VTU 8th Sem Notes Simulation

Computer Science, Informatik 4
Communication and Distributed Systems
Simulation
“Discrete-Event System Simulation”
Dr. Mesut Güneş

Chapter 3
General Principles

Dr. Mesut Güneş
3Chapter 3. General Principles
General Principles – Introduction
Framework for modeling systems by discrete-event
simulation
• A system is modeled in terms of its state at each point in time
• This is appropriate for systems where changes occur only at
discrete points in time

Dr. Mesut Güneş
Concepts in Discrete-Event Simulation
Concepts of dynamic, stochastic systems that change in a discrete
manner
A record of an event to occur at the current or some future time, along with any
associated data necessary to execute the event.
Event notice
An instantaneous occurrence that changes the state of a system.Event
A collection of associated entities ordered in some logical fashion in a waiting line.
Holds entities and event notices
Entities on a list are always ordered by some rule, e.g. FIFO, LIFO, or ranked by
some attribute, e.g. priority, due date
List, Set
The properties of a given entity.Attributes
An object in the system that requires explicit representation in the model, e.g., people,
machines, nodes, packets, server, customer.
Entity
A collection of variables that contain all the information necessary to describe the
system at any time.
System state
An abstract representation of a system, usually containing structural, logical, or
mathematical relationships that describe the system.
Model
A collection of entities that interact together over time to accomplish one or more
goals.
System

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A variable representing the simulated time.Clock
A duration of time of unspecified indefinite length, which is not known until it ends.
Customer’s delay in waiting line depends on the number and service times of other
customers.
Typically a desired output of the simulation run.
Delay
A duration of time of specified length, which is known when it begins.
Represents a service time, interarrival time, or any other processing time whose
duration has been characterized by the modeler. The duration of an activity can be
specified as:
• Deterministic – Always 5 time units
• Statistical – Random draw from {2, 5, 7}
• A function depending on system variables and entities
The duration of an activity is computable when it begins
The duration is not affected by other events
To track activities, an event notice is created for the completion time, e.g., let
clock=100 and service with duration 5 time units is starting
• Schedule an “end of service”-event for clock + 5 = 105
Activity
A list of event notices for future events, ordered by time of occurrence; known as the
future event list (FEL).
Always ranked by the event time
Event list

Dr. Mesut Güneş
Activity vs. Delay
Activity
• Activity is known as unconditional wait
• End of an activity is an event, for this an event notice is placed in
the future event list
• This event is a primary event
Delay
• Delay is known as conditional wait
• Delays are managed by placing the entity on another list, e.g.,
representing a waiting line
• Completion of delay is a secondary event, but they are not
placed in the future event list

Dr. Mesut Güneş
Activity vs. Delay
A1 A2 A3D1 D2
Activity1 Activity2
Delay
Delay
t

Dr. Mesut Güneş
A model consists of
• static description of the model and
• the dynamic relationships and interactions between the components
Some questions that need to be answered for the dynamic behavior
• Events
- How does each event affect system state, entity attributes, and set contents?
• Activities
- How are activities defined?
- What event marks the beginning or end of each activity?
- Can the activity begin regardless of system state, or is its beginning conditioned on the
system being in a certain state?
• Delays
- Which events trigger the beginning (and end) of each delay?
- Under what condition does a delay begin or end?
• System state initialization
- What is the system state at time 0?
- What events should be generated at time 0 to “prime” the model – that is, to get the
simulation started?

