Mobile Survey on Simulation for Networks

Simulation and modeling of mobile protocols
Mobile computing survey

Edwin Hernandez
David Witter

Mobile Computing – CIS 6930
Dr. Sumi Helal
Feb 24th, 1999

TABLE OF CONTENTS

SIMULATION AND MODELING OF MOBILE PROTOCOLS ........................................................ 3
ABSTRACT ............................................................................................................................................ 3
INTRODUCTION - NOMADIC COMPUTING OVER THE INTERNET................................................................. 3
Address binding................................................................................................................................ 4
Network Infrastructure...................................................................................................................... 4
TCP connection management............................................................................................................ 5
MOBILITY PERFORMANCE.............................................................................................................. 6
HAND-OFF MANAGEMENT ALGORITHMS FOR URBAN AND SUB-URBAN ENVIRONMENTS UNDER REALISTIC
VEHICLE MOBILITY CONDITIONS ........................................................................................................... 6
PERFORMANCE OF TRANSPORT PROTOCOLS OVER A MULTICASTING-BASED ARCHITECTURE FOR INTERNET
HOST MOBILITY .................................................................................................................................... 7
PERFORMANCE E VALUATION OF MOBILE IP PROTOCOLS IN A WIRELESS ENVIRONMENT ......................... 8
REPLICATED SERVERS FOR IP-HOST MOBILITY....................................................................................... 10
ANALITICAL SIMULATION OF MOBILE NETWORKS .............................................................. 13
MOBILITY AND PERFORMANCE MODELING IN CELLULAR COMMUNICATION NETWORKS .......................... 13
Network Modeling .......................................................................................................................... 13
Cell modeling ................................................................................................................................. 15
REFERENCES................................................................................................................................... 18

2

Simulation and modeling of mobile protocols

Abstract
Mobile computing protocols are becoming one of the most important issues in state-of-the-art
technologies. In this paper we will provide important issues in terms of modeling and simulation of mobile
protocols. First, the survey discusses the theoretical issues in mobile or nomadic computing environment,
afterwards some performance measurements papers are explained, they show simulations done to routing
and hand-off optimizations. Finally, an analytical point of view is presented using queuing theory analysis
in pico-cell networks.

Introduction - Nomadic computing over the internet
There are several answers to the problem of mobility, mobile-IP is one of them, but there are other
frameworks found for instance in [Li98], where an universal personal computing (UPC) paradigm is
presented. The term nomadicity refers to the system support needed to provide a rich set of computing and
communication capabilities and services for mobile users in a transparent, integrated and convenient form
as they move between different places. The desired characteristics for nomadicity include independence of
location, motion, computing platform, communication device, and communication bandwidth, and the
widespread availability of access to remote files, systems and services.
There are some other standards for nomadicity, such as the Universal Personal
Telecommunication, studied by the CCITT (ITU), which is based on the intelligent network architecture
and focused on extending point-to-point connection-oriented services provided by the public switched
telephone network to mobile users. In addition to those efforts, the Telecommunications Information
Networking Architecture (TINA) has defined and validated an open architecture for telecommunications
systems providing personal mobility functions. Both frameworks, as explained before are designed to be
applicable in the Intelligent Network (IN) and Broadband ISDN (Integrated Services Digital Network).

The UPC paradigm presented by [Li98] follows these design issues:
• Only regular users of the internet are considered, each user should belong to a home network, a place
where the user is properly registered.
• Each mobile user has a service profile at her home network where all the services are defined.
• Services and terminal control have to be logically separated.
• Each user and her current terminal has to be identified by the Logical User Identifier (LIU) and Logical
Terminal Identifier (LTI), respectively, that are independent of each others as well as their curretn
location.

3

• Location information management of mobile objects is a key issue on UPC, the algorithms for
searching and updating locations of mobile users and terminals should not adversely burden the
internet in terms of traffic overhead and protocol processing.
• Adaptation capabilities should be provided to harmonize the differences in operating environments,
input, output, display and storage formats.
• Certain intelligent agents may be incorporated to optimize the UPC operations through optimal
functional divisions between terminals and networks.

Address binding
To enable personal mobility, a logical user identifier or LUI is needed to uniquely and directly
identify a user irrespective of a terminal used. The LUI is used as the basis for sending and receiving
messages and for charging a user for services. The terminals are identified by the LTI regardless of whether
they are fixed or mobile. LUI should be unique and it might be a number or a name or even a picture, it
might be the user@domain string. The IP address could be the analog to the LTI.

