OF PARALLEL COMPUTING: MODELS, ALGORITHMS AND APPLICATIONS Sanguthevar Rajasekaran and John Reif HANDBOOK OF REAL-TIME AND EMBEDDED SYSTEMS Insup Lee, Joseph Y-T. Leung, and Sang H. Son HANDBOOK OF SCHEDULING: ALGORITHMS, MODELS, AND PERFORMANCE ANALYSIS Joseph Y.-T. Leung HIGH PERFORMANCE COMPUTING IN REMOTE SENSING Antonio J. Plaza and Chein-I Chang HUMAN ACTIVITY RECOGNITION: USING WEARABLE SENSORS AND SMARTPHONES Miguel A. Labrador and Oscar D. Lara Yejas IMPROVING THE PERFORMANCE OF WIRELESS LANs:A PRACTICAL GUIDE Nurul Sarkar INTEGRATION OF SERVICES INTO WORKFLOW APPLICATIONS Paweł Czarnul INTRODUCTION TO NETWORK SECURITY Douglas Jacobson LOCATION-BASED INFORMATION SYSTEMS: DEVELOPING REAL-TIME TRACKING APPLICATIONS Miguel A. Labrador, Alfredo J. Pérez, and Pedro M.Wightman PUBLISHED TITLES CONTINUED
METHODS IN ALGORITHMIC ANALYSIS Vladimir A. Dobrushkin MULTICORE COMPUTING: ALGORITHMS, ARCHITECTURES, AND APPLICATIONS Sanguthevar Rajasekaran, Lance Fiondella, Mohamed Ahmed, and Reda A. Ammar NETWORKS OF THE FUTURE: ARCHITECTURES, TECHNOLOGIES, AND IMPLEMENTATIONS Mahmoud Elkhodr, Qusay F. Hassan, and Seyed Shahrestani PERFORMANCE ANALYSIS OF QUEUING AND COMPUTER NETWORKS G. R. Dattatreya THE PRACTICAL HANDBOOK OF INTERNET COMPUTING Munindar P. Singh SCALABLE AND SECURE INTERNET SERVICES AND ARCHITECTURE Cheng-Zhong Xu SOFTWARE APPLICATION DEVELOPMENT: A VISUAL C++® , MFC, AND STL TUTORIAL Bud Fox, Zhang Wenzu, and Tan May Ling SPECULATIVE EXECUTION IN HIGH PERFORMANCE COMPUTER ARCHITECTURES David Kaeli and Pen-Chung Yew TRUSTWORTHY CYBER-PHYSICAL SYSTEMS ENGINEERING Alexander Romanovsky and Fuyuki Ishikawa VEHICULAR NETWORKS: FROM THEORY TO PRACTICE Stephan Olariu and Michele C.Weigle X-MACHINES FOR AGENT-BASED MODELING: FLAME PERSPECTIVES Mariam Kiran PUBLISHED TITLES CONTINUED
Yahya E. Osais Computer Simulation A Foundational Approach Using Python
CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20171024 International Standard Book Number-13: 978-1-498-72682-5 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
To my wife, Asmahan, and my daughters, Renad, Retal, and Remas.
Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais
Contents List of Programs xv List of Figures xix List of Tables xxvii Foreword xxix Preface xxxi About the Author xxxiii Abbreviations xxxv Symbols xxxvii Part I The Fundamentals Chapter 1 Introduction 3 1.1 THE PILLARS OF SCIENCE AND ENGINEERING 3 1.2 STUDYING THE QUEUEING PHENOMENON 4 1.3 WHAT IS SIMULATION? 5 1.4 LIFECYCLE OF A SIMULATION STUDY 6 1.5 ADVANTAGES AND LIMITATIONS OF SIMULATION 9 1.6 OVERVIEW OF THE BOOK 10 1.7 SUMMARY 11 Chapter 2 Building Conceptual Models 13 2.1 WHAT IS A CONCEPTUAL MODEL? 13 2.2 ELEMENTS OF A CONCEPTUAL MODEL 15 2.2.1 Entities 15 ix
x Contents 2.2.2 Attributes 15 2.2.3 State Variables 16 2.2.4 Events 17 2.2.5 Activities 17 2.3 THE SINGLE-SERVER QUEUEING SYSTEM 18 2.4 STATE DIAGRAMS 22 2.5 ACTUAL TIME VERSUS SIMULATED TIME 23 2.6 SUMMARY 24 2.7 EXERCISES 24 Chapter 3 Simulating Probabilities 27 3.1 RANDOM EXPERIMENTS AND EVENTS 27 3.2 WHAT IS PROBABILITY? 28 3.3 COMPUTING PROBABILITIES 30 3.4 PROBABILITY AS A SAMPLE MEAN 32 3.5 SUMMARY 36 3.6 EXERCISES 36 Chapter 4 Simulating Random Variables and Stochastic Pro- cesses 39 4.1 WHAT ARE RANDOM VARIABLES? 39 4.1.1 Probability Mass Functions 40 4.1.2 Cumulative Distribution Functions 41 4.1.3 Probability Density Functions 43 4.1.4 Histograms 44 4.2 SOME USEFUL RANDOM VARIABLES 46 4.2.1 Bernoulli 46 4.2.2 Binomial 47 4.2.3 Geometric 48 4.2.4 Poisson 49 4.2.5 Uniform 50 4.2.6 Exponential 53 4.2.7 Erlang 54 4.2.8 Normal 54 4.2.9 Triangular 55 4.3 STOCHASTIC PROCESSES 56
Contents xi 4.4 DYNAMIC SYSTEM EVOLUTION 58 4.5 SIMULATING QUEUEING PROCESSES 60 4.5.1 Discrete-Time Markov Chains 62 4.5.2 Continuous-Time Markov Chains 64 4.6 SUMMARY 67 4.7 EXERCISES 67 Chapter 5 Simulating the Single-Server Queueing System 69 5.1 SIMULATION MODEL 69 5.2 COLLECTING SIMULATED DATA 75 5.3 PERFORMANCE LAWS 76 5.3.1 Throughput 76 5.3.2 Utilization 76 5.3.3 Response Time 77 5.3.4 E[N(t)] 79 5.3.5 P[N] 82 5.4 INDEPENDENT SIMULATION RUNS 84 5.5 TRANSIENT AND STEADY PHASES 86 5.6 SUMMARY 91 5.7 EXERCISES 91 Chapter 6 Statistical Analysis of Simulated Data 93 6.1 POPULATIONS AND SAMPLES 93 6.2 PROBABILITY DISTRIBUTION OF THE SAMPLE MEAN 95 6.3 CONFIDENCE INTERVALS 97 6.3.1 Interpretations 100 6.3.2 Why Not Always Use a 99% Confidence Interval? 102 6.4 COMPARING TWO SYSTEM DESIGNS 104 6.5 SUMMARY 105 6.6 EXERCISES 105 Part II Managing Complexity Chapter 7 Event Graphs 109 7.1 WHAT IS AN EVENT GRAPH? 109 7.2 EXAMPLES 111
xii Contents 7.2.1 The Arrival Process 111 7.2.2 Single-Server Queueing System 112 7.2.3 Multiple-Server Queueing System 114 7.2.4 Single-Server Queueing System with a Limited Queue Capacity 114 7.2.5 Single-Server Queuing System with Failure 115 7.2.6 Single-Server Queuing System with Reneging 116 7.2.7 Single-Server Queuing System with Balking 116 7.3 TRANSLATING EVENT GRAPHS INTO CODE 117 7.4 SUMMARY 120 7.5 EXERCISES 120 Chapter 8 Building Simulation Programs 123 8.1 TIME-DRIVEN SIMULATION 123 8.2 EVENT-DRIVEN SIMULATION 126 8.3 WRITING EVENT-DRIVEN SIMULATION PROGRAMS 127 8.4 PROGRAMMING ISSUES 134 8.4.1 Event Collision 134 8.4.2 Identifiers for Packets 134 8.4.3 Stopping Conditions for the Simulation Loop 134 8.5 SUMMARY 135 8.6 EXERCISES 135 Part III Problem-Solving Chapter 9 The Monte Carlo Method 139 9.1 ESTIMATING THE VALUE OF π 139 9.2 NUMERICAL INTEGRATION 142 9.3 ESTIMATING A PROBABILITY 144 9.3.1 Buffon’s Needle Problem 144 9.3.2 Reliability 146 9.4 VARIANCE REDUCTION TECHNIQUES 149 9.4.1 Control Variates 149 9.4.2 Stratified Sampling 151 9.4.3 Antithetic Sampling 153 9.4.4 Dagger Sampling 156 9.4.5 Importance Sampling 158
Contents xiii 9.5 SUMMARY 161 9.6 EXERCISES 161 Part IV Sources of Randomness Chapter 10 Random Variate Generation 165 10.1 THE INVERSION METHOD 165 10.1.1 Continuous Random Variables 167 10.1.2 Discrete Random Variables 169 10.1.2.1 Generating a Bernoulli Variate 171 10.1.2.2 Generating a Binomial Variate 172 10.1.2.3 Generating a Geometric Variate 173 10.2 THE REJECTION METHOD 173 10.3 THE COMPOSITION METHOD 177 10.4 THE CONVOLUTION METHOD 179 10.5 SPECIALIZED METHODS 182 10.5.1 The Poisson Distribution 182 10.5.2 The Normal Distribution 184 10.6 SUMMARY 186 10.7 EXERCISES 186 Chapter 11 Random Number Generation 187 11.1 PSEUDO-RANDOM NUMBERS 187 11.2 CHARACTERISTICS OF A GOOD GENERATOR 189 11.3 JUST ENOUGH NUMBER THEORY 190 11.3.1 Prime Numbers 190 11.3.2 The Modulo Operation 190 11.3.3 Primitive Roots for a Prime Number 191 11.4 THE LINEAR CONGRUENTIAL METHOD 192 11.5 THE MULTIPLICATIVE CONGRUENTIAL METHOD 193 11.5.1 2k Modulus 193 11.5.2 Prime Modulus 194 11.6 LINEAR FEEDBACK SHIFT REGISTERS 194 11.7 STATISTICAL TESTING OF RNGs 199 11.7.1 The Chi-Squared Test 199 11.7.2 The Poker Test 201
xiv Contents 11.7.3 The Spectral Test 202 11.7.4 The Lag Plot 204 11.8 SUMMARY 205 11.9 EXERCISES 205 Part V Case Studies Chapter 12 Case Studies 209 12.1 NETWORK RELIABILITY 209 12.2 PACKET DELIVERY OVER A WIRELESS CHANNEL 218 12.3 SIMPLE ARQ PROTOCOL 226 12.4 SUMMARY 233 12.5 EXERCISES 233 Appendix A Overview of Python 235 A.1 BASICS 235 A.2 INPUT AND OUTPUT 237 A.3 BITWISE OPERATORS 238 A.4 LISTS 239 A.5 LIST FUNCTIONS 240 A.6 GENERATING RANDOM NUMBERS AND RANDOM VARI- ATES 241 A.7 IMPLEMENTING THE EVENT LIST 242 A.7.1 Priority Queue 242 A.7.2 Heap Queue 242 A.7.3 Sorting a List 243 A.8 PASSING A FUNCTION NAME AS AN ARGUMENT 244 A.9 TUPLES AS RECORDS 245 A.10 PLOTTING 245 Appendix B An Object-Oriented Simulation Framework 251 Appendix C The Chi-Squared Table 267 Appendix D The t-Distribution Table 269 Bibliography 271 Index 273
List of Programs 3.1 Simulating the experiment of throwing a die. The output is shown as a comment on each line. 31 3.2 Approximating the probability of an outcome in the experiment of throwing a die. 31 3.3 Simulation program for studying the running mean of the ran- dom experiment of tossing a coin. This program is also used to generate Figure 3.4. 35 4.1 Python program for generating the histogram from an exponen- tial data set (see Figure 4.6). 44 4.2 Python program for plotting the CDF and PDF of a uniform random variable (see Figures 4.9(a) and 4.9(b)). 51 4.3 Simulating a two-state discrete-time Markov chain given its probability transition matrix and an initial state. 63 4.4 Simulating a Poisson process. 64 4.5 Simulating a birth-death process and plotting its sample path (see Figure 4.21). 66 5.1 Simulation program of the single-server queueing system. 71 5.2 Estimating the average response time of the system. 77 5.3 Estimating the average number of customers in the sytem (E[N(t)]). 80 5.4 Estimating the steady-state probability distribution (P[N = k]). 82 5.5 Performing multiple independent simulation runs of the simula- tion model of the single-server queueing system. 86 5.6 Determining a good trunction point using the average of several realizations of an output variable. 90 6.1 Calculating the confidence interval using Python. 99 6.2 Plotting confidence intervals and population mean. 101 7.1 Python implementation of the event graph in Figure 7.4. 118 8.1 A time-driven simulation program for the discrete-time single- server queueing system. 124 xv
xvi Contents 8.2 An event-driven simulation program for the single-server queue- ing system. 129 9.1 Python procedure for estimating π using MC simulation. 141 9.2 Python procedure for estimating a one-dimensional integral. 143 9.3 Python procedure for the Buffon’s needle experiment. 145 9.4 Estimating the reliability of the system in Figure 9.6(b). 148 9.5 Estimating an integral in Eqn. (9.19) using the method of con- trol variates. 150 9.6 Estimating the integral R 1 0 e−x dx using the crude Monte Carlo and stratified methods. 152 9.7 Estimating the mean of a uniform random variable using anti- thetic sampling. 154 9.8 Estimating the value of the integral in Eqn. (9.25) using CMC and antithetic sampling. The reduction in variance is about 12%. 155 9.9 Estimating the reliability of the system in Figure 9.6(b) using dagger sampling. 157 9.10 Estimating the average of a function using importance sampling. 160 10.1 Generating random variates using the information in Figure 10.2(a). 170 10.2 Generating Bernoulli random variates. 171 10.3 Generating binomial random variates. 172 10.4 Generating geometric random variates. 173 10.5 Generating random variates based on the rejection method. 176 10.6 Generating an Erlang random variate using the convolution method. 179 10.7 Generating a standard normal random variate using the convo- lution method. 181 10.8 Generating a Poisson random variate. 183 10.9 Generating a random variate from a standard normal distribution. 185 11.1 Testing a set of random numbers if they are uniformly distributed. 188 11.2 Generating the maximum-length random sequence from the four-bit LFSR shown in Figure 11.3. 197 11.3 Generating the maximum-length random sequence from an eight-bit LFSR. 198 11.4 Python program for generating a 3D scatter plot for the spectral test. 202 11.5 Python procedure for generating a lag plot for a random sequence. 204 12.1 Computing unreliability for the graph in Figure 12.2 using the exact expression in Eqn. (12.1). 212
Contents xvii 12.2 Computing unreliability for the graph in Figure 12.2 using crude Monte Carlo simulation. 213 12.3 Computing unreliability for the graph in Figure 12.2 using strat- ified sampling. 214 12.4 Computing unreliability for the graph in Figure 12.2 using an- tithetic sampling. 215 12.5 Computing unreliability for the graph in Figure 12.2 using dag- ger sampling. The number of samples is significantly less. 216 12.6 Python implementation of the event graph in Figure 12.4 220 12.7 Python implementation of the event graph of the simple stop- and-wait ARQ protocol in Figure 12.8. 228 A.1.1 Starting a new Python interactive session. 235 A.1.2 Running a Python program from the command line. 236 A.1.3 A Python source file. It can also be referred to as a Python script. 236 A.2.1 Input and output functions. 237 A.3.1 Binary operations on integer numbers. 238 A.3.2 Handling unsigned binary numbers. 239 A.4.1 Lists and some of their operations. 239 A.5.1 Transposing a matrix using the zip function. Matrix is first un- packed using the start (*) operator. 240 A.6.1 Importing the random module and calling some of the functions inside it. 241 A.7.1 Implementing the event list using the queue module. 242 A.7.2 Implementing the event list using the hqueue module. 243 A.7.3 Implementing the event list by sorting a list. 243 A.8.1 The name of the function can be stored in a list and then used to call the function. 244 A.8.2 The name of the function can be passed as an argument to another function. 244 A.9.1 A tuple can be used as a record that represents an item in the event list. 245 A.10.1 Code for generating Figure 4.12(b). 245 A.10.2 Code for generating Figure 10.6(a). 247 A.10.3 Code for generating Figure 10.6(b). 248 B.1 Event. 251 B.2 Simulation Entity. 252 B.3 Event list and scheduler. 252 B.4 Example 1. 254
xviii Contents B.5 Example 2. 255 B.6 Example 3. 256 B.7 Example 4. 258 B.8 M/M/1. 259 B.9 State. 262 B.10 State Machine. 263 B.11 Simple Protocol. 263
List of Figures 1.1 The three pillars of science and engineering: Observation (O), Experimentation (E), and Computation (C). By analogy, the table needs the three legs to stay up. 4 1.2 A queue at a checkout counter in a supermarket. A phenomenon arising whenever there is a shared resource (i.e., the cashier) and multiple users (i.e., the shoppers). 5 1.3 Types of models and the data generated from them. 6 1.4 Phases of a simulation study. 6 2.1 A mental image of the system and its behavior must be devel- oped before a conceptual model can be constructed. 14 2.2 Different mental images can be developed for the same system. They include different levels of details. Complexity increases as you add more details. 14 2.3 A continuous state variable takes values from a continuous set (e.g., [0, 5] in (a)). A discrete state variable, on the other hand, takes values from a discrete set (e.g., {0, 1, 2, 3, 4, 5} in (b)). 16 2.4 Events are used to move dynamic entities through a system. A packet is moved from a source to a destination through two routers using eight events. 17 2.5 An activity is delimited by two events and lasts for a random duration of time. 18 2.6 A queueing phenomenon emerges whenever there is a shared resource and multiple users. 19 2.7 Conceptual model of the queueing situation in Figure 2.6. 20 2.8 A sample path of the state variable Q which represents the number of persons in the single-server queueing system. Note the difference in the time between every two consecutive arrival events. 20 2.9 Four activities occur inside the single-server queueing system: (a) Generation, (b) Waiting, (c) Service, and (d) Delay. The length of each activity is a random variable of time. 21 xix