Dr. Mesut Güneş
A discrete-event simulation proceeds by producing a
sequence of system snapshots over time
A snapshot of the system at a given time includes
• System state
• Status of all entities
• Status of all sets
- Sets are used to collect required information for calculating
performance metrics
• List of activities (FEL)
• Statistics
........................
(3,t1) – Type 3 event to occur at t1(x, y, z, ...)t
StatisticsFuture event list (FEL)...Set 2Set 1Entities and
attributes
System stateClock

Dr. Mesut Güneş
Event-scheduling/Time-advance algorithm
Future event list (FEL)
• All event notices are chronologically ordered in the FEL
• At current time t, the FEL contains all scheduled events
• The event times satisfy: t < t1 ≤ t2 ≤ t3 ≤ ... ≤ tn
• The event associated with t1 is the imminent event, i.e., the next
event to occur
• Scheduling of an event
- At the beginning of an activity the duration is computed and an end-
of-activity event is placed on the future event list
• The content of the FEL is changing during simulation run
- Efficient management of the FEL has a major impact on the
performance of a simulation run
- Class: Data structures and algorithms

Dr. Mesut Güneş
(2,tn) – Type 2 event to occur at tn
...
(1,t3) – Type 1 event to occur at t3
(3,t1) – Type 3 event to occur at t1(5,1,6)t
Future event list…StateClock
(2,tn) – Type 2 event to occur at tn
...
(4,t*) – Type 4 event to occur at t*
(1,t2) – Type 1 event to occur at t2(5,1,5)t1
Future event list…StateClock
Old system snapshot at time t
New system snapshot at time t1
Step 1: Remove the event notice for the
imminent event from FEL
• event (3, t1) in the example
Step 2: Advance Clock to imminent event time
• Set clock = t1
Step 3: Execute imminent event
• update system state
• change entity attributes
• set membership as needed
Step 4: Generate future events and place their
event notices on FEL
Event (4, t*)
Step 5: Update statistics and counters

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System snapshot at time 0
• Initial conditions
• Generation of exogenous events
- Exogenous event, is an event which happens outside the system,
but impinges on the system, e.g., arrival of a customer

Dr. Mesut Güneş
Generation of events
• Arrival of a customer
- At t=0 first arrival is generated and scheduled
- When the clock is advanced to the time of the
first arrival, a second arrival is generated
- Generate an interarrival time a*
- Calculate t* = clock + a*
- Place event notice at t* on the FEL
Bootstrapping

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• Service completion of a customer
- A customer completes service at t
- If the next customer is present a new service time s* is generated
- Calculate t* = clock + s*
- Schedule next service completion at t*
- Additionally: Service completion event will scheduled at the arrival
time, when there is an idle server
- Service time is an activity
- Beginning service is a conditional event
– Conditions: Customer is present and server is idle
- Service completion is a primary event

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• Alternate generation of runtimes and downtimes
- At time 0, the first runtime will be generated and an end-of-runtime
event will be scheduled
- Whenever an end-of-runtime event occurs, a downtime will be
generated, and a end-of-downtime event will be scheduled
- At the end-of-downtime event, a runtime is generated and an end-
of-runtime event is scheduled
- Runtimes and downtimes are activities
- end-of-runtime and end-of-downtime are primary events
Time
runtimedowntimeruntime
Time 0

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Stopping a simulation
1. At time 0, schedule a stop simulation event at a specified future
time TE Simulation will run over [0, TE]
2. Run length TE is determined by the simulation itself.
• TE is not known ahead.
• Example: TE = When FEL is empty

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World Views
World view
• A world view is an
orientation for the model
developer
• Simulation packages
typically support some
world views
• Here, only world views for
discrete simulations
Discrete Simulation
Event-scheduling Process-interaction Activity-scanning

Dr. Mesut Güneş
World Views
Event-scheduling
• Focus on events
• Identify the entities and their
attributes
• Identify the attributes of the
system
• Define what causes a change
in system state
• Write a routine to execute for
each event
• Variable time advance
Start
Initialization
Select next event
Event
routine 1
Terminate?
Output
End
Event
routine 2
Event
routine n
No
Yes