Network Infrastructure
It is composed by a User’s Home Agent (UHA), a Terminal’s Home Agent (THA) and a Foreign
Agent (FA) which are configured in each self-administrative domain of the conceptual multi-network
internet architecture to support personal and terminal mobility in UPC.
User’s Home Agent (UHA): Each mobile user has a home network. The UHA in each network maintains
a list of users calling the network home, and the pertinent information for each user, including service
profile and location information.
Terminal’s Home Agent (THA): The network should have a THA which maintains a home list of
database identifiers of all mobile terminals that call the network home. They are the mobile hosts in
mobile-ip. Terminal related information such as LTI, terminal profile, terminal authentication key, and
current terminal location are stored in the THA.
Foreign Agent (FA): As mobile users and terminals migrate over the internet, they need to access network
computing resources and services from different networks connected to the internet. Each network serving
mobile terminals should have a FA which enables users and terminals to be temporarily associated with the
network. Each FA should provide two list one of visiting users and another one of visiting terminals. There
is a binding to the UHA and THA to enable packet redirection.

4

TCP connection management
Another important issue is the TCP connection management. TCP utilizes the three way
handshake protocol, with a sequence of ACK – SYN – ACK, we have to recall the state machine for the
TCP handshake defined in the TCP protocol.. In [Li98] is proposed three different solutions for mobile
communication in TCP links. a) a Transparent Solution b) The TCP layer solution c) the middleware layer
solution.

In the Transparent Solution, the UHA has two finite states machines, it establishes a
communication link using TCP between the source and then initiates a communication link to the Mobile
Terminal (MT) or host. In fact [Li98] point out that the TCP connection between the UHA and the MT is
supported by mobile-ip. However, movements of the MT will require routing optimization and cache
validation techniques.

Meanwhile the TCP Layer Solution , the source request to set up a connection to the UAH using
an IP address of the MT. The UHA transfers the message to the MT, the message is tunneled and the MT
piggyback the source. The TCP layer of the source is modified with the new IP address piggybacked by the
MT. The main problem with this solution is the lack of transparency between the source and the
destination, and this modification should be taken into consideration by the IETF which is not feasible.

Finally the Middleware Layer Solution, in which the middleware is aware of the mobility of the
MT at the UHA, therefore when the MT is moved and the directory service is requested the middleware
should provide the source of information with updated addresses. This is similar to the TCP layer solution
but it can be implemented in alignment with OSI principles.

5

Mobility Performance
A common subject for research in mobile computing is performance of protocols and wireless
simulation. At the physical access level, one can discuss hand-off issues between micro and macrocells.
Moving to a higher level, issues involving the performance of Mobile IP versus Route Optimization Mobile
IP are of keen importance as to which will be implemented in the future Internet. Another solution to
mobility in IP is multicasting. This approach is promising due to the mobile host not needing to change IP
addresses as it roams. Finally, a paper on replicated home-agents improving the load balance and
availability.

Hand-off Management Algorithms for Urban and Sub-urban Environments Under
Realistic Vehicle Mobility Conditions
While studying mobile computing and the challenges this field faces, one begins to realize that
many of the problems parallel those faced by the cellular communication community. This paper discusses
ways to lower the number of hand-offs needed when traveling through an urban area. The technique
discussed here for cellular service could be targeted at the same challenge facing mobile computing.
Before begin, the basics must be discussed. In a wireless environment, there are two types of
coverage. Microcells usually provide coverage to congested areas such as an airport or business area.
These are also called hot spots. Microcells cover an area with a radius of approximately 100m.
Macrocells, on the other hand, are much larger and usually cover and area with several microcells within it.
Macrocells are responsible for providing service to the suburban area as well as travelers through the urban
area. See the figure below.

