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Instituto Tecnol ogico y de Estudios Superiores de Monterrey Campus Monterrey Divisi on de Electr onica, Computaci on, Informaci on, y Comunicaciones Programa de Graduados MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST

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Instituto Tecnol´

gico y de Estudios Superiores de

Monterrey

Campus Monterrey Divisi´

n de Electr´
nica, Computaci´
n, Informaci´
n, y

Comunicaciones

Programa de Graduados

MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST LOADED ROUTING THESIS Presented as a partial fulfillment of the requeriments for the degree of Master of Science in Electronic Engineering Major in Telecommunications

Ing. Enrique Stevens Navarro

Monterrey, N.L. May 2002

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c Enrique Stevens Navarro, 2002

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Instituto Tecnol´

gico y de Estudios Superiores de

Monterrey

Campus Monterrey Divisi´

n de Electr´
nica, Computaci´
n, Informaci´
n, y

Comunicaciones

Programa de Graduados The members of the thesis committee recommended the acceptance of the thesis of Enrique Stevens Navarro as a partial fulfillment of the requeriments for the degree of Master of Science in: Electronic Engineering Major in Telecommunications THESIS COMMITTEE Cesar Vargas Rosales, Ph.D.

Advisor

Jos´ e Ram´

n Rodr´

ıguez Cruz, Ph.D.

Synodal

Artemio Aguilar Couti˜ no, M.Sc.

Synodal

Approved

David Garza Salazar, Ph.D.

Director of the Graduate Program

May 2002

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My work is dedicated with love To God, To Lupita, To Guillermo, To Adri´ an, To Sol.

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I am really thankful to the Ph.D. Cesar Vargas Rosales for all this two years of work together and his always professional advice, without his guidance this thesis would not be possible. I also want to thank Ph.D. Jos´ e Ram´

n Rodr´

ıguez Cruz and M.Sc. Artemio Aguilar Couti˜ no, for their feedback comments about this work. Special thanks to my uncle Ing. Hugo Stevens Amaro for all his support during my stay in Monterrey. Thanks to Ulises and Eduardo for their help in the realization of this thesis, figures design and programming advices , respectively. Also thanks to all my friends of the “6th floor” and beyond, specially to Miguel, Isabel, Oscar, Fortino, Yuri, Pepe and his family, Servando, Selene, Evelia, Vladimir, Eric, Martha, Marco, Cuitlahuac, Fernando and German. To all my “La Banda” friends because together with my brother Adri´ an we are a brotherhood, specially to Cesar, Rocio and Ale.

Enrique Stevens Navarro

Instituto Tecnol´

gico y de Estudios Superiores de Monterrey

May 2002

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MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST LOADED ROUTING

Enrique Stevens Navarro, M.Sc. Instituto Tecnol´

gico y de Estudios Superiores de Monterrey, 2002

The demand for services provided by wireless networks has been increasing during the last years, particularly cellular telephony networks. Now users expect Quality and Services similar to fixed networks (QoS). A very important key factor in the performance perceived by the user of cellular networks is the treatment of handoffs. When an active user is moving from one cell to another, and the new cell does not have a channel available, the handoff call will be blocked, which is considered to be more detrimental than the rejection of new incoming calls. Hence, the handoff blocking probability is an important performance measure of wireless networks. A previous work proposed agreements between different carriers in one coverage area to share idle resources to connect blocked users in overloaded carriers to give better service to their users. To decide to which carrier to offer the blocked call, now 3 schemes were evaluated and compared. A uniform selection between carriers, a fixed sequence of alternate carriers, both of these schemes already evaluated in previous work. And the new scheme proposed is, with a state-dependent approach, the Least Loaded Routing (LLR) Algorithm implemented to select a carrier to offer the blocked call. The LLR scheme se- lects the carrier with more free channels based on the state of the cells. The performance of the multicarrier wireless network is evaluated and the 3 schemes are compared with fixed point models, at cell level, at carrier level and also the network rate of return is presented.