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World Views
Process-interaction
• Modeler thinks in terms of processes
• A process is the lifecycle of one entity, which consists of various events and activities
• Simulation model is defined in terms of entities or objects and their life cycle as they flow
through the system, demanding resources and queueing to wait for resources
• Some activities might require the use of one or more resources whose capacities are limited
• Processes interact, e.g., one process has to wait in a queue because the resource it needs is
busy with another process
• A process is a time-sequenced list of events, activities and delays, including demands for
resource, that define the life cycle of one entity as it moves through a system
• Variable time advance

Dr. Mesut Güneş
World Views
Activity-scanning
• Modeler concentrates on activities
of a model and those conditions
that allow an activity to begin
• At each clock advance, the
conditions for each activity are
checked, and, if the conditions are
true, then the corresponding
activity begins
• Fix time advance
• Disadvantage: The repeated
scanning to discover whether an
activity can begin results in slow
runtime
Improvement: Three-phase
approach
- Combination of event scheduling
with activity scanning
Start
Initialization
Phase 2: Activity Scan
Activity 1
Condition
Actions
Other condition
satisfied?
Output
End
Activity 2
Condition
Actions
Activity n
Condition
Actions
Yes
Phase 1: Time Scan
Terminate?
Yes
No
No

Dr. Mesut Güneş
World Views
Three-phase approach
• Events are activities of duration
zero time units
• Two types of activities
- B activities: activities bound to
occur; all primary events and
unconditional activities
- C activities: activities or events
that are conditional upon certain
conditions being true
• The B-type activites can be
scheduled ahead of time, just as
in the event-scheduling approach
- Variable time advance
- FEL contains only B-type events
• Scanning to learn whether any C-
type activities can begin or C-type
events occur happen only at the
end of each time advance, after
all B-type events have completed
Start
Initialization
Phase C: Scan all C activities
Activity 1
Condition
Actions
Other condition
satisfied?
Output
End
Activity 2
Condition
Actions
Activity n
Condition
Actions
Yes
Phase A: Time Scan
Terminate?
Yes
No
No
Phase B: Execute B activities due now

Dr. Mesut Güneş
World Views
Time
E1 E2
A1 A2
P1
E3 E4
A3 A4
P2
E5 E6
A5 A6
P3
E7 E8
A7 A8
P4

Dr. Mesut Güneş
Manual Simulation Using Event Scheduling – Grocery
Reconsider grocery example from Chapter 2
• In chapter 2: We used an ad hoc method to simulate the grocery
System state = ( LQ(t), LS(t) )
• LQ(t) = Number of customers in the waiting line at t
• LS(t) = Number of customers being served at t (0 or 1)
Entities
• Server and customers are not explicitly modeled
Events
• Arrival (A)
• Departure (D)
• Stopping event (E)
Event notices
• (A, t) arrival event at future time t
• (D, t) departure event at future time t
• (E, t) simulation stop at future time t
Activities
• Interarrival time
• Service time
Delay
• Customer time spent in waiting line
ServerWaiting line
Calling population

Dr. Mesut Güneş
System state = ( LQ(t), LS(t) ) is affected by the events
• Arrival
• Departure

Dr. Mesut Güneş
Maximum Queue Length
Server Busy time
Initial conditions
First customer arrives at t=0
and gets service
An arrival and a departure
event is on FEL
Server was busy for 21 of
23 time units
Maximum queue length
was 2

Dr. Mesut Güneş
When event scheduling is implemented, consider
• Only one snapshot is kept in the memory
• A new snapshot can be derived only from the previous snapshot
• Past snapshot are ignored for advancing the clock
• The current snapshot must contain all information necessary to
continue the simulation!
In the example
• No information about particular customer
• If needed, the model has to be extended

Dr. Mesut Güneş
Analyst wants estimates per customer basis
• Mean response time (system time)
• Mean proportion of customers who spend more than 5 time units
Extend the model to represent customers explicitly
• Entities: Customer entities denoted as C1, C2, C3, …
- (Ci, t) customer Ci arrived at t
• Event notices
- (A, t, Ci) arrival of customer Ci at t
- (D, t, Cj) departure of customer Cj at t
• Set
- “Checkout Line” set of customers currently at the checkout counter ordered
by time of arrival
• Statistics
- S: sum of customer response times for all customers who have departed by
the current time
- F: total number of customers who spend ≥ 5 time units
- ND: number of departures up to the current simulation time