Macrocell

Microcells

The process used to determine whether a user should be handed from the macrocell to the
microcell depends on the classification of the user. A fast user, one that is travelling quickly through the
region, would be assigned to the macrocell. A slow user, one that may be seated at a conference, would be

6

assigned to a microcell. This scheme works well except when a user is travelling through the region but is
slowed considerably by a congested area with many traffic lights and is classified as slow. Under the
current approach, the user would experience many hand-offs from one macrocell to the other. This method
is grossly inefficient and increases the chance of the user becoming disconnected.
Dr. Iera of the University of Reggio Calabrai, Italy [Iera08] purposed a solution to this problem.
A fast user connected to the macrocell is given a time bonus when he reaches the border of a microcell. If
the user travels through the microcell in time less than t_threshold, the user gets keeps 100% of the time
bonus for the next microcell. If the traveler takes time less than t_threshold + time bonus, but greater than
t_threshold, the time bonus us decreased for the next microcell. If the traveler takes more time than
t_threshold + time bonus, then the traveler is immediately assigned to a microcell.
In order to test this method, an elaborate traffic simulator was used in conjunction with the newly
purposed algorithm. Varying the number of traffic lights as well as varying the light duration set the
simulator parameters. Results were rather promising, as the average number of hand-offs per call
decreased from 4.25 to 2.8. This improvement came at a cost though, as the number of calls blocked and
forcefully terminated increased slightly with the new algorithm. This drawback can be contributed to the
overloading of the macrocell in this scheme. Since the drawback seems small compared to the
improvement in the number of hand-offs, this algorithm show promise for both the wireless communication
environment.

Performance of Transport Protocols over a Multicasting-based Architecture for
Internet Host Mobility
Although Mobile IP is gaining momentum towards being the standard, other solutions to mobility
have been researched. One of those possible solutions is to use IP multicasting. IP multicasting provides
packet delivery to location independent addresses and allows hosts to leave and join multicast groups.
These abilities parallel the needs of host mobility in the wireless network environment.
Jayanth Mysore and Vaduvur Bharghavan wrote this paper to explore the performance of Mobility
Support using Multicasting in IP (MSM-IP) versus the standard Mobile IP protocol. In order to provide
more complete results, both UDP and TCP were run over both MSM-IP and Mobile IP. Before discussing
the results, the reader needs to understand how MSM-IP and Mobile IP work.
In Mobile IP, each mobile host has its own home address. When the host moves from its home
subnetwork to another, the mobile host receives a care-of-address. The care-of-address is a dynamic
identifier that reflects the current point of attachment. When a correspondent host sends packets to the
mobile host, the packets first go to the home agent. The home agent, who knows the care-of-address,
forwards these packets to the mobile host. The mobile host, on the other hand, can send packets directly to
the correspondent host. Thus, the name triangle routing originated.
MSM-IP takes advantage of multicast routing to support host mobility. Multicast routing uses the
virtual interconnection of tunnels over the existing internet. The source of data packets is the root of the

7

distribution tree, while the mobile host would be at lowest level. When a mobile host moves to a different
network, it sends an IGMP registration message to the local multicast router. Due to common case
mobility, the new multicast router will be close to the previous multicast router that was servicing the
mobile host. Therefore, on the lowest level of the distribution tree will have to be modified making
handoff with MSM-IP efficient.
In order to test UDP performance with MSM-IP, 16 different test were run. The variables for each
test were cold versus hot switching, uploading or downloading, 100Kbps or 400Kbps throughput and
constant versus Poisson traffic distributions. Cold switching means the mobile host handed of before
registering with the new network, while hot switching means the mobile host did register with the new
network before handoff. Performance results were impressive as the maximum packet loss was 1 and the
maximum number of duplicates was 3. In most cases thought, the number of duplicates was 0.
To study the performance of TCP, the authors compared the distribution of the sequence numbers
of the packets received to time during a switch. A constant slope on a graph would represent a constant
steam of data uninterrupted during a switch. MSM-IP performed well, only showing less than a two-
second delay before full recovery. When compared to Mobile IP, MSM-IP once again faired well. MSM-
IP showed a significant performance gain, especially when the network was simulated with a larger delay.
With a delay larger than 100ms, ACKs sent by the mobile host from its new location are not recognized, so
the correspondent host continues to send packets to the old interface. Since the mobile host is no longer at
this interface, all the data packets get lost. These lost data packets are interpreted as network congestion,
and TCP consequently slows down transmission. MSM-IP does not have this problem, as the mobile host
does not need to change multicast addresses.
This paper has presented a reasonable alternative to Mobile IP through MSM-IP. MSM-IP uses
multicasting so that packets destined for a mobile host do not need to travel through a home agent. It also
reduces the number of packets lost during handoff because the correspondent host does not need a binding
update to learn the new care-of-address. Although MSM-IP looks like a promising alternative, it is not a
realistic widely-used solution because an effective IP multicasting infrastructure covering the entire internet
is not in place.