xx LIST OF FIGURES 2.10 A simple electrical circuit and its state diagram. Only the switch and lamp are modeled. Events are generated by the switch to change the state of the lamp. 22 2.11 State diagrams of the state variables associated with the queue and server in the single-server queueing system in Figure 2.7. A portion of the state space of the system is shown in (c). 23 3.1 A random experiment of tossing a coin. There are two possible outcomes. 28 3.2 A random experiment of throwing a die. There are six possible outcomes. 28 3.3 Three different samples for the random experiment of tossing a coin 10 times. The running mean is computed for the third sample using cumulative sums. The last value at position 10 of the list of running means is equal to the sample mean. The sample mean is the probability of seeing a head. 33 3.4 Running mean for the random experiment of tossing a coin. The mean eventually converges to the true value as more samples are generated. 34 4.1 Sample space for the random experiment of throwing two dice. The outcome of the experiment is a random variable X ∈ {2, 3, ..., 12}. 40 4.2 The PMF of a discrete random variable representing the out- come of the random experiment of throwing two dice. 41 4.3 The cumulative distribution function of a discrete random vari- able representing the outcome of the random experiment of throwing two dice. 42 4.4 Probability density function of a continuous random variable. 43 4.5 Elements of a histogram. Bins can be of different widths. Length of a bar could represent frequency or relative frequency. 45 4.6 Histogram for an exponential data set. This figure is generated using Listing 4.1. 46 4.7 The situation of observing four successes in a sequence of seven Bernoulli trials can be modeled as a binomial random variable. 48 4.8 The PMF of the Poisson random variable for λ = 10. Notice that P(x) approaches zero as x increases. 49 4.9 Probability distribution functions for the uniform random vari- able where a = 3 and b = 10. 50 4.10 Probability distribution functions of the exponential random variable where µ = 1.5. 53
LIST OF FIGURES xxi 4.11 The PDF of the normal random variable with µ = 30 and σ = 10. 55 4.12 Probability distribution functions of the triangular random vari- able with a = 1, b = 10, and c = 7. 56 4.13 A stochastic process maps each outcome in the sample space to a time function. Time functions are combined (convoluted) to produce two sample paths: g1 and g2. Two kinds of means can be defined for a stochastic process. 57 4.14 The Bernoulli random process: (a) sample space, (b) random variable, (c) time functions, (d) result of running the random experiment in each slot, and (e) final sample path. 58 4.15 A sample path through the state space of a dynamic system. Entry and exit points are random. Data is generated along this sample path and a time average is computed as an estimate of the performance metric of interest. 59 4.16 A sample path through the state space of the single-server queueing system. The initial state does not have to be (0, ‘F’). 59 4.17 A sample path of a discrete-time Markov chain over nine time units. Events occur at integer times only. N(1) is the number of entities in the system during the first time slot. 61 4.18 A sample path of a continuous-time Markov chain. Events occur at random times. The time spent in a state has an exponential distribution. 61 4.19 A graphical representation of a two-state, discrete-time Markov chain. 62 4.20 Sample path of a Poisson process. Only arrival events occur inside a Poisson process. 64 4.21 Sample path of a birth-death process. 65 5.1 Physical structure of the single-server queueing system. 70 5.2 Graphical representation of the relationship between random variables and simulation events. 72 5.3 A sample path of the random process N(t). 72 5.4 Random processes present in the single-server queueing system. Both the arrival and departure processes are Poisson processes. (a) Places where the random processes are defined. (b) Total number of arrivals which have occurred up to time t1 is three. (c) The sample path of the departure process is a shifted version of the sample path of the arrival process. (d) Sample path of the queueing (birth-death) process which tracks the number of packets in the system. 73
xxii LIST OF FIGURES 5.5 A simulation experiment represents an execution of a simulation model with a specific set of parameters, inputs, and outputs. 76 5.6 A sample path of the number of packets in the single-server queueing system. There are eight rectangles under the curve of the sample path. 80 5.7 Raw data generated when running a simulation program. 85 5.8 Cumulative average versus number of simulated packets. The theoretical value is Wavg = 10. After the transient phase is over, the cumulative average starts approaching the theoretical value. 87 5.9 Z is the average of the five output sequences Y[0]-Y[4]. A trun- cation point can visually be determined by using the curve of Z. In this example, a good truncation point is n = 3000. 89 5.10 The first two steps in the Welch’s method. In step 1, multiple realizations of the output variable are generated. These realiza- tions are combined into one sequence in step 2. 89 5.11 A two-server queueing system with a finite buffer of size three. 91 6.1 Population and samples for the simulation experiment of esti- mating the delay through the single-server queueing system by simulating five packets. The population is (0, ∞). 94 6.2 Probability distribution of the sample mean is normal. 95 6.3 Frequency distribution of the average delay D through the single-server queueing system with λ = 1 and µ = 1.25. The population mean is 4. 96 6.4 The empirical rule for the distribution of samples around the population mean. 95% of the area under the curve of the normal distribution lies within two standard deviations (equal to 1.96) of the mean. 97 6.5 Two of the calculated confidence intervals do not include the population mean. The population mean is 15. 101 7.1 Types of edges in event graphs. 110 7.2 State diagram (a) and event graph (b) for the Poisson arrival process. 112 7.3 Event graph for the single-server queueing system. 113 7.4 Reduced event graph for the single-server queueing system. 113 7.5 Event graph for the K-server queueing system. 114 7.6 Event graph for the single-server queueing system with a limited queue capacity. 114 7.7 Event graph for the single-server queueing system with a server that fails. 115
LIST OF FIGURES xxiii 7.8 Event graph for the single-server queueing system with reneging. 116 7.9 Event graph for the single-server queueing system with balking. 116 7.10 A template for synthesizing simulation programs from event graphs. 121 7.11 Two parallel single-server queueing systems with one shared traffic source. 122 7.12 A simple network setup where a user communicates with a server in a data center over a communication channel created inside a network. Propagation delay (Pd) and rate (R) are two important characteristics of a channel. 122 8.1 In time-driven simulation, simulated time evolves in increments of size ∆t. 124 8.2 Arrival and departure processes and their random variables in continuous- and discrete-time queues. 126 8.3 In event-driven simulation, simulated time evolves in steps of random sizes (∆t1 6= ∆t2). 127 8.4 An event-driven simulation program has two independent com- ponents: simulator and model. 128 8.5 How a random number u is used to generate an event. 128 8.6 A flowchart of the event-driven simulation program. 129 8.7 Two single-server queueing systems in series with external ar- rivals. 136 9.1 Setup used for performing MC simulation to estimate π. 140 9.2 Setup used for performing MC simulation to estimate a one- dimensional integral. 142 9.3 The goal of the Buffon’s needle experiment is to compute the probability that a needle of length l will intersect a horizontal line in a set of horizontal lines separated by a distance equal to d. 144 9.4 Two random variables (a and φ) are used in the simulation. The needle will intersect with the closest horizontal line if b ≥ a. 145 9.5 According to trigonometry, the length of the line segment b is equal to the value of the y-coordinate of the upper tip of the needle. 146 9.6 Reliability is the probability that the input is connected to the output. (a) The input is connected to the output if the swtich is closed. (b) Reliability of the overall system is a function of the reliabilities of the individual blocks. In this case, Relsys = R3 , where R is the reliability of a block. 147
xxiv LIST OF FIGURES 9.7 Sample space of the random experiment of throwing two dice. For the random variate 4, 4+10 2 = 7 is generated instead if anti- thetic sampling is used. 154 9.8 With dagger sampling, three trials are performed using a single random number. Hence, three samples are generated. 157 9.9 Values of g(x) are very close to zero over region 1. Probabil- ity distribution of x is very close to zero over region 1. Another probability distribution has to be used in order to generate sam- ples from region 1 where the values of the function g(x) are more interesting. 159 9.10 Estimating the shortest path between nodes A and D (see Ex- ercise 9.2). 161 10.1 Generating random variates from cumulative distribution func- tions. 166 10.2 Generating random variates using the PMF of a discrete random variable. 170 10.3 Generating a random variate from the PDF f(x) using the aux- iliary PDF g(x). x = 3 is accepted if u ≤ f(3) g(3) . 174 10.4 Random variates generated using the rejection method. 175 10.5 Triangular distribution. f(x) is composed of two functions each of which is defined over half the interval over which f(x) exists. 177 10.6 The shape of the histogram constructed using the random vari- ates generated using the convolution method resembles that of the PDF of the Erlang random variable. 180 10.7 Histogram constructed from standard normal variates generated using the convolution method in Listing 10.7. 181 10.8 Arrivals during a time slot can be modeled as a Poisson random variable. 183 10.9 The shape of the histogram constructed using simulated Poisson random variates resembles that of the PMF of a Poisson random variable. 184 10.10 Using the procedure in Listing 10.9, the uniform random num- bers are transformed into random standard normal variates. 185 11.1 Probability distribution of u. 188 11.2 Multiple seeds are used to make different simulation runs. Differ- ent paths in the system state space are explored and the average is computed using the values resulting from these different paths. 193 11.3 A four-bit linear feedback shift register with characteristic poly- nomial c(x) = 1 + x3 + x4 . 195
LIST OF FIGURES xxv 11.4 Computing the first intermediate binary number on line 13 in Listing 11.2. 196 11.5 An eight-bit linear feedback shift register with characteristic polynomial c(x) = 1 + x4 + x5 + x6 + x8 . 197 11.6 104 triplets of successive random numbers generated using List- ing 11.4. Planes can be seen when the figure is viewed from the right angle. 202 11.7 The lag plot for a sequence of sinusoidal values. An elliptical pattern can be clearly identified. 204 11.8 The lag plot generated by the code in Listing 11.5. The sequence uniformly fills the 2D space. 205 12.1 A graph consisting of eight vertices and 11 edges. 210 12.2 Network fails if nodes v1 and v4 become disconnected. The event will occur if any of the following groups of links fail: {(e1, e2), (e1, e3), (e2, e4), (e3, e4)}. 210 12.3 A point-to-point wireless system. The transmitter has a buffer which can store up to B packets. The probability that a trans- mission attempt is successful is 1 − Perr. 218 12.4 Event graph for the system in Figure 12.3. 220 12.5 Average packet delay increases as the quality of the wireless channel degrades. 225 12.6 Percentage of delivered packets drops as the quality of the wire- less channel degrades. 226 12.7 Behavior of the simple stop-and-wait ARQ protocol with two possibilities: acknowledgment and frame loss. 227 12.8 Event graph for the simple stop-and-wait ARQ protocol. 228 12.9 Throughput deteriorates as the packet error rate increases. 232
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custom to refuse it. However, such exchanges are sometimes effected, by allowing them more or less of advantage. They have sometimes accepted of two Moors for a Christian, at others they have refused five or six for one. Perhaps Turkish captives may be objects of greater partiality with them, as their government is entirely in the hands of Turks, who are treated in every instance as a superior order of beings. Exchange, too, will be more practicable in our case, as our captives have not been sold to private individuals, but are retained in the hands of the Government. The liberation of our citizens has an intimate connection with the liberation of our commerce in the Mediterranean, now under the consideration of Congress. The distresses of both proceed from the same cause, and the measures which shall be adopted for the relief of the one, may, very probably, involve the relief of the other. XX.—The Secretary of State, to whom was referred by the House of Representatives, the representation from the General Court of the Commonwealth of Massachusetts, on the subjects of the cod and whale fisheries, together with the several papers accompanying it, has had the same under consideration, and thereupon makes the following report: February 1, 1791. The representation sets forth that, before the late war, about four thousand seamen, and about twenty-four thousand tons of shipping, were annually employed from that State, in the whale fishery, the produce whereof was about three hundred and fifty thousand pounds lawful money a year. That, previous to the same period, the cod fishery of that State employed four thousand men, and twenty-eight thousand tons of shipping, and produced about two hundred and fifty thousand pounds a year.