Dr. Mesut Güneş
83.5
6
35
timeresponse ===
DN
S
5635(A,25,C8)(D,27,C7)(E,60)(C7,23)1023
4530(D,23,C6)(A,23,C7)(E,60)(C6,18)1018
4530(A,18,C6)(E,60)0016
3425(D,16,C4)(A,18,C6)(E,60)(C5,11)1015
2318(D,15,C4)(A,18,C6)(E,60)(C4,8)(C5,11)1111
129(D,11,C3)(A,11,C5)(E,60)(C3,2)(C4,8)118
129(A,8,C4)(D,11,C3)(E,60)(C3,2)106
014(D,6,C2)(A,8,C4)(E,60)(C2,1)(C3,2)114
000(D,4,C1)(A,8,C4)(E,60)(C1,0)(C2,1)(C3,2)122
000(A,2,C3)(D,4,C1)(E,60)(C1,0)(C2,1)111
000(A,1,C2) (D,4,C1)(E,60)(C1,0)100
FNDSFuture Event ListCheckout LineLS(t)LQ(t)Clock
StatisticsSystem State
Extended version of the simulation table from Slide 25
83.0
6
5
5 ===≥
DN
F
N

Dr. Mesut Güneş
Manual Simulation Using Event Scheduling – Dump Truck
The DumpTruck Problem
• Six dump trucks are used to haul coal from the entrace of a small mine
to the railroad
• Each truck is loaded by one of two loaders
• After loading, the truck immediately moves to the scale, to be weighed
• Loader and Scale have a first-come-first-serve (FCFS) queue
• The travel time from loader to scale is negligible
• After being weighed, a truck begins a travel time, afterwards unloads
the coal and returns to the loader queue
• Purpose of the study: Estimation of the loader and scale utilizations.

Dr. Mesut Güneş
System state [ LQ(t), L(t), WQ(t), W(t) ]
• LQ(t) = number of trucks in the loader queue ∈{0,1,2,...}
• L(t) = number of trucks being loaded ∈{0,1,2}
• WQ(t) = number of trucks in weigh queue ∈{0,1,2,...}
• W(t) = number of trucks being weighed ∈{0,1}
Event notices
• (ALQ, t, DTi) dump truck i arrives at loader queue (ALQ) at time t
• (EL, t, DTi) dump truck i ends loading (EL) at time t
• (EW, t, DTi) dump truck i ends weighing (EW) at time t
Entities
• The six dump trucks DT1, DT2, ..., DT6
Lists
• Loader queue – Trucks waiting to begin loading, FCFS
• Weigh queue – Truck waiting to bei weighed, FCFS
Activities
• Loading – Loading time
• Weighing – Weighing time
• Travel – Travel time
Delays
• Delay at loader queue
• Delay at scale
Loading Time Distribution
1.000.2015
0.800.5010
0.300.305
CDFPDFLoading Time
Weighing Time Distribution
1.000.3016
0.700.7012
CDFPDFWeighing Time
1.000.10100
Travel Time Distribution
0.900.2080
0.700.3060
0.400.4040
CDFPDFTravel Time