Performance Evaluation of Mobile IP Protocols in a Wireless Environment
As the need for mobile access to the internet increases, solutions for IP in a wireless environment
are needed. The two protocols with the most momentum are Mobile IP (MIP) and Route Optimization
Mobile IP (ROMIP). In this paper, the performance in terms of overhead for control, packet delay and
packet loss for both MIP and ROMIP are compared using simulation.

8

In order to discuss the performance measurements of the two protocols, the differences between
the protocols must be discussed. Traditional MIP uses triangle routing, as the packet path from the
correspondent host to the mobile host is different than from the mobile host to the correspondent. This is
because the correspondent host only knows the
mobile host’s home address. Any packet sent to the Correspondent Mobile
Host Host
home address is tunneled by the home agent to the
mobile host’s care-of-address. One can see from the
diagram that there is a certain amount of inefficiency
in this method. ROMIP tries to address this Home Agent

inefficiency.
With ROMIP, correspondent host sends packets directly to the mobile host. The correspondent
host maintains a cache of care-of-addresses for mobile hosts receiving packets, which allows the
correspondent to send packets directly to the mobile host. Whenever a mobile host moves to another
foreign subnet, the mobile host must send a binding update to both its home agent and the previous foreign
agent. The home agent then sends a binding update to any correspondent host that needs the new care-of-
address. The previous foreign agent uses the binding update to forward any packets it receives to the
differently located mobile host. This forwarding continues until all the correspondent hosts have updated
their care-of-address for the mobile host.
The results from the simulation are what one would expect. The ROMIP protocol outperformed
the traditional MIP when the session size (time) was substantial (>100kbit). When the session time was
smaller than this, the overhead needed for ROMIP outweighed the benefit from the route optimization. As
the session size increased past 100kbits, ROMIP’s end-to-end packet delay remained constant while MIP’s
skyrocketed exponentially. The greater performance observed for ROMIP at higher session lengths can be
contributed to two factors.
First, the route between the correspondent host and the mobile host must be physically shorter due
to the definition of a triangle. If the physical distance is shorter, the transmission time will also be shorter.
Included in this factor is that the home agent requires processing time to tunnel packets to the mobile host.
These two delays contribute to a constant delay for every packet sent. A second factor contributing for the
higher performance is the flooding of home agents. In MIP, every packet sent to a mobile host must pass
through the home agent. If the home agent is servicing several hosts that roaming, packet congestion at the
home agent becomes a serious problem. This explains why the end-to-end packet delay for MIP increased
exponentially with longer session times.
In this paper, two popular approaches to host mobility in a wireless environment were compared
through simulation. The Route Optimization Mobile IP outperformed the standard Mobile IP at longer
session lengths. At session lengths less than 100kbits, ROMIP performs poorly due to the overhead

9

required for route optimization. Any session exceeding 100Kbits allows the route optimization to be
beneficial. Since most sessions are longer than 100kbits, ROMIP seems to be the most attractive solution.

Replicated servers for ip-host mobility
In [Jue98], an extension for the mobile-ip protocol is presented in terms of the use of replicated
home-agents to handle multiple request for different mobile hosts groups. Replication will provide load-
balancing and avoid the single-point of failure provided by the home-agent.

We have to recall that in the mobile-ip architecture, a foreign agent and a home agent are required
for mobility. The mobile host moves to another network where the foreign agent expect to receive a
`registration packet in order to keep track of the mobile host and make the home-agent forward the
information to the proper destination.

The approach followed here consists in the use of not one, if not several replicated home-agents,
using different techniques to access and load balance between each other. The basic mobile-ip protocol has
evolved out of the efforts of the mobile IP working group and specifies mobility support under Ipv4. The
home-agent is usually a router or host in the mobile host’s home network which maintain mobility bindings
(a permanent IP address to a temporary IP address translation) for the mobile host. Meanwhile, the foreign
agent may be a router or host in the network where the mobile host is visiting, and it provides the mobile
host with a temporary IP address. If the number of available IP addresses in the foreign network is limited,
then the foreign agent may act as a proxy server for the mobile host, in this case the temporary IP address
will belong to the foreign agent’s IP address.