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MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST LOADED ROUTING

Enrique Stevens Navarro, M.Sc. Instituto Tecnol´

gico y de Estudios Superiores de Monterrey, 2002

La demanda por servicios que prestan las redes inal´ ambricas se ha estado incrementado durante los ´ ultimos a˜ nos, particularmente las redes de telefon´ ıa celular. Ahora los usuarios esperan calidad y servicio similares a los de redes fijas. Un factor muy importante en el desempe˜ no percibido por los usuarios de redes celulares es el tratamiento de los handoffs. Cuando un usuario activo se esta moviendo de una celda a otra, y la nueva celda no cuenta con canales disponibles, la llamada en handoff ser´ a bloqueada, lo cual se considera m´ as da˜ nino que el rechazo de una llamada entrante. Por lo tanto, la probabilidad de bloqueo de un hanfoff es una medida importante del desempe˜ no de las redes inal´ ambricas. Un trabajo previo, propuso acuerdos entre diferentes operadores en una ´ area de cober- tura para compartir recursos no utilizados para conectar usuarios bloqueados en operadores con sobrecarga de trafico mejorando el servicio a sus usuarios. En el presente trabajo 3 esquemas son evaluados y comparados para decidir a cual operador ofrecer la llamada blo-

queada. En el trabajo previo fueron presentados y evaluados los esquemas de una selecci´
n

uniforme entre operadores y una secuencia fija de operadores alternos; el nuevo esquema propuesto es con un enfoque dependiente del estado de la red, el algoritmo de enrutamiento del menos cargado (LLR) es implementado para seleccionar el operador al cual ofrecer la llamada bloqueada. El esquema de enrutamiento del menos cargado (LLR) selecciona el

perador que cuenta con mas canales libres, basado en el estado de las celdas.

El desempe˜ no de la red inal´ ambrica de m´ ultiples operadores es evaluado y comparado para los tres esquemas con modelos de punto fijo, a nivel de celda, a nivel de operador y tambi´ en la tasa de retorno de la red es presentada.

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List of Figures iii List of Tables v Chapter 1 Introduction 1 1.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Justification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2 Background 5 2.1 The Cellular Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Elements of the Cellular Concept, [18], [12]. . . . . . . . . . . . . . 6 2.1.2 Frequency Reuse and Cell Splitting, [18]. . . . . . . . . . . . . . . . 7 2.1.3 Channel Assignment Strategies . . . . . . . . . . . . . . . . . . . . 9 2.1.4 Handoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.5 Multiple Access Technologies . . . . . . . . . . . . . . . . . . . . . 10 2.2 Quality of Service in Cellular Networks, [17] . . . . . . . . . . . . . . . . . 11 2.2.1 Traffic Performance at Network Level . . . . . . . . . . . . . . . . . 12 2.3 Networking Cellular Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 Application of Networks of Queues . . . . . . . . . . . . . . . . . . 13 2.4 Methodology for Performance Analysis . . . . . . . . . . . . . . . . . . . . 15 2.4.1 Erlang Fixed Point Approximation . . . . . . . . . . . . . . . . . . 15 2.4.2 Analysis of a Cellular Network with the Fixed Point Approximation 16 Chapter 3 Model Description 19 3.1 Model for a Multicarrier Cellular Network, [14] . . . . . . . . . . . . . . . . 19 3.2 Strategies for Carrier Assignment . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.1 Routing, [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 i

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ii CONTENTS 3.2.2 Circuit-Switched Routing . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3 Alternative Routing Strategies . . . . . . . . . . . . . . . . . . . . . 23 3.2.4 Adaptive Routing Strategies . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Model with State-Dependent Routing . . . . . . . . . . . . . . . . . . . . . 25 3.4 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Chapter 4 Numerical Results 33 4.1 Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Symmetric-Symmetric System Case (SSC) . . . . . . . . . . . . . . . . . . 34 4.2.1 Blocking Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2.2 Revenue Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Asymmetric-Symmetric System Case . . . . . . . . . . . . . . . . . . . . . 44 4.3.1 Blocking Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.2 Revenue Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Chapter 5 Conclusions 51 5.1 General Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Bibliography 53 Vita 55