That these branches of business, annihilated during the war, have been, in some degree, recovered since; but that they labor under many and heavy embarrassments, which, if not removed, or lessened, will render the fisheries every year less extensive and important. That these embarrassments are, heavy duties on their produce abroad, and bounties on that of their competitors; and duties at home on several articles, particularly used in the fisheries. And it asks that the duties be taken off; that bounties be given to the fishermen; and the national influence be used abroad, for obtaining better markets for their produce. The cod and whale fisheries, carried on by different persons, from different ports, in different vessels, in different seas, and seeking different markets, agree in one circumstance, in being as unprofitable to the adventurer, as important to the public. A succinct view of their rise, progress, and present state, with different nations, may enable us to note the circumstances which have attended their prosperity, and their decline; to judge of the embarrassments which are said to oppress ours; to see whether they depend on our own will, and may, therefore, be remedied immediately by ourselves, or, whether depending on the will of others, they are without the reach of remedy from us, either directly or indirectly. Their history being as unconnected as their practice, they shall be separately considered. Within twenty years after the supposed discovery of Newfoundland, by the Cabots, we find that the abundance of fish on its banks, had already drawn the attention of the people of Europe. For, as early as 1517, or 1519, we are told of fifty ships being seen there at one time. The first adventurers in that fishery were the Biscayans, of Spain, the Basques and Bas-Bretons, of France, all united anciently in language, and still in habits, and in extreme poverty. The last circumstance enabled them long to retain a considerable share of
the fishery. In 1577, the French had one hundred and fifty vessels there; the Spaniards had still one hundred, and the Portuguese fifty, when the English had only fifteen. The Spaniards and Portuguese seem at length to have retired silently, the French and English claiming the fishery exclusively, as an appurtenance to their adjacent colonies, and the profits being too small for nations surcharged with the precious metals proceeding from their mines. Without materials to trace the intermediate progress, we only know that, so late as 1744, the French employed there five hundred and sixty-four ships, and twenty-seven thousand five hundred seamen, and took one million two hundred and forty-six thousand quintals of fish, which was three times the extent to which England and her colonies together, carried this fishery at that time. The English, in the beginning of the seventeenth century, had employed, generally, about one hundred and fifty vessels in the Newfoundland fishery. About 1670 we find them reduced to eighty, and one hundred, the inhabitants of New England beginning now to supplant them. A little before this, the British Parliament perceiving that their citizens were unable to subsist on the scanty profits which sufficed for their poorer competitors, endeavored to give them some advantage by prohibiting the importation of foreign fish; and, at the close of the century, they formed some regulations for their government and protection, and remitted to them some duties. A successful war enabled them, in 1713, to force from the French a cession of the Island of Newfoundland; under these encouragements, the English and American fisheries began to thrive. In 1731 we find the English take two hundred thousand quintals of fish, and the Americans two hundred and thirty thousand, besides the refuse fish, not fit for European markets. They continue to gain ground, and the French to lose it, insomuch that, about 1755, they are said to have been on a par; and, in 1768, the French have only two hundred and fifty-nine vessels, of twenty-four thousand four hundred and twenty tons, nine thousand seven hundred and twenty- two seamen, taking two hundred thousand quintals, while America
alone, for some three or four years before that, and so on, to the commencement of the late war, employed six hundred and sixty-five vessels, of twenty-five thousand six hundred and fifty tons, and four thousand four hundred and five seamen, and took from three hundred and fifty thousand to upwards of four hundred thousand quintals of fish, and England a still greater quantity, five hundred and twenty-six thousand quintals, as is said. Spain had formally relinquished her pretensions to a participation in these fisheries, at the close of the preceding war; and, at the end of this, the adjacent continent and islands being divided between the United States, the English and French, (for the last retained two small islands merely for this object,) the right of fishing was appropriated to them also. France, sensible of the necessity of balancing the power of England on the water, and, therefore, of improving every resource for raising seamen, and seeing that her fishermen could not maintain their competition without some public patronage, adopted the experiment of bounties on her own fish, and duties on that of foreign nations brought into her markets. But, notwithstanding this, her fisheries dwindle, from a change taken place, insensibly, in the character of her navigation, which, from being the most economical, is now become the most expensive. In 1786, she is said to have employed but seven thousand men in this fishery, and to have taken four hundred and twenty-six thousand quintals; and, in 1787, but six thousand men, and one hundred and twenty-eight thousand quintals. She seems not yet sensible that the unthriftiness of her fisheries proceeds from the want of economy, and not the want of markets; and that the encouragement of our fishery abridges that of a rival nation, whose power on the ocean has long threatened the loss of all balance on that element. The plan of the English Government, since the peace, has been to prohibit all foreign fish in their markets, and they have given from eighteen to fifty thousand pounds sterling on every fishing vessel complying with certain conditions. This policy is said to have been so
far successful, as to have raised the number of seamen employed in that business, in 1786, to fourteen thousand, and the quantity of fish taken, to 732,000 quintals. * * * * * * * * The fisheries of the United States, annihilated during the war; their vessels, utensils, and fishermen destroyed; their markets in the Mediterranean and British America lost, and their produce dutied in those of France; their competitors enabled by bounties to meet and undersell them at the few markets remaining open, without any public aid, and, indeed, paying aids to the public;—such were the hopeless auspices under which this important business was to be resumed. Yet it was resumed, and, aided by the mere force of natural advantages, they employed, during the years 1786, 1787, 1788, and 1789, on an average, five hundred and thirty-nine vessels, of nineteen thousand one hundred and eighty-five tons, three thousand two hundred and eighty-seven seamen, and took two hundred and fifty thousand six hundred and fifty quintals of fish. * * * And an official paper * * shows that, in the last of those years, our exportation amounted to three hundred and seventy-five thousand and twenty quintals, and thirty thousand four hundred and sixty-one barrels; deduction made of three thousand seven hundred and one quintals, and six thousand three hundred and forty-three barrels of foreign fish, received and re-exported. * * Still, however, the calculations * * which accompany the representation, show that the profits of the sales in the years 1787 and 1788, were too small to afford a living to the fishermen, and on those of 1789, there was such a loss as to withdraw thirty-three vessels, of the town of Marblehead alone, from the further pursuit of this business; and the apprehension is, that, without some public aid, those still remaining will continue to withdraw, and this whole commerce be engrossed by a single nation. This rapid view of the cod fishery enables us to discern under what policy it has nourished or declined in the hands of other nations, and
to mark the fact, that it is too poor a business to be left to itself, even with the nation most advantageously situated. It will now be proper to count the advantages which aid, and the disadvantages which oppose us, in this conflict. Our advantages are— 1. The neighborhood of the great fisheries, which permits our fishermen to bring home their fish to be salted by their wives and children. 2. The shore fisheries, so near at hand, as to enable the vessels to run into port in a storm, and so lessen the risk, for which distant nations must pay insurance. 3. The winter fisheries, which, like household manufactures employ portions of time, which would otherwise be useless. 4. The smallness of the vessels, which the shortness of the voyage enables us to employ, and which, consequently, require but a small capital. 5. The cheapness of our vessels, which do not cost above the half of the Baltic fir vessels, computing price and duration. 6. Their excellence as sea boats, which decreases the risk and quickens the return. 7. The superiority of our mariners in skill, activity, enterprise, sobriety, and order. 8. The cheapness of provisions. 9. The cheapness of casks, which, of itself, is said to be equal to an extra profit of fifteen per cent. These advantages are of such force, that, while experience has proved that no other nation can make a mercantile profit on the
Newfoundland fishery, nor can support it without national aid, we can make a living profit, if vent for our fish can be procured. Of the disadvantages opposed to us, those which depend on ourselves, are— Tonnage and naval duties on the vessels employed in the fishery. Impost duties on salt. On tea, rum, sugar, molasses, hooks, lines, and leads, duck, cordage, and cables, iron, hemp, and twine, used in the fishery; coarse woollens, worn by the fishermen, and the poll tax levied by the State on their persons. The statement No. 6, shows the amount of these, exclusive of the State tax and drawback on the fish exported, to be $5 25 per man, or $57 75 per vessel of sixty-five tons. When a business is so nearly in equilibrio that one can hardly discern whether the profit be sufficient to continue it or not, smaller sums than these suffice to turn the scale against it. To these disadvantages, add ineffectual duties on the importation of foreign fish. In justification of these last, it is urged that the foreign fish received, is in exchange for the produce of agriculture. To which it may be answered, that the thing given, is more merchantable than that received in exchange, and agriculture has too many markets to be allowed to take away those of the fisheries. It will rest, therefore, with the wisdom of the Legislature to decide, whether prohibition should not be opposed to prohibition, and high duty to high duty, on the fish of other nations; whether any, and which, of the naval and other duties may be remitted, or an equivalent given to the fisherman, in the form of a drawback, or bounty; and whether the loss of markets abroad, may not, in some degree, be compensated, by creating markets at home; to which might contribute the constituting fish a part of the military ration, in stations not too distant from navigation, a part of the necessary sea stores of vessels, and the encouraging private individuals to let the fishermen share with the cultivator, in furnishing the supplies of the table. A habit introduced from motives of patriotism, would soon be followed
from motives of taste; and who will undertake to fix the limits to this demand, if it can be once excited, with a nation which doubles, and will continue to double, at very short periods? Of the disadvantages which depend on others, are— 1. The loss of the Mediterranean markets. 2. Exclusions from the markets of some of our neighbors. 3. High duties in those of others; and, 4. Bounties to the individuals in competition with us. The consideration of these will find its place more aptly, after a review of the condition of our whale fishery shall have led us to the same point. To this branch of the subject, therefore, we will now proceed. The whale fishery was first brought into notice of the southern nations of Europe, in the fifteenth century, by the same Biscayans and Basques who led the way to the fishery of Newfoundland. They began it on their own coasts, but soon found that the principal residence of the whale was in the Northern seas, into which, therefore, they pursued him. In 1578 they employed twenty-five ships in that business. The Dutch and Hamburghers took it up after this, and about the middle of the seventeenth century the former employed about two hundred ships, and the latter about three hundred and fifty. The English endeavored also to participate of it. In 1672, they offered to their own fishermen a bounty of six shillings a ton, on the oil they should bring home, and instituted, at different times, different exclusive companies, all of which failed of success. They raised their bounty, in 1733, to twenty shillings a ton, on the admeasurement of the vessel. In 1740, to thirty shillings, with a privilege to the fishermen against being impressed. The Basque fishery, supported by poverty alone, had maintained but a feeble existence, before competitors aided by the bounties of their nation,
and was, in fine, annihilated by the war of 1745, at the close of which the English bounty was raised to forty shillings. From this epoch, their whale fishery went on between the limits of twenty- eight and sixty-seven vessels, till the commencement of the last war. The Dutch, in the meantime, had declined gradually to about one hundred and thirty ships, and have, since that, fallen down to less than half that number. So that their fishery, notwithstanding a bounty of thirty florins a man, as well as that of Hamburg, is now nearly out of competition. In 1715, the Americans began their whale fishery. They were led to it at first by the whales which presented themselves on their coasts. They attacked them there in small vessels of forty tons. As the whale, being infested, retired from the coast, they followed him farther and farther into the ocean, still enlarging their vessels with their adventures, to sixty, one hundred, and two hundred tons. Having extended their pursuit to the Western Islands, they fell in, accidentally, with the spermaceti whale, of a different species from that of Greenland, which alone had hitherto been known in commerce: more fierce and active, and whose oil and head matter was found to be more valuable, as it might be used in the interior of houses without offending the smell. The distinction now first arose between the Northern and Southern fisheries: the object of the former being the Greenland whale, which frequents the Northern coasts and seas of Europe and America; that of the latter being the spermaceti whale, which was found in the Southern seas, from the Western Islands and coast of Africa, to that of Brazil, and still on to the Falkland Islands. Here, again, within soundings, on the coast of Brazil, they found a third species of whale, which they called the black or Brazil whale, smaller than the Greenland, yielding a still less valuable oil, fit only for summer use, as it becomes opaque at 50 degrees of Fahrenheit's termometer, while that of the spermaceti whale is limpid to 41, and of the Greenland whale to 36, of the same thermometer. It is only worth taking, therefore, when it falls in the way of the fishermen, but not worth seeking, except when they have
failed of success against the spermaceti whale, in which case, this kind, easily found and taken, serves to moderate their loss. In 1771 the Americans had one hundred and eighty-three vessels, of thirteen thousand eight hundred and twenty tons, in the Northern fishery, and one hundred and twenty-one vessels, of fourteen thousand and twenty tons, in the Southern, navigated by four thousand and fifty-nine men. At the beginning of the late war, they had one hundred and seventy-seven vessels in the Northern, and one hundred and thirty-two in the Southern fishery. At that period, our fishery being suspended, the English seized the opportunity of pushing theirs. They gave additional bounties of £500, £400, £300, £200, £100 sterling, annually, to the five ships which should take the greatest quantities of oil. The effect of which was such, as, by the year 1786, to double the quantity of common oil necessary for their own consumption. Finding, on a review of the subject, at that time, that their bounties had cost the Government £13 10s. sterling a man, annually, or sixty per cent. on the cargoes, a part of which went consequently to ease the purchases of this article made by foreign nations, they reduced the northern bounty from forty to thirty shillings the ton of admeasurement. They had, some little time before, turned their attention to the Southern fishery, and given very great bounties in it, and had invited the fishermen of the United States to conduct their enterprises. Under their guidance, and with such encouragement, this fishery, which had only begun with them in 1784 or 1785, was rising into value. In 1788 they increased their bounties, and the temptations to our fishermen, under the general description of foreigners who had been employed in the whale fishery, to pass over with their families and vessels to the British dominions, either in America or Europe, but preferably to the latter. The effect of these measures had been prepared, by our whale oils becoming subject, in their market, to the foreign duty of £18 5s. sterling the ton, which, being more than equal to the price of the common oil, operated as a prohibition on
that, and gave to their spermaceti oil a preference over ours to that amount. * * * * * * * * The fishermen of the United States, left without resource, by the loss of their market, began to think of accepting the British invitation, and of removing, some to Nova Scotia, preferring smaller advantages in the neighborhood of their ancient country and friends, others to Great Britain, postponing country and friends to high premiums. The Government of France could not be inattentive to these proceedings. They saw the danger of letting four or five thousand seamen, of the best in the world, be transferred to the marine strength of another nation, and carry over with them an art, which they possessed almost exclusively. To give time for a counterplan, the Marquis de Lafayette, the valuable friend and citizen of this, as well as that country, wrote to a gentleman in Boston, to dissuade the fishermen from accepting the British proposals, and to assure them that their friends in France would endeavor to do something for them. A vessel was then arrived from Halifax at Nantucket, to take off those who had proposed to remove. Two families had gone abroad, and others were going. In this moment, the letter arriving, suspended their designs. Not another went abroad, and the vessel returned to Halifax with only the two families. The plan adopted by the French ministry, very different from that of the first mover, was to give a counter invitation to the Nantucket men to remove and settle in Dunkirk, offering them a bounty of fifty livres (between nine and ten dollars) a ton on the admeasurement of the vessels they should equip for the whale fishery, with some other advantages. Nine families only, of thirty-three persons, accepted the invitation. This was in 1785. In 1786, the ministry were led to see that their invitation would produce but little effect, and that the true means of preventing the emigration of our fishermen to the British dominions would be to enable them still to follow their calling from
their native country, by giving them a new market for their oils, instead of the old one they had lost. The duties were, therefore, abated on American whale oil immediately, and a further abatement promised by the letter No. 8, and, in December, 1787, the arrêt No. 9 was passed. The rival fishermen immediately endeavored to turn this measure to their own advantage, by pouring their whale oils into the markets of France, where they were enabled, by the great premiums received from their Government, perhaps, too, by extraordinary indemnifications, to undersell both the French and American fishermen. To repel this measure, France shut her ports to all foreign fish oils whatever, by the arrêt No. 10. The British whale fishery fell, in consequence, the ensuing year from two hundred and twenty-two to one hundred and seventy-eight ships. But this general exclusion has palsied our fishery also. On the 7th of December, 1788, therefore, by the arrêt No. 11, the ports of France still remaining shut to all other nations, were again opened to the produce of the whale fisheries of the United States, continuing, however, their endeavors to recover a share in this fishery themselves, by the aid of our fishermen. In 1784, 1785, 1786, they had had four ships. In 1787, three. In 1788, seventeen in the two fisheries of four thousand five hundred tons. These cost them in bounty 225,000 livres, which divided on one thousand five hundred and fifty tons of oil, the quantity they took, amounted to 145 livres (near twenty-seven dollars) the ton, and, on about one hundred natives on board the seventeen ships, (for there were one hundred and fifty Americans engaged by the voyage) came to 2,225 livres, or about 416⅔ dollars a man. We have had, during the years 1787, 1788 and 1789, on an average, ninety-one vessels, of five thousand eight hundred and twenty tons, in the northern, and thirty-one of four thousand three hundred and ninety tons in the southern fishery. * * * * * These details will enable Congress to see with what a competition we have to struggle for the continuance of this fishery, not to say its
increase. Against prohibitory duties in one country, and bounties to the adventurers in both of those which are contending with each other for the same object, ours have no auxiliaries, but poverty and rigorous economy. The business, unaided, is a wretched one. The Dutch have peculiar advantages for the northern fishery, as being within six or eight days' sail of the grounds, as navigating with more economy than any other nation in Europe, their seamen content with lower wages, and their merchants with lower profit. Yet the memorial No. 13, from a committee of the whale merchants to the States General of Holland, in the year 1775, states that fourteen millions of guilders, equal to five million six hundred thousand dollars, has been lost in that fishery in forty-seven years, being about one hundred and twenty thousand dollars a year. The States General, thereupon, gave a bounty of thirty guilders a man to the fishermen. A person immediately acquainted with the British whale fishery, and whose information merits confidence, has given assurance that the ships employed in their northern fishery, in 1788, sunk £800 each, on an average, more than the amount of the produce and bounties. An English ship of three hundred tons and forty-two seamen, in this fishery, generally brings home, after a four months' voyage, twenty-five tons of oil, worth £437 10s. sterling; but the wages of the officers and seamen will be £400; there remain but £37 10s., not worth taking into account, towards the outfit and merchants' profit. These, then, must be paid by the Government; and it is on this idea that the British bounty is calculated. Our vessels for the northern fishery average sixty-four tons, and cost, when built, fitted out, and victualled for the first voyage, about three thousand dollars. They have taken, on an average, the three last years, according to the statement No. 12, eighteen tons of oil, worth, at our market, nine hundred dollars, which are to pay all expenses, and subsist the fishermen and merchant. Our vessels for the southern fishery average one hundred and forty tons, and cost, when built, fitted out, and victualled, for their first voyage, about six thousand five hundred dollars. They have taken on an average, the three last years, according to the same statement, thirty-two tons of
oil each, worth at our market three thousand two hundred dollars, which are, in like manner, to pay all expenses, and subsist the owners and navigators. These expenses are great, as the voyages are generally of twelve months' duration. No hope can arise of their condition being bettered by an augmentation of the price of oil. This is kept down by the competition of the vegetable oils, which answer the same purposes, not quite so well, but well enough to become preferable, were the price to be raised, and so well, indeed, as to be more generally used than the fish oils for lighting houses and cities. The American whale fishery is principally followed by the inhabitants of the island of Nantucket—a sand bar of about fifteen miles long, and three broad, capable of maintaining, by its agriculture, about twenty families; but it employed in these fisheries, before the war, between five or six thousand men and boys; and, in the only harbor it possesses, it had one hundred and forty vessels, one hundred and thirty-two of which were of the larger kind, as being employed in the southern fishery. In agriculture, then, they have no resource; and, if that of their fishery cannot be pursued from their own habitations, it is natural they should seek others from which it can be followed, and preferably those where they will find a sameness of language, religion, laws, habits, and kindred. A foreign emissary has lately been among them, for the purpose of renewing the invitations to a change of situation. But, attached to their native country, they prefer continuing in it, if their continuance there can be made supportable. This brings us to the question, what relief does the condition of this fishery require? 1. A remission of duties on the articles used for their calling. 2. A retaliating duty on foreign oils, coming to seek a competition with them in or from our ports. 3. Free markets abroad. 1. The remission of duties will stand on nearly the same ground with that to the cod fishermen.