The protocol proposed in [Jue98] the mobile host will have the IP addresses of all the home agents in
the home network. When the mobile hosts sends a registration request (issue of Mobile-IP protocol). It will
randomly choose one of the home agents to service the request. As defined in the mobile-IP protocol, it is
assumed that each mobile registration request has an unique identification and a lifetime which defines the
time for which the registration is valid. This time is defined by Treg. The registration packet also contains
the IP address of the mobile host, and the temporary IP address of the mobile host. As part of the mobility
binding, the agent maintains the following information:
1. The unique registration numbers
2. The permanent IP address of the mobile host
3. The temporary IP address of the mobile host
4. A boolean variable called PROXY (on or off), which indicates if the proxy is on or not. If proxy is ON,
then the home agent is acting as a proxy for the mobile host and responds with a proxy ARP reply
whenever an ARP query is received for the mobile host. If it is off, a different home agent is serving
the mobile host.

10

5. Treg which defines the time for which the registration is valid.

With multiple home agents load balancing will be achieved by allowing a home agent to transfer
control of a mobile host to another home agent based on some load balancing algorithm. The load
balancing algorithms consist of two parts: a) A transfer policy which determines when a transfer should
take place and b) a Selection policy which determines to which home agent the control should be
transferred.

In fact, [Jue98] choose different load balancing strategies, for instance for policy transfer, three
approaches were made:
• Timer-based: In this approach, each home agent maintains a timer for each mobile host that is serving.
The time value will be referred to as the stream transfer time and will be denoted as Tstt. When a home
agent acquires control of a mobile host, it starts the timer after the first packet for the mobile host is
received. When Tstt expires, a new home agent is selected, and a registration request is forwarded to a
new home agent.
• Counter-based: This approach is different, the home agent counts the number of packets forwarded to
each mobile host. When the counter reaches a specified limit, the home agent transfers the registration
of the mobile host to another home-agent. This counter is referred as Tstc
• Threshold-based: For each mobile host, the home-agent maintains a count of the number of packets in
its queue which are destined to the mobile host. When the number of packets in the queue for a given
mobile host exceeds the threshold, the home-agent forwards that mobile host’s registration to another
home agent. The threshold value will be referred as Tsth

There is not much difference between policies requires some extra overhead, in other words, re-register
the mobile host to a new home-agent and selection procedure involved. As shown here is expected to see
that the Timer-based approach will lead to switching from home-agents even though the traffic is zero. This
situation is not present in the counter based approach. The values for thresholds and timeouts were modeled
in the paper.

There is another factor in this protocol, and it is the selection of the next home-agent, three different
policies where also studied in this paper:
• Random policy: The next home-agent is selected randomly from all home agents, including the home
agent attempting the transfer.
• Round-robin policy (RR): The home agent are logically ordered and the next home agent is selected
using a simple round-robin policy

11

• Join the Shortest Queue (JSQ) policy. The home agent which has the minimum number of queued
packets is selected as the next home-agent. Similar to the random policy, the current home-agent may
also be selected as the next home-agent.

Random and RR are easier to implement, intuitively JSW will provide a better performance, but
leading to a lot of overhead.

The simulation was executed using the following assumptions:
• There are N identical home-agents
• A home-agent is modeled as a single-server queue which servers both data packets and overhead
packets
• The arrival process is modeled as a MMPP (Markov Modulated Poisson Process) with arrival rate λ
during an ON period and 0 during an off period.
• The duration of an off period is exponentially distributed and with a mean 1/σ1 seconds
• The duration of the on period is exponentially distributed and with a mean 1/σ2 seconds
• The service time of a data packet is defined by µ per second
• The service time of an overhead packet is exponentially distributed with a service rate of µ/C packets
per second, by changing C it is possible to model different overhead costs.
• The registration overhead is negligible

The analytical model was tested using non-preemptive queues and shadow-servers approximations,
having the sources or mobile hosts equally distributed and assigned to the home-agents and burst-level load
balancing, where Tstt is set to an infinite value and is used as a reference point for comparison with the
proposed load balancing scheme

All the simulative analysis lead to conclude that by providing a mechanism which allows incoming
packet streams to be transferred from one home-agent to another, the system’s performance is improved
taken as a reference a single-server. The results provided here showed that a random policy yielded to
modes load balancing gains, and the JSQ policy performs much better than the random selection.