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List of Figures

2.1 Architecture of the Wireless Network. . . . . . . . . . . . . . . . . . . . . . 6 2.2

Handoff. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 2.3 Frequency Reuse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Cluster Sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Cell Splitting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Access Technologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.7 Network of Queues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.8 Link with Capacity C and offered Poisson Traffic with mean λ. . . . . . . . 15 3.1 Birth-Death process for cell i of operator W. . . . . . . . . . . . . . . . . . 20 3.2 Handoff rate offered from adjacent cells and operators with agreement. . . 22 3.3 Sequences for alternate carrier assignment. . . . . . . . . . . . . . . . . . . 24 3.4 Birth-Death process for cell i of operator W. . . . . . . . . . . . . . . . . . 26 3.5 Sequences for LLR carrier assignment. . . . . . . . . . . . . . . . . . . . . 28 4.1 New Call Blocking Probability, Case LM. SSC. . . . . . . . . . . . . . . . . 35 4.2 Handoff Blocking Probability, Case LM, T = 2. SSC. . . . . . . . . . . . . 36 4.3 New Call Blocking Probability, Case MM. SSC. . . . . . . . . . . . . . . . 37 4.4 Handoff Blocking Probability, Case MM, T = 2. SSC. . . . . . . . . . . . . 37 4.5 Handoff Blocking Probability, Case HM, T = 2. SSC. . . . . . . . . . . . . 38 4.6 New Call Blocking Probability, Case NM. SSC. . . . . . . . . . . . . . . . 38 4.7 Carrier Blocking Probability, Case LM. SSC. . . . . . . . . . . . . . . . . . 40 4.8 Carrier Blocking Probability, Case MM. SSC. . . . . . . . . . . . . . . . . 41 4.9 Carrier Blocking Probability. Random Scheme. SSC. . . . . . . . . . . . . 41 4.10 Carrier Blocking Probability. Sequence Scheme. SSC. . . . . . . . . . . . . 42 4.11 Carrier Blocking Probability. LLR Scheme. SSC. . . . . . . . . . . . . . . 42 4.12 Carrier Blocking Probability. LLR Scheme. SSC. . . . . . . . . . . . . . . 43 4.13 Network Rate or Return. LM. SSC. . . . . . . . . . . . . . . . . . . . . . . 43 4.14 Network Rate or Return. MM. SSC. . . . . . . . . . . . . . . . . . . . . . 44 4.15 New Call Blocking Probability, Case MM. ASC. . . . . . . . . . . . . . . . 45 iii

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iv LIST OF FIGURES 4.16 Handoff Blocking Probability, Case MM, T = 2. ASC. . . . . . . . . . . . . 45 4.17 Carrier Blocking Probability, Case MM. ASC. . . . . . . . . . . . . . . . . 46 4.18 Carrier Blocking Probability. LLR Scheme. ASC. . . . . . . . . . . . . . . 47 4.19 Carrier Blocking Probability. LLR Scheme. ASC. . . . . . . . . . . . . . . 48 4.20 Network Rate or Return. MM. ASC. . . . . . . . . . . . . . . . . . . . . . 48 4.21 Network Rate of Return, Case LM, MM and HM. ASC. . . . . . . . . . . . 49

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List of Tables

4.1 Parameters for the SSC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2 Parameters for the mobility cases. . . . . . . . . . . . . . . . . . . . . . . . 35 4.3 Blocking probabilities for cell i in carriers I and III with LM. . . . . . . . 39 4.4 Blocking probabilities for cell i in carriers I and III with MM. . . . . . . . 39 4.5 Blocking probabilities for cell i in carriers I and III with HM. . . . . . . . 40 4.6 Parameters for the ASC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.7 Blocking Probabilities for cell i on Carrier I. . . . . . . . . . . . . . . . . . 47 v

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vi LIST OF TABLES

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Chapter 1

Introduction

During the last years the growth and development of the telecommunications networks have been incredible. Each day is more important to be “on line” or stay in contact with the world all the time and in any place. Being “on line” or reachable let us make important decisions or exchange information in any moment of the day [16]. Because all of this, wireless networks growth faster than ever and always increase their coverage, services and the quality of them. With the evolution and development of wireless networks, mainly lead by the market and the telecommunications companies, some specific issues have been generated. Issues like: mobility of the users, interference, capacity of the system and bandwidth, have become very familiar parameters in the design and evaluation of wireless networks. And maybe the more important issue in the wireless communications is the spectrum available for the

service. Due to political and regulatory affairs this is a very scarce resource therefore many