Dr. Mesut Güneş
Initialization
• It is assumed that five trucks are at the loader and one is at the scale at
time 0
Activity times
• Loading time: 10, 5, 5, 10, 15, 10, 10
• Weighing time: 12, 12, 12, 16, 12, 16
• Travel time: 60, 100, 40, 40 80
2444(EL,25,DT6) (EW,24+12,DT2)
(ALQ,72,DT1) (ALQ,24+100,DT3)
DT4, DT5121024
2040(EW,24,DT3) (EL,25,DT6) (ALQ,72,DT1)DT2, DT4, DT5131020
1224(EL,20,DT5) (EW,12+12,DT3)
(EL,25,DT6) (ALQ,12+60,DT1)
DT2, DT4122012
1020(EW,12,DT1) (EL,20,DT5)
(EL,10+15,DT6)
DT3, DT2, DT4132010
1020(EL,10,DT4) (EW,12,DT1)
(EL,10+10,DT5)
DT3, DT2DT6122110
510(EL,10,DT2) (EL,5+5,DT4) (EW,12,DT1)DT3DT5, DT611225
00(EL,5,DT3) (EL,10,DT2) (EW,12,DT1)DT4, DT5, DT610230
BSBLFuture Event ListWeigh QueueLoader QueueW(t)WQ(t)L(t)LQ(t)Clock
StatisticsListsSystem State
Both loaders
are busy!

Simulation in Java

Dr. Mesut Güneş
Simulation in Java
Java is a general purpose
programming language
• Object-oriented
First simple specific
simulation implementation
Later, object-oriented
framework for discrete event
simulation
Again the grocery example
• Single server queue
• Run for 1000 customers
• Interarrival times are
exponentially distributed with
mean 4.5
• Service times are also
exponentially distributed with
mean 3.2
• Known as: M/M/1 queueing
system
ServerWaiting line
Calling population
titi+1
Arrivals

Dr. Mesut Güneş
Simulation in Java
System state
• queueLength
• numberInService
Entity attributes
• customers
Future event list
• futureEventList
Activity durations
• meanInterArrivalTime
• meanServiceTime
Input parameters
• meanInterarrivalTime
• meanServiceTime
• totalCustomers
Simulation variables
• clock
• lastEventTime
• totalBusy
• maxQueueLength
• sumResponseTime
Statistics
• rho = BusyTime/Clock
• avgr = Average response time
• pc4 = Number of customers who spent
more than 4 minutes
Help functions
• exponential(mu)
Methods
• initialization
• processArrival
• processDeparture
• reportGeneration

Dr. Mesut Güneş
Simulation in Java
Overall structure of an event-scheduling
simulation program
Overall structure of the Java program

Dr. Mesut Güneş
Simulation in Java – Class Event
class Event {
public double time;
private int type;
public Event(int _type, double _time) {
type = _type;
time = _time;
}
public int getType() {
return type;
}
public double getTime() {
return time;
}
}

Dr. Mesut Güneş
Simulation in Java – Sim Class
class Sim {
// Class Sim variables
public static double clock,
meanInterArrivalTime,
meanServiceTime,
lastEventTime,
totalBusy,
maxQueueLength,
sumResponseTime;
public static long numberOfCustomers,
queueLength,
numberInService,
totalCustomers,
numberOfDepartures,
longService;
public final static int arrival = 1; // Event type for an arrival
public final static int departure = 2; // Event type for a departure
public static EventList futureEventList;
public static Queue customers;
public static Random stream;

Dr. Mesut Güneş
Simulation in Java – Main program
public static void main(String argv[]) {
meanInterArrivalTime = 4.5;
meanServiceTime = 3.2;
totalCustomers = 1000;
long seed = Long.parseLong(argv[0]);
stream = new Random(seed); // Initialize rng stream
futureEventList = new EventList();
customers = new Queue();
initialization();
// Loop until first “totalCustomers" have departed
while( numberOfDepartures < totalCustomers ) {
Event event = (Event)futureEventList.getMin(); // Get imminent event
futureEventList.dequeue(); // Be rid of it
clock = event.getTime(); // Advance simulation time
if( event.getType() == arrival ) {
processArrival(event);
}
else {
processDeparture(event);
}
}
reportGeneration();
}