12

ANALITICAL SIMULATION OF MOBILE NETWORKS

Mobility and performance modeling in cellular communication networks
A simply analytical model for cellular communication networks can be found in [Camar98], where the
model assumes a finite population of mobiles moving in a finite number of cells. This model tries to
evaluate the Fixed Channel Allocation (FCA) factor, as well as, user load, mobility and distribution of users
among cells. This model is suitable for the future of Pico-cellular systems.

The main assumptions of the model are:
• A finite population of users moving in a finite set of cells
• Users are indistinguishable from each other and pass from a cell to another following a probability
transition patters with the same transmission rate
• A parameter called µP, or the cell transition rate. The model assumes a FCA assignment for the channel
frequencies.

According to the results shown in [Camar98], the use of uniform channel allocation scheme is worse
than the use of a non uniform one. In fact, minimum-blocking probability is obtained with a number of
channels allocated to each cell approximately proportional to the number of users in the cell.

Network Modeling

Hexagonal cells arranged in (2R –1) rows, as shown in Figure 1 can represent an ideal network.
As shown, there are R rows of K cells and (R-1) row of (K+1) cells. The total number of cells is M=RK +
(R-1)(K+1). We assume N users circulating in the network. It is supposed that the occupation time of a user
is defined by an exponential distribution with mean 1/µP i.e. the pdf of this random variable (called TP) is:

f T p (t ) = µ P e − µ Pt

13

K-1

K
1

2

K+K+1
K+1

K+2

M-K-1
M- 2K

M-K
M-K+1

M-1

M
Figure 1. Cellular Network

As far as mobility is concerned, each cell is modeled by an infinite server to consider its
occupation time. They also have assumed a probability of transition from one cell to another, indicated by
Pij

Now it is assumed a λI, for each cell, which is the effective arrival rate of users to the cell i. Where,

λi = ∑ j λ j pij , where I=1,2,…. M, (1)
M

however this term is used in conjunction with nI is the number of users in the ith cell, and by n=(n1, n2, …. ,
nM), is the state vector for the system.
The probability of a state n can be evaluated by:

1 M
P ( n) = ∏ hi (ni ) ,(2)
G 1
hi ( n i )
now the factor can be calculated by:
ni
1 λ 
hi ( ni ) =  i 
ni !  µ P 
(3)
 

where the arrival rate is given by (1), now the normalization constant G from (2) is calculated in the paper
as:
G=g(N,M), where g(N,M) is a recursive function defined by:

g(n,m)=1, n=0; m=1…M

14

g(n,m)=hm(n), m=1; n=1…N
n
g (n, m) = ∑ hm (k ) g (n − k , m − 1) , n=1…N, m=2…M,
k =0

the marginal state probability of the Mth cell is given by:
1
P ( nM = k ) = hM (k ) g ( N − k , M − 1) (4)
G
while the average number of users is given by:
N
E[nm ] = ∑ kP(nM = k ) =
k =1

1 N
= ∑ k ⋅ hM (k ) g ( N − k , M − 1) (5)
G k =1

Using little’s formula, the true arrival rate can be easily calculated as:
E ( nM )
λM ( N ) = = E (nM ) µ P (6)
E (T p )
it can be also shown that, the Utilization of the queue M, that is cell M, are given respectively by:

g ( N , M − 1)
U M (N ) = 1− (7)
G
g ( N − 1, M )
X M (N ) = 1− (8)
G

In this case Xm which is the throughput is expected to be:

λ M ( N ) = X M ( N ) (9)

Cell modeling
In addition to the Throughput and utilization equation mentioned in the previous section,
[Camar98] points out the need to model de cells in the network and specific processes such as call blocking
and hand-off blocking. For example, when considering the service offered to the users, the possibility to
make a call, the cell can be represented by a finite population (n) in a M/M/m/m/n queue. This is a loss
system where the maximum number of contemporary calls in progress is given by the number of channels
m assigned to the cell. As a resulting equation, the steady state probabilitie is given by:

15

n γ k
 ( )
k  µ
Pk =   c , where k=0,1,….,m (10)
m n γ
∑i=0  i ( µ )
 
i

  c

And the probability that a user in a call attempt does not find a free channel is given by the probability that
all cell channels have been allocated to another users in the cell, and therefore:

 n − 1 γ m
 m ( µ )
 
PL = m   c (11)
 n − 1 γ i
∑  i ( µ )

i =0 

 c
in both equations (10) and (11), γ/µc represents the required load per user in erlangs, where γ is the average
number of call attempts in the time unit per user and 1/µc represents the average call duration.