research is being done in an efficient use of it. A specific and inherent issue of wireless networks is the mobility of the user generating the so called handoffs between different geographic areas (cells) within a wireless network. A handoff occur when an user is active and moving from one cell to another, so the call have to be “handed off”. But if the new cell does not have a channel available, the handoff call will be blocked and therefore lost. The lost of a call generate a customer indignation bigger than the rejection of a new incoming call. Hence, handoff blocking probability and new call blocking probability become very important performance parameters in wireless networks. So today is very important to measure and improve the performance of the wireless networks already deployed. In the present work wireless networks means basically telephony wireless networks. And this networks, also known as cellular telephony networks, are growing due to a increase in the demand of this kind of service by many customers. All this lead us to look for efficient ways to use the resources. One way to evaluate the performance

f a network is with the use of mathematical models who describe the behavior of the

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2 CHAPTER 1. INTRODUCTION network.

1.1 Previous Work

With the growth on demand of services provided by wireless networks the market is also growing too. In every region within the country new operators or carriers are joining the competitive telecommunications market to offer new services and hopefully better quality

f service. Due to this, we can assume that in one coverage region co-exist some carriers

each one with its own wireless network and providing this kind of services. A previous work [14], [15], proposed agreements between the carriers to share resources to improve the service in the treatment of handoffs. The agreements consider the case when a user needs service and this cannot be provided by the subscribing company. In this case the user has to experience a hard handoff since the carrier frequencies will be

changed. Hence, there will be inter-cell handoffs (same carrier), inter-carrier handoffs (to
ther carrier) and new call arrivals to each cell of the network for each carrier. To treat

the handoffs, each cell of the carrier could give priority to handoffs over new calls or treats them equally. Based on that, the number of users in the system represents the revenue for the operator, then if they have some channels reserved for handoffs and have those channels idle they could take advantage of this and use them, by sharing those resources with the

ther carriers. But at this point exist a trade off between the users in the system and the

blocking probability (revenue vs quality), because the blocking probability increase when there are more users in the system. As shown in [14], if a carrier has a significant increase in its handoff rate, there are

thers carriers that can give attention to those users from the overloaded carrier, then their

blocking probability will increase, with this, the overloaded carrier will decrease its blocking probability thanks to the increase in the number of users in the other systems. But all the carriers will have a revenue from the users that were going to be blocked in the overloaded carrier and now are going to be connected in other carrier, and those users are going to pay for this connection. The carrier assignment methods in [14], [15], were independent of the state of occupancy of the network, that was, the arrival and departure rates to and from the cells do not depend on the number of users in the cell, hence all decisions are based on the blocking state of the cell. The allocation of the resources presented some methods based in a selection of the carrier: a fixed sequence of alternate carriers, a uniform probability selection of carrier and a modified case of the last one. These methods improve the performance of the “multicarrier system” but it could be better with a state dependent assignment method as mentioned at the end of that work.

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1.2. OBJECTIVE 3 In the eventual case of a state dependent method in the assignment of the carrier to handoff, the system must take a decision on to whom send the call or “route” the call based

n the state of the network, that is, the number of users in the system in that moment.

The state dependent method proposed for this work is the Least Loaded Routing (LLR) algorithm [4].

1.2 Objective

The objective of this thesis is to obtain an analytical model for the performance of the multicarrier wireless system by implementing the LLR state dependent strategy to choose an alternate carrier.

1.3 Justification

Lately, telecommunications companies start implementing state dependent schemes in circuit-switched networks by making use of common channel signaling and stored program control [1], [6], [10], [22]. In these schemes, routing decisions are based on the current number of idle circuits in each link throughout the networks. We can extend this to wireless networks with the assumption of idle circuits like radio channels and link to cells. In the scheme Least Loaded Routing (LLR) [4], if the call cannot be set up along the direct route, the two link alternate route with the largest number of free circuits is chosen. Again if the user handed off cannot be connected with a channel of his carrier the scheme must select the carrier with the largest number of free channels available. A version of LLR has been implemented in ATT’s long distance network [1], [2]. Due to the growth of demand of wireless network services, the evolution and search

f efficient use of the resources of the wireless networks already deployed, we attack the

necessity of evaluate the performance of the multicarrier system with state dependent methods.