2. The only nation whose oil is brought hither for competition with our own, makes ours pay a duty of about eighty-two dollars the ton, in their ports. Theirs is brought here, too, to be reshipped fraudulently, under our flag, into ports where it could not be received under theirs, and ought not to be covered by ours, if we mean to preserve our own admission into them. The 3d and principal object is to find markets for the vent of oil. Portugal, England, Holland, Sweden, Denmark, Prussia, Russia, the Hanse towns, supply themselves and something more. Spain and Italy receive supplies from England, and need the less, as their skies are clearer. France is the only country which can take our surplus, and they take principally of the common oil; as the habit is but commencing with them of ascribing a just value to spermaceti whale. Some of this, however, finds its vent there. There was, indeed, a particular interest perpetually soliciting the exclusion of our oils from their markets. The late government there saw well that what we should lose thereby would be gained by others, not by themselves. And we are to hope that the present government, as wise and friendly, will also view us, not as rivals, but as co-operators against a common rival. Friendly arrangements with them, and accommodation to mutual interest, rendered easier by friendly dispositions existing on both sides, may long secure to us this important resource for our seamen. Nor is it the interest of the fisherman alone, which calls for the cultivation of friendly arrangements with that nation; besides five-eights of our whale oil, and two-thirds of our salted fish, they take from us one-fourth of our tobacco, three-fourths of our live stock * * * * * a considerable and growing portion of our rice, great supplies, occasionally, of other grain; in 1789, which, indeed, was extraordinary, four millions of bushels of wheat, and upwards of a million of bushels of rye and barley * * * * * and nearly the whole carried in our own vessels. * * * * * They are a free market now, and will, in time, be a valuable one for ships and ship timber, potash, and peltry.
England is the market for the greatest part of our spermaceti oil. They impose on all our oils a duty of eighteen pounds five shillings sterling the ton, which, as to the common kind, is a prohibition, as has been before observed, and, as to the spermaceti, gives a preference of theirs over ours to that amount, so as to leave, in the end, but a scanty benefit to the fishermen; and, not long since, by a change of construction, without any change of law, it was made to exclude our oils from their ports, when carried in our vessels. On some change of circumstance, it was construed back again to the reception of our oils, on paying always, however, the same duty of eighteen pounds five shillings. This serves to show that the tenure by which we hold the admission of this commodity in their markets, is as precarious as it is hard. Nor can it be announced that there is any disposition on their part to arrange this or any other commercial matter, to mutual convenience. The ex parte regulations which they have begun for mounting their navigation on the ruins of ours, can only be opposed by counter regulations on our part. And the loss of seamen, the natural consequence of lost and obstructed markets for our fish and oil, calls, in the first place, for serious and timely attention. It will be too late when the seaman shall have changed his vocation, or gone over to another interest. If we cannot recover and secure for him these important branches of employment, it behooves us to replace them by others equivalent. We have three nurseries for forming seamen: 1. Our coasting trade, already on a safe footing. 2. Our fisheries, which, in spite of natural advantages, give just cause of anxiety. 3. Our carrying trade, our only resource of indemnification for what we lose in the other. The produce of the United States, which is carried to foreign markets, is extremely bulky. That part of it which is now in the hands of foreigners, and which we may resume into our own, without touching the rights of those nations who have met us in fair arrangements by treaty, or the interests of those who, by their voluntary regulations, have paid so just and liberal a respect to our
interests, as being measured back to them again, places both parties on as good ground, perhaps, as treaties could place them—the proportion, I say, of our carrying trade, which may be resumed without affecting either of these descriptions of nations, will find constant employment for ten thousand seamen, be worth two millions of dollars, annually, will go on augmenting with the population of the United States, secure to us a full indemnification for the seamen we lose, and be taken wholly from those who force us to this act of self protection in navigation. Hence, too, would follow, that their Newfoundland ships, not receiving provisions from us in their bottoms, nor permitted (by a law of their own) to receive in ours, must draw their subsistence from Europe, which would increase that part of their expenses in the proportion of four to seven, and so far operate as a duty towards restoring the level between them and us. The tables No. 2 and 12, will show the quantity of tonnage, and, consequently, the mass of seamen whose interests are in distress; and No. 17, the materials for indemnification. If regulations exactly the counterpart of those established against us, would be ineffectual, from a difference of circumstances, other regulations equivalent can give no reasonable ground of complaint to any nation. Admitting their right of keeping their markets to themselves, ours cannot be denied of keeping our carrying trade to ourselves. And if there be anything unfriendly in this, it was in the first example. The loss of seamen, unnoticed, would be followed by other losses in a long train. If we have no seamen, our ships will be useless, consequently our ship timber, iron, and hemp; our ship building will be at an end, ship carpenters go over to other nations, our young men have no call to the sea, our produce, carried in foreign bottoms, be saddled with war-freight and insurance in times of war; and the history of the last hundred years shows, that the nation which is our carrier has three years of war for every four years of peace. (No. 18.) We lose, during the same periods, the carriage for belligerent
powers, which the neutrality of our flag would render an incalculable source of profit; we lose at this moment the carriage of our own produce to the annual amount of two millions of dollars, which, in the possible progress of the encroachment, may extend to five or six millions, the worth of the whole, with an increase in the proportion of the increase of our numbers. It is easier, as well as better, to stop this train at its entrance, than when it shall have ruined or banished whole classes of useful and industrious citizens. It will doubtless be thought expedient that the resumption suggested should take effect so gradually, as not to endanger the loss of produce for the want of transportation; but that, in order to create transportation, the whole plan should be developed, and made known at once, that the individuals who may be disposed to lay themselves out for the carrying business, may make their calculations on a full view of all circumstances. On the whole, the historical view we have taken of these fisheries, proves they are so poor in themselves, as to come to nothing with distant nations, who do not support them from their treasury. We have seen that the advantages of our position place our fisheries on a ground somewhat higher, such as to relieve our treasury from giving them support; but not to permit it to draw support from them, nor to dispense the government from the obligation of effectuating free markets for them; that, for the great proportion of our salted fish, for our common oil, and a part of our spermaceti oil, markets may perhaps be preserved, by friendly arrangements towards those nations whose arrangements are friendly to us, and the residue be compensated by giving to the seamen thrown out of business the certainty of employment in another branch, of which we have the sole disposal. XXI.—Opinion against the constitutionality of a National Bank.
February 15, 1791. The bill for establishing a National Bank undertakes among other things:— 1. To form the subscribers into a corporation. 2. To enable them in their corporate capacities to receive grants of land; and so far is against the laws of Mortmain.[26] 3. To make alien subscribers capable of holding lands; and so far is against the laws of alienage. 4. To transmit these lands, on the death of a proprietor, to a certain line of successors; and so far changes the course of Descents. 5. To put the lands out of the reach of forfeiture or escheat; and so far is against the laws of Forfeiture and Escheat. 6. To transmit personal chattels to successors in a certain line; and so far is against the laws of Distribution. 7. To give them the sole and exclusive right of banking under the national authority; and so far is against the laws of Monopoly. 8. To communicate to them a power to make laws paramount to the laws of the States; for so they must be construed, to protect the institution from the control of the State legislatures; and so, probably, they will be construed. I consider the foundation of the Constitution as laid on this ground: That all powers not delegated to the United States, by the Constitution, nor prohibited by it to the States, are reserved to the States or to the people. [XIIth amendment.] To take a single step beyond the boundaries thus specially drawn around the powers of Congress, is to take possession of a boundless field of power, no longer susceptible of any definition. The incorporation of a bank, and the powers assumed by this bill, have not, in my opinion, been delegated to the United States, by the
Constitution. 1. They are not among the powers specially enumerated: for these are: 1st. A power to lay taxes for the purpose of paying the debts of the United States; but no debt is paid by this bill, nor any tax laid. Were it a bill to raise money, its origination in the Senate would condemn it by the Constitution. 2d. To borrow money. But this bill neither borrows money nor ensures the borrowing it. The proprietors of the bank will be just as free as any other money holders, to lend or not to lend their money to the public. The operation proposed in the bill, first, to lend them two millions, and then to borrow them back again, cannot change the nature of the latter act, which will still be a payment, and not a loan, call it by what name you please. 3. To regulate commerce with foreign nations, and among the States, and with the Indian tribes. To erect a bank, and to regulate commerce, are very different acts. He who erects a bank, creates a subject of commerce in its bills; so does he who makes a bushel of wheat, or digs a dollar out of the mines; yet neither of these persons regulates commerce thereby. To make a thing which may be bought and sold, is not to prescribe regulations for buying and selling. Besides, if this was an exercise of the power of regulating commerce, it would be void, as extending as much to the internal commerce of every State, as to its external. For the power given to Congress by the Constitution does not extend to the internal regulation of the commerce of a State, (that is to say of the commerce between citizen and citizen,) which remain exclusively with its own legislature; but to its external commerce only, that is to say, its commerce with another State, or with foreign nations, or with the Indian tribes. Accordingly the bill does not propose the measure as a regulation of trade, but as productive of considerable advantages to trade. Still less are these powers covered by any other of the special enumerations.
II. Nor are they within either of the general phrases, which are the two following:— 1. To lay taxes to provide for the general welfare of the United States, that is to say, to lay taxes for the purpose of providing for the general welfare. For the laying of taxes is the power, and the general welfare the purpose for which the power is to be exercised. They are not to lay taxes ad libitum for any purpose they please; but only to pay the debts or provide for the welfare of the Union. In like manner, they are not to do anything they please to provide for the general welfare, but only to lay taxes for that purpose. To consider the latter phrase, not as describing the purpose of the first, but as giving a distinct and independent power to do any act they please, which might be for the good of the Union, would render all the preceding and subsequent enumerations of power completely useless. It would reduce the whole instrument to a single phrase, that of instituting a Congress with power to do whatever would be for the good of the United States; and, as they would be the sole judges of the good or evil, it would be also a power to do whatever evil they please. It is an established rule of construction where a phrase will bear either of two meanings, to give it that which will allow some meaning to the other parts of the instrument, and not that which would render all the others useless. Certainly no such universal power was meant to be given them. It was intended to lace them up straitly within the enumerated powers, and those without which, as means, these powers could not be carried into effect. It is known that the very power now proposed as a means was rejected as an end by the Convention which formed the Constitution. A proposition was made to them to authorize Congress to open canals, and an amendatory one to empower them to incorporate. But the whole was rejected, and one of the reasons for rejection urged in debate was, that then they would have a power to erect a bank, which would render the great cities, where there were prejudices and
jealousies on the subject, adverse to the reception of the Constitution. 2. The second general phrase is, to make all laws necessary and proper for carrying into execution the enumerated powers. But they can all be carried into execution without a bank. A bank therefore is not necessary, and consequently not authorized by this phrase. It has been urged that a bank will give great facility or convenience in the collection of taxes. Suppose this were true: yet the Constitution allows only the means which are necessary, not those which are merely convenient for effecting the enumerated powers. If such a latitude of construction be allowed to this phrase as to give any non-enumerated power, it will go to every one, for there is not one which ingenuity may not torture into a convenience in some instance or other, to some one of so long a list of enumerated powers. It would swallow up all the delegated powers, and reduce the whole to one power, as before observed. Therefore it was that the Constitution restrained them to the necessary means, that is to say, to those means without which the grant of power would be nugatory. But let us examine this convenience and see what it is. The report on this subject, page 3, states the only general convenience to be, the preventing the transportation and re-transportation of money between the States and the treasury, (for I pass over the increase of circulating medium, ascribed to it as a want, and which, according to my ideas of paper money, is clearly a demerit.) Every State will have to pay a sum of tax money into the treasury; and the treasury will have to pay, in every State, a part of the interest on the public debt, and salaries to the officers of government resident in that State. In most of the States there will still be a surplus of tax money to come up to the seat of government for the officers residing there. The payments of interest and salary in each State may be made by treasury orders on the State collector. This will take up the great export of the money he has collected in his State, and consequently prevent the great mass of it from being drawn out of the State. If
there be a balance of commerce in favor of that State against the one in which the government resides, the surplus of taxes will be remitted by the bills of exchange drawn for that commercial balance. And so it must be if there was a bank. But if there be no balance of commerce, either direct or circuitous, all the banks in the world could not bring up the surplus of taxes, but in the form of money. Treasury orders then, and bills of exchange may prevent the displacement of the main mass of the money collected, without the aid of any bank; and where these fail, it cannot be prevented even with that aid. Perhaps, indeed, bank bills may be a more convenient vehicle than treasury orders. But a little difference in the degree of convenience, cannot constitute the necessity which the constitution makes the ground for assuming any non-enumerated power. Besides; the existing banks will, without a doubt, enter into arrangements for lending their agency, and the more favorable, as there will be a competition among them for it; whereas the bill delivers us up bound to the national bank, who are free to refuse all arrangement, but on their own terms, and the public not free, on such refusal, to employ any other bank. That of Philadelphia, I believe, now does this business, by their post-notes, which, by an arrangement with the treasury, are paid by any State collector to whom they are presented. This expedient alone suffices to prevent the existence of that necessity which may justify the assumption of a non-enumerated power as a means for carrying into effect an enumerated one. The thing may be done, and has been done, and well done, without this assumption; therefore, it does not stand on that degree of necessity which can honestly justify it. It may be said that a bank whose bills would have a currency all over the States, would be more convenient than one whose currency is limited to a single State. So it would be still more convenient that there should be a bank, whose bills should have a currency all over the world. But it does not follow from this superior conveniency, that
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Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais

  • 1. Computer Simulation A Foundational Approach Using Python 1st Edition Yahya Esmail Osais download https://textbookfull.com/product/computer-simulation-a- foundational-approach-using-python-1st-edition-yahya-esmail- osais/ Download full version ebook from https://textbookfull.com
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  • 5. Computer Simulation A Foundational Approach Using Python
  • 6. CHAPMAN & HALL/CRC COMPUTER and INFORMATION SCIENCE SERIES Series Editor: Sartaj Sahni ADVERSARIAL REASONING: COMPUTATIONAL APPROACHES TO READING THE OPPONENT’S MIND Alexander Kott and William M. McEneaney COMPUTER-AIDED GRAPHING AND SIMULATION TOOLS FOR AUTOCAD USERS P. A. Simionescu COMPUTER SIMULATION: A FOUNDATIONAL APPROACH USING PYTHON Yahya E. Osais DELAUNAY MESH GENERATION Siu-Wing Cheng, Tamal Krishna Dey, and Jonathan Richard Shewchuk DISTRIBUTED SENSOR NETWORKS, SECOND EDITION S. Sitharama Iyengar and Richard R. Brooks DISTRIBUTED SYSTEMS: AN ALGORITHMIC APPROACH, SECOND EDITION Sukumar Ghosh ENERGY-AWARE MEMORY MANAGEMENT FOR EMBEDDED MULTIMEDIA SYSTEMS: A COMPUTER-AIDED DESIGN APPROACH Florin Balasa and Dhiraj K. Pradhan ENERGY EFFICIENT HARDWARE-SOFTWARE CO-SYNTHESIS USING RECONFIGURABLE HARDWARE Jingzhao Ou and Viktor K. Prasanna EVOLUTIONARY MULTI-OBJECTIVE SYSTEM DESIGN: THEORY AND APPLICATIONS Nadia Nedjah, Luiza De Macedo Mourelle, and Heitor Silverio Lopes FROM ACTION SYSTEMS TO DISTRIBUTED SYSTEMS: THE REFINEMENT APPROACH Luigia Petre and Emil Sekerinski FROM INTERNET OF THINGS TO SMART CITIES: ENABLING TECHNOLOGIES Hongjian Sun, Chao Wang, and Bashar I. Ahmad FUNDAMENTALS OF NATURAL COMPUTING: BASIC CONCEPTS, ALGORITHMS, AND APPLICATIONS Leandro Nunes de Castro HANDBOOK OF ALGORITHMS FOR WIRELESS NETWORKING AND MOBILE COMPUTING Azzedine Boukerche PUBLISHED TITLES
  • 7. HANDBOOK OF APPROXIMATION ALGORITHMS AND METAHEURISTICS Teofilo F. Gonzalez HANDBOOK OF BIOINSPIRED ALGORITHMS AND APPLICATIONS Stephan Olariu and Albert Y. Zomaya HANDBOOK OF COMPUTATIONAL MOLECULAR BIOLOGY Srinivas Aluru HANDBOOK OF DATA STRUCTURES AND APPLICATIONS Dinesh P. Mehta and Sartaj Sahni HANDBOOK OF DYNAMIC SYSTEM MODELING Paul A. Fishwick HANDBOOK OF ENERGY-AWARE AND GREEN COMPUTING Ishfaq Ahmad and Sanjay Ranka HANDBOOK OF GRAPH THEORY, COMBINATORIAL OPTIMIZATION, AND ALGORITHMS Krishnaiyan “KT” Thulasiraman, Subramanian Arumugam, Andreas Brandstädt, and Takao Nishizeki HANDBOOK OF PARALLEL COMPUTING: MODELS, ALGORITHMS AND APPLICATIONS Sanguthevar Rajasekaran and John Reif HANDBOOK OF REAL-TIME AND EMBEDDED SYSTEMS Insup Lee, Joseph Y-T. Leung, and Sang H. Son HANDBOOK OF SCHEDULING: ALGORITHMS, MODELS, AND PERFORMANCE ANALYSIS Joseph Y.-T. Leung HIGH PERFORMANCE COMPUTING IN REMOTE SENSING Antonio J. Plaza and Chein-I Chang HUMAN ACTIVITY RECOGNITION: USING WEARABLE SENSORS AND SMARTPHONES Miguel A. Labrador and Oscar D. Lara Yejas IMPROVING THE PERFORMANCE OF WIRELESS LANs:A PRACTICAL GUIDE Nurul Sarkar INTEGRATION OF SERVICES INTO WORKFLOW APPLICATIONS Paweł Czarnul INTRODUCTION TO NETWORK SECURITY Douglas Jacobson LOCATION-BASED INFORMATION SYSTEMS: DEVELOPING REAL-TIME TRACKING APPLICATIONS Miguel A. Labrador, Alfredo J. Pérez, and Pedro M.Wightman PUBLISHED TITLES CONTINUED
  • 8. METHODS IN ALGORITHMIC ANALYSIS Vladimir A. Dobrushkin MULTICORE COMPUTING: ALGORITHMS, ARCHITECTURES, AND APPLICATIONS Sanguthevar Rajasekaran, Lance Fiondella, Mohamed Ahmed, and Reda A. Ammar NETWORKS OF THE FUTURE: ARCHITECTURES, TECHNOLOGIES, AND IMPLEMENTATIONS Mahmoud Elkhodr, Qusay F. Hassan, and Seyed Shahrestani PERFORMANCE ANALYSIS OF QUEUING AND COMPUTER NETWORKS G. R. Dattatreya THE PRACTICAL HANDBOOK OF INTERNET COMPUTING Munindar P. Singh SCALABLE AND SECURE INTERNET SERVICES AND ARCHITECTURE Cheng-Zhong Xu SOFTWARE APPLICATION DEVELOPMENT: A VISUAL C++® , MFC, AND STL TUTORIAL Bud Fox, Zhang Wenzu, and Tan May Ling SPECULATIVE EXECUTION IN HIGH PERFORMANCE COMPUTER ARCHITECTURES David Kaeli and Pen-Chung Yew TRUSTWORTHY CYBER-PHYSICAL SYSTEMS ENGINEERING Alexander Romanovsky and Fuyuki Ishikawa VEHICULAR NETWORKS: FROM THEORY TO PRACTICE Stephan Olariu and Michele C.Weigle X-MACHINES FOR AGENT-BASED MODELING: FLAME PERSPECTIVES Mariam Kiran PUBLISHED TITLES CONTINUED
  • 9. Yahya E. Osais Computer Simulation A Foundational Approach Using Python
  • 10. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20171024 International Standard Book Number-13: 978-1-498-72682-5 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
  • 11. To my wife, Asmahan, and my daughters, Renad, Retal, and Remas.