In terms of call blocking, a state vector n=(n1, n2, …. , nM) is assumed. Then, the probability of the
jth cell (which contains nj users) a new call attempt is blocked Pbj(nj) can be obtained from PL on equation
11. Assuming only mobile-to-land and land-to-mobile calls and a perfect wired network, the blocking
probability of the entire cellular network is evaluated by a weighted mean of cells blocking probabilities,
where:
M nj
PB (n) = ∑ Pb j (n j ) (12)
j =1 N
Which if applied to the average equation for the whole system, it is obtained:
M N nj
PB = ∑ ∑ Pb j (n j ) P(n j ) (13)
j =1 n j = k j +1 N

Where kj and P(nj) represent respectively the number of channels and the probability to have nj
users in the jth cell. The index starts for nj ≤ kj because less users than channels the probability of blocking
is zero.

Now, it is also mention the way to model the hand-off blocking probability, which the probability
that a user with a call in progress; passing from one cell to another one, does not find a free channel in the
destination cell and thus the call has to be terminated. And by knowing the blocking probability it is easier
to say that:

16

N −1
Pbhj = ∑ Pb (n
n j = k j +1
j j ) P(n j ) (14)

in addition to taking into account Pb and P(n), the equation must take into consideration the probability of
transition, and the instant of transition it must consider N-1 users instead of N. The network hand-off
blocking probability PBH is obtained by the weighed sum of cell hand-off blocking probabilities where the
weights are given by the fraction of the arrival rate λaj(N) of users with a call in progress.

M λ aj ( N )
PBH = ∑ Pbhj (15)
∑i=1 λai ( N )
M
j =1

and the rate λaj(N) is given by:
M
λ aj ( N ) = ∑ X ai ( N ) pij (16)
i =1

The results coming out of the model, represent an analytical solution. According to the paper the
results provided were compared with a simulation executed in SMPL language, however no details and
comparisons are explained, however for simulation purposes several parameters where used such as:

B H H H +B
PB = PBH = PFT = PUC =
T T −H T −B T

Where B represents the blocked calls, T the new tried calls, TH the tried with Hand-off, H the
unsuccessful hand-offs. And FT stands for forced termination and UC for unsuccessful completion.

There are several assumptions from this model, first the matrix for transition probabilities between
cells, which can lead to have a non-homogeneous model in the network, but it requires son previous studies
of the cells in the model.

17

REFERENCES

[Camar98] P. Camarda, G. Shiraldi, et.al. “ Mobility and Performance Modeling in Cellular
Communication Networks”, Mobile Computing and Communication Review, Vol.1 No.
4, 1998, 25-32.

[Jue98] J. Jue, D. Ghosal “Design and Analysis of Replicated Server Architecture for Supporting
IP-Host Mobility”, Mobile Computing and Communication Review, Vol 2, No. 3, 1998,
16-23,

[Li98] Y. Li and V. Leung. “Supporting Personal Mobility for Nomadic Computing over the
Internet”, Mobile Computing and Communication Review, Vol. 1, Number 1, 1998,
22-31.

[Iera98] A. Iera, A. Fazio, et.al. “Hand-off management algorithms for urban and sub-urban
environments under realistic vehicle mobility conditions”, IEEE International Conference
on Communications v 3 1998. IEEE, Piscataway, NJ, USA,98CH36220. p 1375-1379

[Dell98] M. Dell’Abate, M. DeMarco and V. Trecordi “Performance evaluation of mobile IP
protocols in a wireless environment” IEEE International Conference on Communications
v 3 1998. IEEE, Piscataway, NJ, USA,98CH36220. p 1810-1816

[Mysore98] J. Mysore, B. Vaduvur. “Performance of transport protocols over a multicasting-based
architecture for Internet host mobility” IEEE International Conference on
Communications v 3 1998. IEEE, Piscataway, NJ, USA,98CH36220. p 1817-1823

18

Mobile Survey on Simulation for Networks

More Related Content

What's hot (20)

Similar to Mobile Survey on Simulation for Networks (20)

More from Dr. Edwin Hernandez (20)

Mobile Survey on Simulation for Networks