1.4 Contributions

In this thesis, the multicarrier system fixed point model, [14], is extended to cover a state- dependent strategy to choose an alternate carrier. A model based on the generalized Erlang Fixed Point approximation for state-dependent routing is implemented, evaluated and compared. The routing algorithm proposed is the Least Loaded Routing, examined in [4]. The performance of LLR strategy is compared with the random uniform and sequential strategy.

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4 CHAPTER 1. INTRODUCTION

1.5 Organization

The organization of the present work is as follows. Chapter 2 includes all the technical background of wireless networks, specifically cellular networks, handoff and access tech-

nologies. Also includes a brief introduction of network concepts, shows important results

and techniques for performance evaluation of the network like the Erlang Fixed Point Ap-

proximation. Chapter 3 presents the notation, the original analytical model and the new

model with further modifications to cover the LLR strategy in the election of operator, also the fixed point equations and performance measures are determined. In Chapter 4, numerical results are presented and discussed. And finally Chapter 5 contain the conclusions

f this work.

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Chapter 2

Background

Radio communication can trace its origin to the discovery of electromagnetic waves by Hertz in 1888 and therefore the subsequent demonstration of transatlantic radio telegraphy by Marconi in 1901 all this 100 years ago. Mobile radio systems using simplex channels (push-to-talk) were introduced in the 1920´s for police and emergency services. The first public mobile radio system in the United States of America was introduced in 1946 and can perhaps be considered the born of the public communications mobile services era. The development of the cellular concept [13], in the 1970´s by the Bell Laboratories was a defining event which has played a significant part in the evolution of mobile communication systems and wireless networks as we know them today [16].

2.1 The Cellular Concept

The Cellular Concept, [13], [18], appear as the solution to increase the number of users in radio communication systems. It replaces a single high-powered antenna mounted on a tall building given coverage to all the region with just one big cell with a set of organized lower antennas covering the service area with smaller cells [18]. A cellular system is generally characterized as a high capacity land mobile system in which available frequency spectrum is partitioned into discrete channels which are assigned in groups to geographic cells covering a service area. The discrete channels are capable of being reused in different cells within the service area. The cellular networks has generated some well defined design objectives that has to be accomplished based on the interest of the users and services providers. The objectives are:

Large system capacity.
Efficient use of the spectrum available.

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6 CHAPTER 2. BACKGROUND

Include portable and mobile units.
Widespread compatibility.
Widespread availability.
Adaptive to traffic density.
Affordability.

2.1.1 Elements of the Cellular Concept, [18], [12].

The architecture of a cellular network is defined as follows: the coverage area is partitioned into a number of smaller areas or cells with each cell served by a base station (BS) for radio coverage. The base stations are connected through fixed links (ie: fiber, microwave

r copper) to a mobile switching center (MSC), which is a local switching exchange office

with additional special features to handle mobility management requirements of a cellular

system. See Figure 2.1. Some of this special functions are call handling and processing,

billing and eventually fraud detection. To handle the dynamic nature of users location information and subscription data, the MSC interacts with some form of database that maintains subscriber data and location information. Those databases are called Home Lo- cation Register (HLR) and Visiting Location Register (VLR). The MSC is interconnected by land-line trunks lines with the PSTN and a tandem switch. The MSC is also connected with other MSC for exchange of information, validation and calling information. Figure 2.1: Architecture of the Wireless Network. Although the cells have irregular shapes due to the terrain, the constructions and the propagations conditions in the service area, its customary to represent them with hexagons. See Figure 2.2. This provide us with a systematic form to grow up the network.

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2.1. THE CELLULAR CONCEPT 7 The definition of boundaries between cells generate the problem of a handoff, which is the event of crossing a boundary cell when a user is already having a conversation through that BS and the query for service from the new BS of adjacent cell to which the user is moving to. See Figure 2.2. This event is performed between BSs with the management support of the MSC. Figure 2.2: Handoff. The communication between user and carrier is done through the establishment of two links, the forward channel and the reverse channel. The forward channel is the link from BS to user, and the reverse channel is the link from user to BS. The features of the cellular concept are based on two essential aspects: Frequency Reuse and cell splitting.