  • 13. Contents List of Programs xv List of Figures xix List of Tables xxvii Foreword xxix Preface xxxi About the Author xxxiii Abbreviations xxxv Symbols xxxvii Part I The Fundamentals Chapter 1 Introduction 3 1.1 THE PILLARS OF SCIENCE AND ENGINEERING 3 1.2 STUDYING THE QUEUEING PHENOMENON 4 1.3 WHAT IS SIMULATION? 5 1.4 LIFECYCLE OF A SIMULATION STUDY 6 1.5 ADVANTAGES AND LIMITATIONS OF SIMULATION 9 1.6 OVERVIEW OF THE BOOK 10 1.7 SUMMARY 11 Chapter 2 Building Conceptual Models 13 2.1 WHAT IS A CONCEPTUAL MODEL? 13 2.2 ELEMENTS OF A CONCEPTUAL MODEL 15 2.2.1 Entities 15 ix
  • 14. x Contents 2.2.2 Attributes 15 2.2.3 State Variables 16 2.2.4 Events 17 2.2.5 Activities 17 2.3 THE SINGLE-SERVER QUEUEING SYSTEM 18 2.4 STATE DIAGRAMS 22 2.5 ACTUAL TIME VERSUS SIMULATED TIME 23 2.6 SUMMARY 24 2.7 EXERCISES 24 Chapter 3 Simulating Probabilities 27 3.1 RANDOM EXPERIMENTS AND EVENTS 27 3.2 WHAT IS PROBABILITY? 28 3.3 COMPUTING PROBABILITIES 30 3.4 PROBABILITY AS A SAMPLE MEAN 32 3.5 SUMMARY 36 3.6 EXERCISES 36 Chapter 4 Simulating Random Variables and Stochastic Pro- cesses 39 4.1 WHAT ARE RANDOM VARIABLES? 39 4.1.1 Probability Mass Functions 40 4.1.2 Cumulative Distribution Functions 41 4.1.3 Probability Density Functions 43 4.1.4 Histograms 44 4.2 SOME USEFUL RANDOM VARIABLES 46 4.2.1 Bernoulli 46 4.2.2 Binomial 47 4.2.3 Geometric 48 4.2.4 Poisson 49 4.2.5 Uniform 50 4.2.6 Exponential 53 4.2.7 Erlang 54 4.2.8 Normal 54 4.2.9 Triangular 55 4.3 STOCHASTIC PROCESSES 56
  • 15. Contents xi 4.4 DYNAMIC SYSTEM EVOLUTION 58 4.5 SIMULATING QUEUEING PROCESSES 60 4.5.1 Discrete-Time Markov Chains 62 4.5.2 Continuous-Time Markov Chains 64 4.6 SUMMARY 67 4.7 EXERCISES 67 Chapter 5 Simulating the Single-Server Queueing System 69 5.1 SIMULATION MODEL 69 5.2 COLLECTING SIMULATED DATA 75 5.3 PERFORMANCE LAWS 76 5.3.1 Throughput 76 5.3.2 Utilization 76 5.3.3 Response Time 77 5.3.4 E[N(t)] 79 5.3.5 P[N] 82 5.4 INDEPENDENT SIMULATION RUNS 84 5.5 TRANSIENT AND STEADY PHASES 86 5.6 SUMMARY 91 5.7 EXERCISES 91 Chapter 6 Statistical Analysis of Simulated Data 93 6.1 POPULATIONS AND SAMPLES 93 6.2 PROBABILITY DISTRIBUTION OF THE SAMPLE MEAN 95 6.3 CONFIDENCE INTERVALS 97 6.3.1 Interpretations 100 6.3.2 Why Not Always Use a 99% Confidence Interval? 102 6.4 COMPARING TWO SYSTEM DESIGNS 104 6.5 SUMMARY 105 6.6 EXERCISES 105 Part II Managing Complexity Chapter 7 Event Graphs 109 7.1 WHAT IS AN EVENT GRAPH? 109 7.2 EXAMPLES 111
  • 16. xii Contents 7.2.1 The Arrival Process 111 7.2.2 Single-Server Queueing System 112 7.2.3 Multiple-Server Queueing System 114 7.2.4 Single-Server Queueing System with a Limited Queue Capacity 114 7.2.5 Single-Server Queuing System with Failure 115 7.2.6 Single-Server Queuing System with Reneging 116 7.2.7 Single-Server Queuing System with Balking 116 7.3 TRANSLATING EVENT GRAPHS INTO CODE 117 7.4 SUMMARY 120 7.5 EXERCISES 120 Chapter 8 Building Simulation Programs 123 8.1 TIME-DRIVEN SIMULATION 123 8.2 EVENT-DRIVEN SIMULATION 126 8.3 WRITING EVENT-DRIVEN SIMULATION PROGRAMS 127 8.4 PROGRAMMING ISSUES 134 8.4.1 Event Collision 134 8.4.2 Identifiers for Packets 134 8.4.3 Stopping Conditions for the Simulation Loop 134 8.5 SUMMARY 135 8.6 EXERCISES 135 Part III Problem-Solving Chapter 9 The Monte Carlo Method 139 9.1 ESTIMATING THE VALUE OF π 139 9.2 NUMERICAL INTEGRATION 142 9.3 ESTIMATING A PROBABILITY 144 9.3.1 Buffon’s Needle Problem 144 9.3.2 Reliability 146 9.4 VARIANCE REDUCTION TECHNIQUES 149 9.4.1 Control Variates 149 9.4.2 Stratified Sampling 151 9.4.3 Antithetic Sampling 153 9.4.4 Dagger Sampling 156 9.4.5 Importance Sampling 158
  • 17. Contents xiii 9.5 SUMMARY 161 9.6 EXERCISES 161 Part IV Sources of Randomness Chapter 10 Random Variate Generation 165 10.1 THE INVERSION METHOD 165 10.1.1 Continuous Random Variables 167 10.1.2 Discrete Random Variables 169 10.1.2.1 Generating a Bernoulli Variate 171 10.1.2.2 Generating a Binomial Variate 172 10.1.2.3 Generating a Geometric Variate 173 10.2 THE REJECTION METHOD 173 10.3 THE COMPOSITION METHOD 177 10.4 THE CONVOLUTION METHOD 179 10.5 SPECIALIZED METHODS 182 10.5.1 The Poisson Distribution 182 10.5.2 The Normal Distribution 184 10.6 SUMMARY 186 10.7 EXERCISES 186 Chapter 11 Random Number Generation 187 11.1 PSEUDO-RANDOM NUMBERS 187 11.2 CHARACTERISTICS OF A GOOD GENERATOR 189 11.3 JUST ENOUGH NUMBER THEORY 190 11.3.1 Prime Numbers 190 11.3.2 The Modulo Operation 190 11.3.3 Primitive Roots for a Prime Number 191 11.4 THE LINEAR CONGRUENTIAL METHOD 192 11.5 THE MULTIPLICATIVE CONGRUENTIAL METHOD 193 11.5.1 2k Modulus 193 11.5.2 Prime Modulus 194 11.6 LINEAR FEEDBACK SHIFT REGISTERS 194 11.7 STATISTICAL TESTING OF RNGs 199 11.7.1 The Chi-Squared Test 199 11.7.2 The Poker Test 201
  • 18. xiv Contents 11.7.3 The Spectral Test 202 11.7.4 The Lag Plot 204 11.8 SUMMARY 205 11.9 EXERCISES 205 Part V Case Studies Chapter 12 Case Studies 209 12.1 NETWORK RELIABILITY 209 12.2 PACKET DELIVERY OVER A WIRELESS CHANNEL 218 12.3 SIMPLE ARQ PROTOCOL 226 12.4 SUMMARY 233 12.5 EXERCISES 233 Appendix A Overview of Python 235 A.1 BASICS 235 A.2 INPUT AND OUTPUT 237 A.3 BITWISE OPERATORS 238 A.4 LISTS 239 A.5 LIST FUNCTIONS 240 A.6 GENERATING RANDOM NUMBERS AND RANDOM VARI- ATES 241 A.7 IMPLEMENTING THE EVENT LIST 242 A.7.1 Priority Queue 242 A.7.2 Heap Queue 242 A.7.3 Sorting a List 243 A.8 PASSING A FUNCTION NAME AS AN ARGUMENT 244 A.9 TUPLES AS RECORDS 245 A.10 PLOTTING 245 Appendix B An Object-Oriented Simulation Framework 251 Appendix C The Chi-Squared Table 267 Appendix D The t-Distribution Table 269 Bibliography 271 Index 273
  • 19. List of Programs 3.1 Simulating the experiment of throwing a die. The output is shown as a comment on each line. 31 3.2 Approximating the probability of an outcome in the experiment of throwing a die. 31 3.3 Simulation program for studying the running mean of the ran- dom experiment of tossing a coin. This program is also used to generate Figure 3.4. 35 4.1 Python program for generating the histogram from an exponen- tial data set (see Figure 4.6). 44 4.2 Python program for plotting the CDF and PDF of a uniform random variable (see Figures 4.9(a) and 4.9(b)). 51 4.3 Simulating a two-state discrete-time Markov chain given its probability transition matrix and an initial state. 63 4.4 Simulating a Poisson process. 64 4.5 Simulating a birth-death process and plotting its sample path (see Figure 4.21). 66 5.1 Simulation program of the single-server queueing system. 71 5.2 Estimating the average response time of the system. 77 5.3 Estimating the average number of customers in the sytem (E[N(t)]). 80 5.4 Estimating the steady-state probability distribution (P[N = k]). 82 5.5 Performing multiple independent simulation runs of the simula- tion model of the single-server queueing system. 86 5.6 Determining a good trunction point using the average of several realizations of an output variable. 90 6.1 Calculating the confidence interval using Python. 99 6.2 Plotting confidence intervals and population mean. 101 7.1 Python implementation of the event graph in Figure 7.4. 118 8.1 A time-driven simulation program for the discrete-time single- server queueing system. 124 xv
  • 20. xvi Contents 8.2 An event-driven simulation program for the single-server queue- ing system. 129 9.1 Python procedure for estimating π using MC simulation. 141 9.2 Python procedure for estimating a one-dimensional integral. 143 9.3 Python procedure for the Buffon’s needle experiment. 145 9.4 Estimating the reliability of the system in Figure 9.6(b). 148 9.5 Estimating an integral in Eqn. (9.19) using the method of con- trol variates. 150 9.6 Estimating the integral R 1 0 e−x dx using the crude Monte Carlo and stratified methods. 152 9.7 Estimating the mean of a uniform random variable using anti- thetic sampling. 154 9.8 Estimating the value of the integral in Eqn. (9.25) using CMC and antithetic sampling. The reduction in variance is about 12%. 155 9.9 Estimating the reliability of the system in Figure 9.6(b) using dagger sampling. 157 9.10 Estimating the average of a function using importance sampling. 160 10.1 Generating random variates using the information in Figure 10.2(a). 170 10.2 Generating Bernoulli random variates. 171 10.3 Generating binomial random variates. 172 10.4 Generating geometric random variates. 173 10.5 Generating random variates based on the rejection method. 176 10.6 Generating an Erlang random variate using the convolution method. 179 10.7 Generating a standard normal random variate using the convo- lution method. 181 10.8 Generating a Poisson random variate. 183 10.9 Generating a random variate from a standard normal distribution. 185 11.1 Testing a set of random numbers if they are uniformly distributed. 188 11.2 Generating the maximum-length random sequence from the four-bit LFSR shown in Figure 11.3. 197 11.3 Generating the maximum-length random sequence from an eight-bit LFSR. 198 11.4 Python program for generating a 3D scatter plot for the spectral test. 202 11.5 Python procedure for generating a lag plot for a random sequence. 204 12.1 Computing unreliability for the graph in Figure 12.2 using the exact expression in Eqn. (12.1). 212
  • 21. Contents xvii 12.2 Computing unreliability for the graph in Figure 12.2 using crude Monte Carlo simulation. 213 12.3 Computing unreliability for the graph in Figure 12.2 using strat- ified sampling. 214 12.4 Computing unreliability for the graph in Figure 12.2 using an- tithetic sampling. 215 12.5 Computing unreliability for the graph in Figure 12.2 using dag- ger sampling. The number of samples is significantly less. 216 12.6 Python implementation of the event graph in Figure 12.4 220 12.7 Python implementation of the event graph of the simple stop- and-wait ARQ protocol in Figure 12.8. 228 A.1.1 Starting a new Python interactive session. 235 A.1.2 Running a Python program from the command line. 236 A.1.3 A Python source file. It can also be referred to as a Python script. 236 A.2.1 Input and output functions. 237 A.3.1 Binary operations on integer numbers. 238 A.3.2 Handling unsigned binary numbers. 239 A.4.1 Lists and some of their operations. 239 A.5.1 Transposing a matrix using the zip function. Matrix is first un- packed using the start (*) operator. 240 A.6.1 Importing the random module and calling some of the functions inside it. 241 A.7.1 Implementing the event list using the queue module. 242 A.7.2 Implementing the event list using the hqueue module. 243 A.7.3 Implementing the event list by sorting a list. 243 A.8.1 The name of the function can be stored in a list and then used to call the function. 244 A.8.2 The name of the function can be passed as an argument to another function. 244 A.9.1 A tuple can be used as a record that represents an item in the event list. 245 A.10.1 Code for generating Figure 4.12(b). 245 A.10.2 Code for generating Figure 10.6(a). 247 A.10.3 Code for generating Figure 10.6(b). 248 B.1 Event. 251 B.2 Simulation Entity. 252 B.3 Event list and scheduler. 252 B.4 Example 1. 254
  • 22. xviii Contents B.5 Example 2. 255 B.6 Example 3. 256 B.7 Example 4. 258 B.8 M/M/1. 259 B.9 State. 262 B.10 State Machine. 263 B.11 Simple Protocol. 263
  • 23. List of Figures 1.1 The three pillars of science and engineering: Observation (O), Experimentation (E), and Computation (C). By analogy, the table needs the three legs to stay up. 4 1.2 A queue at a checkout counter in a supermarket. A phenomenon arising whenever there is a shared resource (i.e., the cashier) and multiple users (i.e., the shoppers). 5 1.3 Types of models and the data generated from them. 6 1.4 Phases of a simulation study. 6 2.1 A mental image of the system and its behavior must be devel- oped before a conceptual model can be constructed. 14 2.2 Different mental images can be developed for the same system. They include different levels of details. Complexity increases as you add more details. 14 2.3 A continuous state variable takes values from a continuous set (e.g., [0, 5] in (a)). A discrete state variable, on the other hand, takes values from a discrete set (e.g., {0, 1, 2, 3, 4, 5} in (b)). 16 2.4 Events are used to move dynamic entities through a system. A packet is moved from a source to a destination through two routers using eight events. 17 2.5 An activity is delimited by two events and lasts for a random duration of time. 18 2.6 A queueing phenomenon emerges whenever there is a shared resource and multiple users. 19 2.7 Conceptual model of the queueing situation in Figure 2.6. 20 2.8 A sample path of the state variable Q which represents the number of persons in the single-server queueing system. Note the difference in the time between every two consecutive arrival events. 20 2.9 Four activities occur inside the single-server queueing system: (a) Generation, (b) Waiting, (c) Service, and (d) Delay. The length of each activity is a random variable of time. 21 xix