Dr. Mesut Güneş
Simulation in Java – Initialization
// Seed the event list with TotalCustomers arrivals
public static void initialization() {
clock = 0.0;
queueLength = 0;
numberInService = 0;
lastEventTime = 0.0;
totalBusy = 0 ;
maxQueueLength = 0;
sumResponseTime = 0;
numberOfDepartures = 0;
longService = 0;
// Create first arrival event
double eventTime = exponential(stream, MeanInterArrivalTime);
Event event = new Event(arrival, eventTime);
futureEventList.enqueue(event);
}

Dr. Mesut Güneş
Simulation in Java – Event Arrival
public static void processArrival(Event event) {
customers.enqueue(event);
queueLength++;
// If the server is idle, fetch the event, do statistics and put into service
if( numberInService == 0 ) {
scheduleDeparture();
}
else {
totalBusy += (clock - lastEventTime); // server is busy
}
// Adjust max queue length statistics
if(maxQueueLength < queueLength) {
maxQueueLength = queueLength;
}
// Schedule the next arrival
Double eventTime = clock + exponential(stream, meanInterArrivalTime);
Event nextArrival = new Event(arrival, eventTime);
futureEventList.enqueue( nextArrival );
lastEventTime = clock;
}

Dr. Mesut Güneş
Simulation in Java – Event Departure
public static void scheduleDeparture() {
double serviceTime = exponential(stream, meanServiceTime);
Event depart = new Event(departure, clock + serviceTime);
futureEventList.enqueue(depart);
queueLength--;
}
public static void processDeparture(Event e) {
// Get the customer description
Event finished = (Event) customers.dequeue();
// If there are customers in the queue then schedule the departure of the next one
if( queueLength > 0 ) {
scheduleDeparture();
}
else {
}
// Measure the response time and add to the sum
double response = clock - finished.getTime();
sumResponseTime += response;
if( response > 4.0 )
longService++; // record long service
totalBusy += (clock - lastEventTime);
numberOfDepartures++;
lastEventTime = clock;
}

Dr. Mesut Güneş
Simulation in Java – Report Generator
public static void reportGeneration() {
double rho = totalBusy/clock;
double avgr = sumResponseTime/totalCustomers;
double pc4 = ((double)longService)/totalCustomers;
System.out.println( "SINGLE SERVER QUEUE SIMULATION - GROCERY STORE CHECKOUT COUNTER ");
System.out.println( "tMEAN INTERARRIVAL TIME " + meanInterArrivalTime );
System.out.println( "tMEAN SERVICE TIME " + meanServiceTime );
System.out.println( "tNUMBER OF CUSTOMERS SERVED " + totalCustomers );
System.out.println();
System.out.println( "tSERVER UTILIZATION " + rho );
System.out.println( "tMAXIMUM LINE LENGTH " + maxQueueLength );
System.out.println( "tAVERAGE RESPONSE TIME " + avgr + " Time Units");
System.out.println( "tPROPORTION WHO SPEND FOUR ");
System.out.println( "t MINUTES OR MORE IN SYSTEM " + pc4 );
System.out.println( "tSIMULATION RUNLENGTH " + clock + " Time Units");
System.out.println( "tNUMBER OF DEPARTURES " + totalCustomers );
}

Dr. Mesut Güneş
Simulation in Java - Output
SINGLE SERVER QUEUE SIMULATION - GROCERY STORE CHECKOUT COUNTER
MEAN INTERARRIVAL TIME 4.5
MEAN SERVICE TIME 3.2
NUMBER OF CUSTOMERS SERVED 1000
SERVER UTILIZATION 0.718
MAXIMUM LINE LENGTH 13.0
AVERAGE RESPONSE TIME 9.563
PROPORTION WHO SPEND FOUR
MINUTES OR MORE IN SYSTEM 0.713
SIMULATION RUNLENGTH 4485.635
NUMBER OF DEPARTURES 1000

Object-oriented Discrete-Event Simulation
Framework

Dr. Mesut Güneş
Object-Oriented Simulation Framework
Package core Package rng

Dr. Mesut Güneş
OO Discrete-Event Simulation Framework consists of
• Two packages
Package core
• SimEvent
• SimEntity
• SimQueue
• SimControl
Package rng
• RNG

Dr. Mesut Güneş
Object-Oriented Simulation Framework – SimEvent
public class SimEvent {
double time;
int type;
SimEntity src;
SimEntity dst;
public long id;
public SimEvent(SimEntity _dst) {
type = 0;
time = 0;
src = null;
dst = _dst;
}
public SimEvent(double _time, SimEntity _dst) {
type = 0;
time = _time;
src = null;
dst = _dst;
}
public SimEvent(double _time, SimEntity _src, SimEntity _dst) {
type = 0;
time = _time;
src = _src;
dst = _dst;
}

Dr. Mesut Güneş
Object-Oriented Simulation Framework – SimEntity
public abstract class SimEntity {
protected SimControl simControl;
/**
* An entity has to know the current instance of the simulator.
* @param _simControl
* @see SimControl
*/
public SimEntity(SimControl _simControl) {
simControl = _simControl;
}
/**
* This method handles the events destined to this entity.
* @param event
* @see SimEvent
*/
abstract public void handleEvent(SimEvent event);
}

Dr. Mesut Güneş
Object-Oriented Simulation Framework – SimQueue
public abstract class SimQueue {
/**
* Schedule the given event according to the event time.
* @param event
* @see SimEvent
*/
abstract public void schedule(SimEvent event);
/**
* Return the next event in the queue.
* @return imminent event in queue.
* @see SimEvent
*/
abstract public SimEvent getNextEvent();
/**
* This method dumps the content of the queue.
* It is for debugging purposes.
*/
abstract public void dump();
abstract public boolean isEmpty();
}

Dr. Mesut Güneş
Object-Oriented Simulation Framework – SimControl
public class SimControl {
private SimQueue queue;
private double time;
private double endTime;
public SimControl(SimQueue _queue) {
queue = _queue;
}
public void run() {
SimEvent event;
while( queue.isEmpty() == false ) {
// If there is an event in FEL and the sim-end is not reached ...
event = queue.getNextEvent();
time = event.getTime();
if( event.getTime() <= endTime )
dispatch(event); // ... call the destination object of this event
else
break;
}
}
private void dispatch(SimEvent event) {
event.getDestination().handleEvent(event);
}

Dr. Mesut Güneş
Object-Oriented Simulation Framework – SimControl
... public class SimControl ...
public void setRunTime(double _runTime) {
endTime = _runTime;
}
public void schedule(SimEvent event) {
queue.schedule(event);
}
public void schedule(SimEvent event, double _delta) {
event.setTime(time +_delta);
schedule(event);
}

Dr. Mesut Güneş
Object-Oriented Simulation Framework – RNG
public abstract class RNG {
abstract public double getNext();
}
public class Exponential extends RNG {
double lambda;
Random uniform;
public Exponential(double _lambda) {
lambda = _lambda;
uniform = new Random(System.currentTimeMillis());
}
/*
* @see rng.RNG#getNext()
*/
public double getNext() {
return -Math.log(uniform.nextDouble())/lambda;
}
}

Dr. Mesut Güneş
Again our Grocery
example
• Use of the object-
oriented simulation
framework
MM1Generator
• Generates new
customer
MM1Server
• Serves customer

Dr. Mesut Güneş

Dr. Mesut Güneş
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SystemTime
rho
Simulation
Theory
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QueueingTime
rho
Simulation
Theory
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ProbabilityofEmptySystem
rho
Simulation
Theory
System Time Queueing Time
p0 – Probability that
a customer finds the
system idle
p0

Dr. Mesut Güneş
Summary
Introduced a general framework for discrete event
simulations
Event-scheduling and time-advance algorithm
World views for discrete simulations
Introduced manual discrete event simulation
Introduced simulation in Java
Object-oriented simulation framework in Java

VTU 8th Sem Notes Simulation

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VTU 8th Sem Notes Simulation