  • 24. xx LIST OF FIGURES 2.10 A simple electrical circuit and its state diagram. Only the switch and lamp are modeled. Events are generated by the switch to change the state of the lamp. 22 2.11 State diagrams of the state variables associated with the queue and server in the single-server queueing system in Figure 2.7. A portion of the state space of the system is shown in (c). 23 3.1 A random experiment of tossing a coin. There are two possible outcomes. 28 3.2 A random experiment of throwing a die. There are six possible outcomes. 28 3.3 Three different samples for the random experiment of tossing a coin 10 times. The running mean is computed for the third sample using cumulative sums. The last value at position 10 of the list of running means is equal to the sample mean. The sample mean is the probability of seeing a head. 33 3.4 Running mean for the random experiment of tossing a coin. The mean eventually converges to the true value as more samples are generated. 34 4.1 Sample space for the random experiment of throwing two dice. The outcome of the experiment is a random variable X ∈ {2, 3, ..., 12}. 40 4.2 The PMF of a discrete random variable representing the out- come of the random experiment of throwing two dice. 41 4.3 The cumulative distribution function of a discrete random vari- able representing the outcome of the random experiment of throwing two dice. 42 4.4 Probability density function of a continuous random variable. 43 4.5 Elements of a histogram. Bins can be of different widths. Length of a bar could represent frequency or relative frequency. 45 4.6 Histogram for an exponential data set. This figure is generated using Listing 4.1. 46 4.7 The situation of observing four successes in a sequence of seven Bernoulli trials can be modeled as a binomial random variable. 48 4.8 The PMF of the Poisson random variable for λ = 10. Notice that P(x) approaches zero as x increases. 49 4.9 Probability distribution functions for the uniform random vari- able where a = 3 and b = 10. 50 4.10 Probability distribution functions of the exponential random variable where µ = 1.5. 53
  • 25. LIST OF FIGURES xxi 4.11 The PDF of the normal random variable with µ = 30 and σ = 10. 55 4.12 Probability distribution functions of the triangular random vari- able with a = 1, b = 10, and c = 7. 56 4.13 A stochastic process maps each outcome in the sample space to a time function. Time functions are combined (convoluted) to produce two sample paths: g1 and g2. Two kinds of means can be defined for a stochastic process. 57 4.14 The Bernoulli random process: (a) sample space, (b) random variable, (c) time functions, (d) result of running the random experiment in each slot, and (e) final sample path. 58 4.15 A sample path through the state space of a dynamic system. Entry and exit points are random. Data is generated along this sample path and a time average is computed as an estimate of the performance metric of interest. 59 4.16 A sample path through the state space of the single-server queueing system. The initial state does not have to be (0, ‘F’). 59 4.17 A sample path of a discrete-time Markov chain over nine time units. Events occur at integer times only. N(1) is the number of entities in the system during the first time slot. 61 4.18 A sample path of a continuous-time Markov chain. Events occur at random times. The time spent in a state has an exponential distribution. 61 4.19 A graphical representation of a two-state, discrete-time Markov chain. 62 4.20 Sample path of a Poisson process. Only arrival events occur inside a Poisson process. 64 4.21 Sample path of a birth-death process. 65 5.1 Physical structure of the single-server queueing system. 70 5.2 Graphical representation of the relationship between random variables and simulation events. 72 5.3 A sample path of the random process N(t). 72 5.4 Random processes present in the single-server queueing system. Both the arrival and departure processes are Poisson processes. (a) Places where the random processes are defined. (b) Total number of arrivals which have occurred up to time t1 is three. (c) The sample path of the departure process is a shifted version of the sample path of the arrival process. (d) Sample path of the queueing (birth-death) process which tracks the number of packets in the system. 73
  • 26. xxii LIST OF FIGURES 5.5 A simulation experiment represents an execution of a simulation model with a specific set of parameters, inputs, and outputs. 76 5.6 A sample path of the number of packets in the single-server queueing system. There are eight rectangles under the curve of the sample path. 80 5.7 Raw data generated when running a simulation program. 85 5.8 Cumulative average versus number of simulated packets. The theoretical value is Wavg = 10. After the transient phase is over, the cumulative average starts approaching the theoretical value. 87 5.9 Z is the average of the five output sequences Y[0]-Y[4]. A trun- cation point can visually be determined by using the curve of Z. In this example, a good truncation point is n = 3000. 89 5.10 The first two steps in the Welch’s method. In step 1, multiple realizations of the output variable are generated. These realiza- tions are combined into one sequence in step 2. 89 5.11 A two-server queueing system with a finite buffer of size three. 91 6.1 Population and samples for the simulation experiment of esti- mating the delay through the single-server queueing system by simulating five packets. The population is (0, ∞). 94 6.2 Probability distribution of the sample mean is normal. 95 6.3 Frequency distribution of the average delay D through the single-server queueing system with λ = 1 and µ = 1.25. The population mean is 4. 96 6.4 The empirical rule for the distribution of samples around the population mean. 95% of the area under the curve of the normal distribution lies within two standard deviations (equal to 1.96) of the mean. 97 6.5 Two of the calculated confidence intervals do not include the population mean. The population mean is 15. 101 7.1 Types of edges in event graphs. 110 7.2 State diagram (a) and event graph (b) for the Poisson arrival process. 112 7.3 Event graph for the single-server queueing system. 113 7.4 Reduced event graph for the single-server queueing system. 113 7.5 Event graph for the K-server queueing system. 114 7.6 Event graph for the single-server queueing system with a limited queue capacity. 114 7.7 Event graph for the single-server queueing system with a server that fails. 115
  • 27. LIST OF FIGURES xxiii 7.8 Event graph for the single-server queueing system with reneging. 116 7.9 Event graph for the single-server queueing system with balking. 116 7.10 A template for synthesizing simulation programs from event graphs. 121 7.11 Two parallel single-server queueing systems with one shared traffic source. 122 7.12 A simple network setup where a user communicates with a server in a data center over a communication channel created inside a network. Propagation delay (Pd) and rate (R) are two important characteristics of a channel. 122 8.1 In time-driven simulation, simulated time evolves in increments of size ∆t. 124 8.2 Arrival and departure processes and their random variables in continuous- and discrete-time queues. 126 8.3 In event-driven simulation, simulated time evolves in steps of random sizes (∆t1 6= ∆t2). 127 8.4 An event-driven simulation program has two independent com- ponents: simulator and model. 128 8.5 How a random number u is used to generate an event. 128 8.6 A flowchart of the event-driven simulation program. 129 8.7 Two single-server queueing systems in series with external ar- rivals. 136 9.1 Setup used for performing MC simulation to estimate π. 140 9.2 Setup used for performing MC simulation to estimate a one- dimensional integral. 142 9.3 The goal of the Buffon’s needle experiment is to compute the probability that a needle of length l will intersect a horizontal line in a set of horizontal lines separated by a distance equal to d. 144 9.4 Two random variables (a and φ) are used in the simulation. The needle will intersect with the closest horizontal line if b ≥ a. 145 9.5 According to trigonometry, the length of the line segment b is equal to the value of the y-coordinate of the upper tip of the needle. 146 9.6 Reliability is the probability that the input is connected to the output. (a) The input is connected to the output if the swtich is closed. (b) Reliability of the overall system is a function of the reliabilities of the individual blocks. In this case, Relsys = R3 , where R is the reliability of a block. 147
  • 28. xxiv LIST OF FIGURES 9.7 Sample space of the random experiment of throwing two dice. For the random variate 4, 4+10 2 = 7 is generated instead if anti- thetic sampling is used. 154 9.8 With dagger sampling, three trials are performed using a single random number. Hence, three samples are generated. 157 9.9 Values of g(x) are very close to zero over region 1. Probabil- ity distribution of x is very close to zero over region 1. Another probability distribution has to be used in order to generate sam- ples from region 1 where the values of the function g(x) are more interesting. 159 9.10 Estimating the shortest path between nodes A and D (see Ex- ercise 9.2). 161 10.1 Generating random variates from cumulative distribution func- tions. 166 10.2 Generating random variates using the PMF of a discrete random variable. 170 10.3 Generating a random variate from the PDF f(x) using the aux- iliary PDF g(x). x = 3 is accepted if u ≤ f(3) g(3) . 174 10.4 Random variates generated using the rejection method. 175 10.5 Triangular distribution. f(x) is composed of two functions each of which is defined over half the interval over which f(x) exists. 177 10.6 The shape of the histogram constructed using the random vari- ates generated using the convolution method resembles that of the PDF of the Erlang random variable. 180 10.7 Histogram constructed from standard normal variates generated using the convolution method in Listing 10.7. 181 10.8 Arrivals during a time slot can be modeled as a Poisson random variable. 183 10.9 The shape of the histogram constructed using simulated Poisson random variates resembles that of the PMF of a Poisson random variable. 184 10.10 Using the procedure in Listing 10.9, the uniform random num- bers are transformed into random standard normal variates. 185 11.1 Probability distribution of u. 188 11.2 Multiple seeds are used to make different simulation runs. Differ- ent paths in the system state space are explored and the average is computed using the values resulting from these different paths. 193 11.3 A four-bit linear feedback shift register with characteristic poly- nomial c(x) = 1 + x3 + x4 . 195
  • 29. LIST OF FIGURES xxv 11.4 Computing the first intermediate binary number on line 13 in Listing 11.2. 196 11.5 An eight-bit linear feedback shift register with characteristic polynomial c(x) = 1 + x4 + x5 + x6 + x8 . 197 11.6 104 triplets of successive random numbers generated using List- ing 11.4. Planes can be seen when the figure is viewed from the right angle. 202 11.7 The lag plot for a sequence of sinusoidal values. An elliptical pattern can be clearly identified. 204 11.8 The lag plot generated by the code in Listing 11.5. The sequence uniformly fills the 2D space. 205 12.1 A graph consisting of eight vertices and 11 edges. 210 12.2 Network fails if nodes v1 and v4 become disconnected. The event will occur if any of the following groups of links fail: {(e1, e2), (e1, e3), (e2, e4), (e3, e4)}. 210 12.3 A point-to-point wireless system. The transmitter has a buffer which can store up to B packets. The probability that a trans- mission attempt is successful is 1 − Perr. 218 12.4 Event graph for the system in Figure 12.3. 220 12.5 Average packet delay increases as the quality of the wireless channel degrades. 225 12.6 Percentage of delivered packets drops as the quality of the wire- less channel degrades. 226 12.7 Behavior of the simple stop-and-wait ARQ protocol with two possibilities: acknowledgment and frame loss. 227 12.8 Event graph for the simple stop-and-wait ARQ protocol. 228 12.9 Throughput deteriorates as the packet error rate increases. 232
  • 30. Another Random Scribd Document with Unrelated Content
  • 31. custom to refuse it. However, such exchanges are sometimes effected, by allowing them more or less of advantage. They have sometimes accepted of two Moors for a Christian, at others they have refused five or six for one. Perhaps Turkish captives may be objects of greater partiality with them, as their government is entirely in the hands of Turks, who are treated in every instance as a superior order of beings. Exchange, too, will be more practicable in our case, as our captives have not been sold to private individuals, but are retained in the hands of the Government. The liberation of our citizens has an intimate connection with the liberation of our commerce in the Mediterranean, now under the consideration of Congress. The distresses of both proceed from the same cause, and the measures which shall be adopted for the relief of the one, may, very probably, involve the relief of the other. XX.—The Secretary of State, to whom was referred by the House of Representatives, the representation from the General Court of the Commonwealth of Massachusetts, on the subjects of the cod and whale fisheries, together with the several papers accompanying it, has had the same under consideration, and thereupon makes the following report: February 1, 1791. The representation sets forth that, before the late war, about four thousand seamen, and about twenty-four thousand tons of shipping, were annually employed from that State, in the whale fishery, the produce whereof was about three hundred and fifty thousand pounds lawful money a year. That, previous to the same period, the cod fishery of that State employed four thousand men, and twenty-eight thousand tons of shipping, and produced about two hundred and fifty thousand pounds a year.
  • 32. That these branches of business, annihilated during the war, have been, in some degree, recovered since; but that they labor under many and heavy embarrassments, which, if not removed, or lessened, will render the fisheries every year less extensive and important. That these embarrassments are, heavy duties on their produce abroad, and bounties on that of their competitors; and duties at home on several articles, particularly used in the fisheries. And it asks that the duties be taken off; that bounties be given to the fishermen; and the national influence be used abroad, for obtaining better markets for their produce. The cod and whale fisheries, carried on by different persons, from different ports, in different vessels, in different seas, and seeking different markets, agree in one circumstance, in being as unprofitable to the adventurer, as important to the public. A succinct view of their rise, progress, and present state, with different nations, may enable us to note the circumstances which have attended their prosperity, and their decline; to judge of the embarrassments which are said to oppress ours; to see whether they depend on our own will, and may, therefore, be remedied immediately by ourselves, or, whether depending on the will of others, they are without the reach of remedy from us, either directly or indirectly. Their history being as unconnected as their practice, they shall be separately considered. Within twenty years after the supposed discovery of Newfoundland, by the Cabots, we find that the abundance of fish on its banks, had already drawn the attention of the people of Europe. For, as early as 1517, or 1519, we are told of fifty ships being seen there at one time. The first adventurers in that fishery were the Biscayans, of Spain, the Basques and Bas-Bretons, of France, all united anciently in language, and still in habits, and in extreme poverty. The last circumstance enabled them long to retain a considerable share of
  • 33. the fishery. In 1577, the French had one hundred and fifty vessels there; the Spaniards had still one hundred, and the Portuguese fifty, when the English had only fifteen. The Spaniards and Portuguese seem at length to have retired silently, the French and English claiming the fishery exclusively, as an appurtenance to their adjacent colonies, and the profits being too small for nations surcharged with the precious metals proceeding from their mines. Without materials to trace the intermediate progress, we only know that, so late as 1744, the French employed there five hundred and sixty-four ships, and twenty-seven thousand five hundred seamen, and took one million two hundred and forty-six thousand quintals of fish, which was three times the extent to which England and her colonies together, carried this fishery at that time. The English, in the beginning of the seventeenth century, had employed, generally, about one hundred and fifty vessels in the Newfoundland fishery. About 1670 we find them reduced to eighty, and one hundred, the inhabitants of New England beginning now to supplant them. A little before this, the British Parliament perceiving that their citizens were unable to subsist on the scanty profits which sufficed for their poorer competitors, endeavored to give them some advantage by prohibiting the importation of foreign fish; and, at the close of the century, they formed some regulations for their government and protection, and remitted to them some duties. A successful war enabled them, in 1713, to force from the French a cession of the Island of Newfoundland; under these encouragements, the English and American fisheries began to thrive. In 1731 we find the English take two hundred thousand quintals of fish, and the Americans two hundred and thirty thousand, besides the refuse fish, not fit for European markets. They continue to gain ground, and the French to lose it, insomuch that, about 1755, they are said to have been on a par; and, in 1768, the French have only two hundred and fifty-nine vessels, of twenty-four thousand four hundred and twenty tons, nine thousand seven hundred and twenty- two seamen, taking two hundred thousand quintals, while America
  • 34. alone, for some three or four years before that, and so on, to the commencement of the late war, employed six hundred and sixty-five vessels, of twenty-five thousand six hundred and fifty tons, and four thousand four hundred and five seamen, and took from three hundred and fifty thousand to upwards of four hundred thousand quintals of fish, and England a still greater quantity, five hundred and twenty-six thousand quintals, as is said. Spain had formally relinquished her pretensions to a participation in these fisheries, at the close of the preceding war; and, at the end of this, the adjacent continent and islands being divided between the United States, the English and French, (for the last retained two small islands merely for this object,) the right of fishing was appropriated to them also. France, sensible of the necessity of balancing the power of England on the water, and, therefore, of improving every resource for raising seamen, and seeing that her fishermen could not maintain their competition without some public patronage, adopted the experiment of bounties on her own fish, and duties on that of foreign nations brought into her markets. But, notwithstanding this, her fisheries dwindle, from a change taken place, insensibly, in the character of her navigation, which, from being the most economical, is now become the most expensive. In 1786, she is said to have employed but seven thousand men in this fishery, and to have taken four hundred and twenty-six thousand quintals; and, in 1787, but six thousand men, and one hundred and twenty-eight thousand quintals. She seems not yet sensible that the unthriftiness of her fisheries proceeds from the want of economy, and not the want of markets; and that the encouragement of our fishery abridges that of a rival nation, whose power on the ocean has long threatened the loss of all balance on that element. The plan of the English Government, since the peace, has been to prohibit all foreign fish in their markets, and they have given from eighteen to fifty thousand pounds sterling on every fishing vessel complying with certain conditions. This policy is said to have been so
  • 35. far successful, as to have raised the number of seamen employed in that business, in 1786, to fourteen thousand, and the quantity of fish taken, to 732,000 quintals. * * * * * * * * The fisheries of the United States, annihilated during the war; their vessels, utensils, and fishermen destroyed; their markets in the Mediterranean and British America lost, and their produce dutied in those of France; their competitors enabled by bounties to meet and undersell them at the few markets remaining open, without any public aid, and, indeed, paying aids to the public;—such were the hopeless auspices under which this important business was to be resumed. Yet it was resumed, and, aided by the mere force of natural advantages, they employed, during the years 1786, 1787, 1788, and 1789, on an average, five hundred and thirty-nine vessels, of nineteen thousand one hundred and eighty-five tons, three thousand two hundred and eighty-seven seamen, and took two hundred and fifty thousand six hundred and fifty quintals of fish. * * * And an official paper * * shows that, in the last of those years, our exportation amounted to three hundred and seventy-five thousand and twenty quintals, and thirty thousand four hundred and sixty-one barrels; deduction made of three thousand seven hundred and one quintals, and six thousand three hundred and forty-three barrels of foreign fish, received and re-exported. * * Still, however, the calculations * * which accompany the representation, show that the profits of the sales in the years 1787 and 1788, were too small to afford a living to the fishermen, and on those of 1789, there was such a loss as to withdraw thirty-three vessels, of the town of Marblehead alone, from the further pursuit of this business; and the apprehension is, that, without some public aid, those still remaining will continue to withdraw, and this whole commerce be engrossed by a single nation. This rapid view of the cod fishery enables us to discern under what policy it has nourished or declined in the hands of other nations, and
  • 36. to mark the fact, that it is too poor a business to be left to itself, even with the nation most advantageously situated. It will now be proper to count the advantages which aid, and the disadvantages which oppose us, in this conflict. Our advantages are— 1. The neighborhood of the great fisheries, which permits our fishermen to bring home their fish to be salted by their wives and children. 2. The shore fisheries, so near at hand, as to enable the vessels to run into port in a storm, and so lessen the risk, for which distant nations must pay insurance. 3. The winter fisheries, which, like household manufactures employ portions of time, which would otherwise be useless. 4. The smallness of the vessels, which the shortness of the voyage enables us to employ, and which, consequently, require but a small capital. 5. The cheapness of our vessels, which do not cost above the half of the Baltic fir vessels, computing price and duration. 6. Their excellence as sea boats, which decreases the risk and quickens the return. 7. The superiority of our mariners in skill, activity, enterprise, sobriety, and order. 8. The cheapness of provisions. 9. The cheapness of casks, which, of itself, is said to be equal to an extra profit of fifteen per cent. These advantages are of such force, that, while experience has proved that no other nation can make a mercantile profit on the
  • 37. Newfoundland fishery, nor can support it without national aid, we can make a living profit, if vent for our fish can be procured. Of the disadvantages opposed to us, those which depend on ourselves, are— Tonnage and naval duties on the vessels employed in the fishery. Impost duties on salt. On tea, rum, sugar, molasses, hooks, lines, and leads, duck, cordage, and cables, iron, hemp, and twine, used in the fishery; coarse woollens, worn by the fishermen, and the poll tax levied by the State on their persons. The statement No. 6, shows the amount of these, exclusive of the State tax and drawback on the fish exported, to be $5 25 per man, or $57 75 per vessel of sixty-five tons. When a business is so nearly in equilibrio that one can hardly discern whether the profit be sufficient to continue it or not, smaller sums than these suffice to turn the scale against it. To these disadvantages, add ineffectual duties on the importation of foreign fish. In justification of these last, it is urged that the foreign fish received, is in exchange for the produce of agriculture. To which it may be answered, that the thing given, is more merchantable than that received in exchange, and agriculture has too many markets to be allowed to take away those of the fisheries. It will rest, therefore, with the wisdom of the Legislature to decide, whether prohibition should not be opposed to prohibition, and high duty to high duty, on the fish of other nations; whether any, and which, of the naval and other duties may be remitted, or an equivalent given to the fisherman, in the form of a drawback, or bounty; and whether the loss of markets abroad, may not, in some degree, be compensated, by creating markets at home; to which might contribute the constituting fish a part of the military ration, in stations not too distant from navigation, a part of the necessary sea stores of vessels, and the encouraging private individuals to let the fishermen share with the cultivator, in furnishing the supplies of the table. A habit introduced from motives of patriotism, would soon be followed
  • 38. from motives of taste; and who will undertake to fix the limits to this demand, if it can be once excited, with a nation which doubles, and will continue to double, at very short periods? Of the disadvantages which depend on others, are— 1. The loss of the Mediterranean markets. 2. Exclusions from the markets of some of our neighbors. 3. High duties in those of others; and, 4. Bounties to the individuals in competition with us. The consideration of these will find its place more aptly, after a review of the condition of our whale fishery shall have led us to the same point. To this branch of the subject, therefore, we will now proceed. The whale fishery was first brought into notice of the southern nations of Europe, in the fifteenth century, by the same Biscayans and Basques who led the way to the fishery of Newfoundland. They began it on their own coasts, but soon found that the principal residence of the whale was in the Northern seas, into which, therefore, they pursued him. In 1578 they employed twenty-five ships in that business. The Dutch and Hamburghers took it up after this, and about the middle of the seventeenth century the former employed about two hundred ships, and the latter about three hundred and fifty. The English endeavored also to participate of it. In 1672, they offered to their own fishermen a bounty of six shillings a ton, on the oil they should bring home, and instituted, at different times, different exclusive companies, all of which failed of success. They raised their bounty, in 1733, to twenty shillings a ton, on the admeasurement of the vessel. In 1740, to thirty shillings, with a privilege to the fishermen against being impressed. The Basque fishery, supported by poverty alone, had maintained but a feeble existence, before competitors aided by the bounties of their nation,
  • 39. and was, in fine, annihilated by the war of 1745, at the close of which the English bounty was raised to forty shillings. From this epoch, their whale fishery went on between the limits of twenty- eight and sixty-seven vessels, till the commencement of the last war. The Dutch, in the meantime, had declined gradually to about one hundred and thirty ships, and have, since that, fallen down to less than half that number. So that their fishery, notwithstanding a bounty of thirty florins a man, as well as that of Hamburg, is now nearly out of competition. In 1715, the Americans began their whale fishery. They were led to it at first by the whales which presented themselves on their coasts. They attacked them there in small vessels of forty tons. As the whale, being infested, retired from the coast, they followed him farther and farther into the ocean, still enlarging their vessels with their adventures, to sixty, one hundred, and two hundred tons. Having extended their pursuit to the Western Islands, they fell in, accidentally, with the spermaceti whale, of a different species from that of Greenland, which alone had hitherto been known in commerce: more fierce and active, and whose oil and head matter was found to be more valuable, as it might be used in the interior of houses without offending the smell. The distinction now first arose between the Northern and Southern fisheries: the object of the former being the Greenland whale, which frequents the Northern coasts and seas of Europe and America; that of the latter being the spermaceti whale, which was found in the Southern seas, from the Western Islands and coast of Africa, to that of Brazil, and still on to the Falkland Islands. Here, again, within soundings, on the coast of Brazil, they found a third species of whale, which they called the black or Brazil whale, smaller than the Greenland, yielding a still less valuable oil, fit only for summer use, as it becomes opaque at 50 degrees of Fahrenheit's termometer, while that of the spermaceti whale is limpid to 41, and of the Greenland whale to 36, of the same thermometer. It is only worth taking, therefore, when it falls in the way of the fishermen, but not worth seeking, except when they have
  • 40. failed of success against the spermaceti whale, in which case, this kind, easily found and taken, serves to moderate their loss. In 1771 the Americans had one hundred and eighty-three vessels, of thirteen thousand eight hundred and twenty tons, in the Northern fishery, and one hundred and twenty-one vessels, of fourteen thousand and twenty tons, in the Southern, navigated by four thousand and fifty-nine men. At the beginning of the late war, they had one hundred and seventy-seven vessels in the Northern, and one hundred and thirty-two in the Southern fishery. At that period, our fishery being suspended, the English seized the opportunity of pushing theirs. They gave additional bounties of £500, £400, £300, £200, £100 sterling, annually, to the five ships which should take the greatest quantities of oil. The effect of which was such, as, by the year 1786, to double the quantity of common oil necessary for their own consumption. Finding, on a review of the subject, at that time, that their bounties had cost the Government £13 10s. sterling a man, annually, or sixty per cent. on the cargoes, a part of which went consequently to ease the purchases of this article made by foreign nations, they reduced the northern bounty from forty to thirty shillings the ton of admeasurement. They had, some little time before, turned their attention to the Southern fishery, and given very great bounties in it, and had invited the fishermen of the United States to conduct their enterprises. Under their guidance, and with such encouragement, this fishery, which had only begun with them in 1784 or 1785, was rising into value. In 1788 they increased their bounties, and the temptations to our fishermen, under the general description of foreigners who had been employed in the whale fishery, to pass over with their families and vessels to the British dominions, either in America or Europe, but preferably to the latter. The effect of these measures had been prepared, by our whale oils becoming subject, in their market, to the foreign duty of £18 5s. sterling the ton, which, being more than equal to the price of the common oil, operated as a prohibition on
  • 41. that, and gave to their spermaceti oil a preference over ours to that amount. * * * * * * * * The fishermen of the United States, left without resource, by the loss of their market, began to think of accepting the British invitation, and of removing, some to Nova Scotia, preferring smaller advantages in the neighborhood of their ancient country and friends, others to Great Britain, postponing country and friends to high premiums. The Government of France could not be inattentive to these proceedings. They saw the danger of letting four or five thousand seamen, of the best in the world, be transferred to the marine strength of another nation, and carry over with them an art, which they possessed almost exclusively. To give time for a counterplan, the Marquis de Lafayette, the valuable friend and citizen of this, as well as that country, wrote to a gentleman in Boston, to dissuade the fishermen from accepting the British proposals, and to assure them that their friends in France would endeavor to do something for them. A vessel was then arrived from Halifax at Nantucket, to take off those who had proposed to remove. Two families had gone abroad, and others were going. In this moment, the letter arriving, suspended their designs. Not another went abroad, and the vessel returned to Halifax with only the two families. The plan adopted by the French ministry, very different from that of the first mover, was to give a counter invitation to the Nantucket men to remove and settle in Dunkirk, offering them a bounty of fifty livres (between nine and ten dollars) a ton on the admeasurement of the vessels they should equip for the whale fishery, with some other advantages. Nine families only, of thirty-three persons, accepted the invitation. This was in 1785. In 1786, the ministry were led to see that their invitation would produce but little effect, and that the true means of preventing the emigration of our fishermen to the British dominions would be to enable them still to follow their calling from
  • 42. their native country, by giving them a new market for their oils, instead of the old one they had lost. The duties were, therefore, abated on American whale oil immediately, and a further abatement promised by the letter No. 8, and, in December, 1787, the arrêt No. 9 was passed. The rival fishermen immediately endeavored to turn this measure to their own advantage, by pouring their whale oils into the markets of France, where they were enabled, by the great premiums received from their Government, perhaps, too, by extraordinary indemnifications, to undersell both the French and American fishermen. To repel this measure, France shut her ports to all foreign fish oils whatever, by the arrêt No. 10. The British whale fishery fell, in consequence, the ensuing year from two hundred and twenty-two to one hundred and seventy-eight ships. But this general exclusion has palsied our fishery also. On the 7th of December, 1788, therefore, by the arrêt No. 11, the ports of France still remaining shut to all other nations, were again opened to the produce of the whale fisheries of the United States, continuing, however, their endeavors to recover a share in this fishery themselves, by the aid of our fishermen. In 1784, 1785, 1786, they had had four ships. In 1787, three. In 1788, seventeen in the two fisheries of four thousand five hundred tons. These cost them in bounty 225,000 livres, which divided on one thousand five hundred and fifty tons of oil, the quantity they took, amounted to 145 livres (near twenty-seven dollars) the ton, and, on about one hundred natives on board the seventeen ships, (for there were one hundred and fifty Americans engaged by the voyage) came to 2,225 livres, or about 416⅔ dollars a man. We have had, during the years 1787, 1788 and 1789, on an average, ninety-one vessels, of five thousand eight hundred and twenty tons, in the northern, and thirty-one of four thousand three hundred and ninety tons in the southern fishery. * * * * * These details will enable Congress to see with what a competition we have to struggle for the continuance of this fishery, not to say its
  • 43. increase. Against prohibitory duties in one country, and bounties to the adventurers in both of those which are contending with each other for the same object, ours have no auxiliaries, but poverty and rigorous economy. The business, unaided, is a wretched one. The Dutch have peculiar advantages for the northern fishery, as being within six or eight days' sail of the grounds, as navigating with more economy than any other nation in Europe, their seamen content with lower wages, and their merchants with lower profit. Yet the memorial No. 13, from a committee of the whale merchants to the States General of Holland, in the year 1775, states that fourteen millions of guilders, equal to five million six hundred thousand dollars, has been lost in that fishery in forty-seven years, being about one hundred and twenty thousand dollars a year. The States General, thereupon, gave a bounty of thirty guilders a man to the fishermen. A person immediately acquainted with the British whale fishery, and whose information merits confidence, has given assurance that the ships employed in their northern fishery, in 1788, sunk £800 each, on an average, more than the amount of the produce and bounties. An English ship of three hundred tons and forty-two seamen, in this fishery, generally brings home, after a four months' voyage, twenty-five tons of oil, worth £437 10s. sterling; but the wages of the officers and seamen will be £400; there remain but £37 10s., not worth taking into account, towards the outfit and merchants' profit. These, then, must be paid by the Government; and it is on this idea that the British bounty is calculated. Our vessels for the northern fishery average sixty-four tons, and cost, when built, fitted out, and victualled for the first voyage, about three thousand dollars. They have taken, on an average, the three last years, according to the statement No. 12, eighteen tons of oil, worth, at our market, nine hundred dollars, which are to pay all expenses, and subsist the fishermen and merchant. Our vessels for the southern fishery average one hundred and forty tons, and cost, when built, fitted out, and victualled, for their first voyage, about six thousand five hundred dollars. They have taken on an average, the three last years, according to the same statement, thirty-two tons of
  • 44. oil each, worth at our market three thousand two hundred dollars, which are, in like manner, to pay all expenses, and subsist the owners and navigators. These expenses are great, as the voyages are generally of twelve months' duration. No hope can arise of their condition being bettered by an augmentation of the price of oil. This is kept down by the competition of the vegetable oils, which answer the same purposes, not quite so well, but well enough to become preferable, were the price to be raised, and so well, indeed, as to be more generally used than the fish oils for lighting houses and cities. The American whale fishery is principally followed by the inhabitants of the island of Nantucket—a sand bar of about fifteen miles long, and three broad, capable of maintaining, by its agriculture, about twenty families; but it employed in these fisheries, before the war, between five or six thousand men and boys; and, in the only harbor it possesses, it had one hundred and forty vessels, one hundred and thirty-two of which were of the larger kind, as being employed in the southern fishery. In agriculture, then, they have no resource; and, if that of their fishery cannot be pursued from their own habitations, it is natural they should seek others from which it can be followed, and preferably those where they will find a sameness of language, religion, laws, habits, and kindred. A foreign emissary has lately been among them, for the purpose of renewing the invitations to a change of situation. But, attached to their native country, they prefer continuing in it, if their continuance there can be made supportable. This brings us to the question, what relief does the condition of this fishery require? 1. A remission of duties on the articles used for their calling. 2. A retaliating duty on foreign oils, coming to seek a competition with them in or from our ports. 3. Free markets abroad. 1. The remission of duties will stand on nearly the same ground with that to the cod fishermen.
  • 45. 2. The only nation whose oil is brought hither for competition with our own, makes ours pay a duty of about eighty-two dollars the ton, in their ports. Theirs is brought here, too, to be reshipped fraudulently, under our flag, into ports where it could not be received under theirs, and ought not to be covered by ours, if we mean to preserve our own admission into them. The 3d and principal object is to find markets for the vent of oil. Portugal, England, Holland, Sweden, Denmark, Prussia, Russia, the Hanse towns, supply themselves and something more. Spain and Italy receive supplies from England, and need the less, as their skies are clearer. France is the only country which can take our surplus, and they take principally of the common oil; as the habit is but commencing with them of ascribing a just value to spermaceti whale. Some of this, however, finds its vent there. There was, indeed, a particular interest perpetually soliciting the exclusion of our oils from their markets. The late government there saw well that what we should lose thereby would be gained by others, not by themselves. And we are to hope that the present government, as wise and friendly, will also view us, not as rivals, but as co-operators against a common rival. Friendly arrangements with them, and accommodation to mutual interest, rendered easier by friendly dispositions existing on both sides, may long secure to us this important resource for our seamen. Nor is it the interest of the fisherman alone, which calls for the cultivation of friendly arrangements with that nation; besides five-eights of our whale oil, and two-thirds of our salted fish, they take from us one-fourth of our tobacco, three-fourths of our live stock * * * * * a considerable and growing portion of our rice, great supplies, occasionally, of other grain; in 1789, which, indeed, was extraordinary, four millions of bushels of wheat, and upwards of a million of bushels of rye and barley * * * * * and nearly the whole carried in our own vessels. * * * * * They are a free market now, and will, in time, be a valuable one for ships and ship timber, potash, and peltry.
  • 46. England is the market for the greatest part of our spermaceti oil. They impose on all our oils a duty of eighteen pounds five shillings sterling the ton, which, as to the common kind, is a prohibition, as has been before observed, and, as to the spermaceti, gives a preference of theirs over ours to that amount, so as to leave, in the end, but a scanty benefit to the fishermen; and, not long since, by a change of construction, without any change of law, it was made to exclude our oils from their ports, when carried in our vessels. On some change of circumstance, it was construed back again to the reception of our oils, on paying always, however, the same duty of eighteen pounds five shillings. This serves to show that the tenure by which we hold the admission of this commodity in their markets, is as precarious as it is hard. Nor can it be announced that there is any disposition on their part to arrange this or any other commercial matter, to mutual convenience. The ex parte regulations which they have begun for mounting their navigation on the ruins of ours, can only be opposed by counter regulations on our part. And the loss of seamen, the natural consequence of lost and obstructed markets for our fish and oil, calls, in the first place, for serious and timely attention. It will be too late when the seaman shall have changed his vocation, or gone over to another interest. If we cannot recover and secure for him these important branches of employment, it behooves us to replace them by others equivalent. We have three nurseries for forming seamen: 1. Our coasting trade, already on a safe footing. 2. Our fisheries, which, in spite of natural advantages, give just cause of anxiety. 3. Our carrying trade, our only resource of indemnification for what we lose in the other. The produce of the United States, which is carried to foreign markets, is extremely bulky. That part of it which is now in the hands of foreigners, and which we may resume into our own, without touching the rights of those nations who have met us in fair arrangements by treaty, or the interests of those who, by their voluntary regulations, have paid so just and liberal a respect to our
  • 47. interests, as being measured back to them again, places both parties on as good ground, perhaps, as treaties could place them—the proportion, I say, of our carrying trade, which may be resumed without affecting either of these descriptions of nations, will find constant employment for ten thousand seamen, be worth two millions of dollars, annually, will go on augmenting with the population of the United States, secure to us a full indemnification for the seamen we lose, and be taken wholly from those who force us to this act of self protection in navigation. Hence, too, would follow, that their Newfoundland ships, not receiving provisions from us in their bottoms, nor permitted (by a law of their own) to receive in ours, must draw their subsistence from Europe, which would increase that part of their expenses in the proportion of four to seven, and so far operate as a duty towards restoring the level between them and us. The tables No. 2 and 12, will show the quantity of tonnage, and, consequently, the mass of seamen whose interests are in distress; and No. 17, the materials for indemnification. If regulations exactly the counterpart of those established against us, would be ineffectual, from a difference of circumstances, other regulations equivalent can give no reasonable ground of complaint to any nation. Admitting their right of keeping their markets to themselves, ours cannot be denied of keeping our carrying trade to ourselves. And if there be anything unfriendly in this, it was in the first example. The loss of seamen, unnoticed, would be followed by other losses in a long train. If we have no seamen, our ships will be useless, consequently our ship timber, iron, and hemp; our ship building will be at an end, ship carpenters go over to other nations, our young men have no call to the sea, our produce, carried in foreign bottoms, be saddled with war-freight and insurance in times of war; and the history of the last hundred years shows, that the nation which is our carrier has three years of war for every four years of peace. (No. 18.) We lose, during the same periods, the carriage for belligerent
  • 48. powers, which the neutrality of our flag would render an incalculable source of profit; we lose at this moment the carriage of our own produce to the annual amount of two millions of dollars, which, in the possible progress of the encroachment, may extend to five or six millions, the worth of the whole, with an increase in the proportion of the increase of our numbers. It is easier, as well as better, to stop this train at its entrance, than when it shall have ruined or banished whole classes of useful and industrious citizens. It will doubtless be thought expedient that the resumption suggested should take effect so gradually, as not to endanger the loss of produce for the want of transportation; but that, in order to create transportation, the whole plan should be developed, and made known at once, that the individuals who may be disposed to lay themselves out for the carrying business, may make their calculations on a full view of all circumstances. On the whole, the historical view we have taken of these fisheries, proves they are so poor in themselves, as to come to nothing with distant nations, who do not support them from their treasury. We have seen that the advantages of our position place our fisheries on a ground somewhat higher, such as to relieve our treasury from giving them support; but not to permit it to draw support from them, nor to dispense the government from the obligation of effectuating free markets for them; that, for the great proportion of our salted fish, for our common oil, and a part of our spermaceti oil, markets may perhaps be preserved, by friendly arrangements towards those nations whose arrangements are friendly to us, and the residue be compensated by giving to the seamen thrown out of business the certainty of employment in another branch, of which we have the sole disposal. XXI.—Opinion against the constitutionality of a National Bank.
  • 49. February 15, 1791. The bill for establishing a National Bank undertakes among other things:— 1. To form the subscribers into a corporation. 2. To enable them in their corporate capacities to receive grants of land; and so far is against the laws of Mortmain.[26] 3. To make alien subscribers capable of holding lands; and so far is against the laws of alienage. 4. To transmit these lands, on the death of a proprietor, to a certain line of successors; and so far changes the course of Descents. 5. To put the lands out of the reach of forfeiture or escheat; and so far is against the laws of Forfeiture and Escheat. 6. To transmit personal chattels to successors in a certain line; and so far is against the laws of Distribution. 7. To give them the sole and exclusive right of banking under the national authority; and so far is against the laws of Monopoly. 8. To communicate to them a power to make laws paramount to the laws of the States; for so they must be construed, to protect the institution from the control of the State legislatures; and so, probably, they will be construed. I consider the foundation of the Constitution as laid on this ground: That all powers not delegated to the United States, by the Constitution, nor prohibited by it to the States, are reserved to the States or to the people. [XIIth amendment.] To take a single step beyond the boundaries thus specially drawn around the powers of Congress, is to take possession of a boundless field of power, no longer susceptible of any definition. The incorporation of a bank, and the powers assumed by this bill, have not, in my opinion, been delegated to the United States, by the
  • 50. Constitution. 1. They are not among the powers specially enumerated: for these are: 1st. A power to lay taxes for the purpose of paying the debts of the United States; but no debt is paid by this bill, nor any tax laid. Were it a bill to raise money, its origination in the Senate would condemn it by the Constitution. 2d. To borrow money. But this bill neither borrows money nor ensures the borrowing it. The proprietors of the bank will be just as free as any other money holders, to lend or not to lend their money to the public. The operation proposed in the bill, first, to lend them two millions, and then to borrow them back again, cannot change the nature of the latter act, which will still be a payment, and not a loan, call it by what name you please. 3. To regulate commerce with foreign nations, and among the States, and with the Indian tribes. To erect a bank, and to regulate commerce, are very different acts. He who erects a bank, creates a subject of commerce in its bills; so does he who makes a bushel of wheat, or digs a dollar out of the mines; yet neither of these persons regulates commerce thereby. To make a thing which may be bought and sold, is not to prescribe regulations for buying and selling. Besides, if this was an exercise of the power of regulating commerce, it would be void, as extending as much to the internal commerce of every State, as to its external. For the power given to Congress by the Constitution does not extend to the internal regulation of the commerce of a State, (that is to say of the commerce between citizen and citizen,) which remain exclusively with its own legislature; but to its external commerce only, that is to say, its commerce with another State, or with foreign nations, or with the Indian tribes. Accordingly the bill does not propose the measure as a regulation of trade, but as productive of considerable advantages to trade. Still less are these powers covered by any other of the special enumerations.
  • 51. II. Nor are they within either of the general phrases, which are the two following:— 1. To lay taxes to provide for the general welfare of the United States, that is to say, to lay taxes for the purpose of providing for the general welfare. For the laying of taxes is the power, and the general welfare the purpose for which the power is to be exercised. They are not to lay taxes ad libitum for any purpose they please; but only to pay the debts or provide for the welfare of the Union. In like manner, they are not to do anything they please to provide for the general welfare, but only to lay taxes for that purpose. To consider the latter phrase, not as describing the purpose of the first, but as giving a distinct and independent power to do any act they please, which might be for the good of the Union, would render all the preceding and subsequent enumerations of power completely useless. It would reduce the whole instrument to a single phrase, that of instituting a Congress with power to do whatever would be for the good of the United States; and, as they would be the sole judges of the good or evil, it would be also a power to do whatever evil they please. It is an established rule of construction where a phrase will bear either of two meanings, to give it that which will allow some meaning to the other parts of the instrument, and not that which would render all the others useless. Certainly no such universal power was meant to be given them. It was intended to lace them up straitly within the enumerated powers, and those without which, as means, these powers could not be carried into effect. It is known that the very power now proposed as a means was rejected as an end by the Convention which formed the Constitution. A proposition was made to them to authorize Congress to open canals, and an amendatory one to empower them to incorporate. But the whole was rejected, and one of the reasons for rejection urged in debate was, that then they would have a power to erect a bank, which would render the great cities, where there were prejudices and
  • 52. jealousies on the subject, adverse to the reception of the Constitution. 2. The second general phrase is, to make all laws necessary and proper for carrying into execution the enumerated powers. But they can all be carried into execution without a bank. A bank therefore is not necessary, and consequently not authorized by this phrase. It has been urged that a bank will give great facility or convenience in the collection of taxes. Suppose this were true: yet the Constitution allows only the means which are necessary, not those which are merely convenient for effecting the enumerated powers. If such a latitude of construction be allowed to this phrase as to give any non-enumerated power, it will go to every one, for there is not one which ingenuity may not torture into a convenience in some instance or other, to some one of so long a list of enumerated powers. It would swallow up all the delegated powers, and reduce the whole to one power, as before observed. Therefore it was that the Constitution restrained them to the necessary means, that is to say, to those means without which the grant of power would be nugatory. But let us examine this convenience and see what it is. The report on this subject, page 3, states the only general convenience to be, the preventing the transportation and re-transportation of money between the States and the treasury, (for I pass over the increase of circulating medium, ascribed to it as a want, and which, according to my ideas of paper money, is clearly a demerit.) Every State will have to pay a sum of tax money into the treasury; and the treasury will have to pay, in every State, a part of the interest on the public debt, and salaries to the officers of government resident in that State. In most of the States there will still be a surplus of tax money to come up to the seat of government for the officers residing there. The payments of interest and salary in each State may be made by treasury orders on the State collector. This will take up the great export of the money he has collected in his State, and consequently prevent the great mass of it from being drawn out of the State. If
  • 53. there be a balance of commerce in favor of that State against the one in which the government resides, the surplus of taxes will be remitted by the bills of exchange drawn for that commercial balance. And so it must be if there was a bank. But if there be no balance of commerce, either direct or circuitous, all the banks in the world could not bring up the surplus of taxes, but in the form of money. Treasury orders then, and bills of exchange may prevent the displacement of the main mass of the money collected, without the aid of any bank; and where these fail, it cannot be prevented even with that aid. Perhaps, indeed, bank bills may be a more convenient vehicle than treasury orders. But a little difference in the degree of convenience, cannot constitute the necessity which the constitution makes the ground for assuming any non-enumerated power. Besides; the existing banks will, without a doubt, enter into arrangements for lending their agency, and the more favorable, as there will be a competition among them for it; whereas the bill delivers us up bound to the national bank, who are free to refuse all arrangement, but on their own terms, and the public not free, on such refusal, to employ any other bank. That of Philadelphia, I believe, now does this business, by their post-notes, which, by an arrangement with the treasury, are paid by any State collector to whom they are presented. This expedient alone suffices to prevent the existence of that necessity which may justify the assumption of a non-enumerated power as a means for carrying into effect an enumerated one. The thing may be done, and has been done, and well done, without this assumption; therefore, it does not stand on that degree of necessity which can honestly justify it. It may be said that a bank whose bills would have a currency all over the States, would be more convenient than one whose currency is limited to a single State. So it would be still more convenient that there should be a bank, whose bills should have a currency all over the world. But it does not follow from this superior conveniency, that
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