2.1.2 Frequency Reuse and Cell Splitting, [18].

Each BS in the network is allocated a group of radio channels to be used within the

cell. BS in adjacent cells are assigned a set of channels which contain completely different

channels than neighboring cells, this allow the carrier to “reuse” its frequency available for the service. The reuse of frequency is the same concept used by the AM/FM radio broadcast stations where the same frequency band can be used in distant cities as long as their signal satisfies the co-channel interference criterion. The frequency reuse can be seen in Figure 2.3, where a geographic area is divided into

cells. The carrier divide its frequency spectrum in sets of discrete channels named A,B and
C. The reuse of set A can be seen in Figure 2.3. Each cell has its owns antenna to provide

the service and an increase in the number of users than can be served with the frequency

f the carrier is shown. Because the total number of possible simultaneous connections has

been increased.

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8 CHAPTER 2. BACKGROUND Figure 2.3: Frequency Reuse. The cells are grouped into clusters. The clusters size follows the hexagon geometry grouping [18], that mean only some cluster sizes are allowed. Some typically sizes of cluster are N = 3, 4, 7, 12. See Figure 2.4. Figure 2.4: Cluster Sizes. The frequency reuse factor of a cellular system is 1/N, and represents the proportion

f the total number of available channels in the system that are assigned to each cell in a

cluster. Once we have applied the cellular concept to build a wireless network, there might be situations where the capacity in one of the cells is reached due to the increasing demand. In this particular case we can apply the cellular concept again, but at the cell level. The use of cell splitting will allow us to increase the capacity of that cell by subdividing the frequency band assigned to it and applying frequency reuse within that cell. See Figure 2.5.

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2.1. THE CELLULAR CONCEPT 9 Figure 2.5: Cell Splitting.

2.1.3 Channel Assignment Strategies

There are two main methods of channel allocation, and can be classified into Fixed and Dynamic.

1. Fixed Channel Assignment (FCA): each cell is allocated a predetermined set of
channels. If all the channels in that cell are busy, the call es blocked and the user

does not receive service.

2. Dynamic Channel Assignment (DCA): channels are not allocated to a cell per-
manently. Each time a user request service, the serving BS request a channel from

the MSC.

2.1.4 Handoffs

As mentioned earlier, when a mobile user is engaged in a conversation, the mobile station (MS) is connected to a BS via a radio link. If the mobile user moves to the coverage area

f other BS, the radio link to the old BS is eventually disconnected, and a radio link to

the new BS should be established to continue the conversation. This process is variously referred to as automatic link transfer, handover, or commonly handoff. See Figure 2.2. In Analog Cellular Systems or First Generation (1G), the surrounding BSs measure the signal from the MS, and the network initiates the handoff process when some handoff criteria are met. The process is named network-controlled handoff (NCHO). In Digital Cellular Systems or Second Generation (2G), the network ask the MS to measure the signal from the surrounding BSs. The network makes the handoff decision based on reports from the MS. The process is named mobile-assisted handoff (MAHO). With the advance in technology, now there are two types of handoffs, hard and soft. The hard handoff follows the rule break before make process where the voice channel from the new BS is not assigned until the mobile breaks the communication with the old BS.

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10 CHAPTER 2. BACKGROUND The soft handoff follows the rule make before break process, when the mobile can have two voice channels at the same time and after the handoff criteria is achieved, it breaks the communication with the old BS. A related issue with the handoff process is Roaming. The process of Roaming occur when a mobile user moves from one Cellular System or region to another (e.g., the system

f Monterrey to the system of Guadalajara), the system should be informed of the current

location of the user. Otherwise, it would be impossible to deliver the services to the mobile

user. In current systems this process usually is achieved automatically within the country.

One of the main goals of the so called Third Generation (3G) is to allow international roaming to the user among other things [12].

2.1.5 Multiple Access Technologies

Its customary in each country to allocate a fixed amount of frequency spectrum to cellular systems regulated by the respective national agency (e.g. FCC in the United States and COFETEL in Mexico). Multiple-access techniques are then deployed so that many users can share the available spectrum in an efficient manner. Multiple-access systems specify how signals from different sources can be combined efficiently for transmission over a given radio frequency band and then separated at the destination without mutual interference. The 3 basic multiple access methods currently in use in cellular systems are:

Frequency Division Multiple Access (FDMA).
Time Division Multiple Access (TDMA).
Code Division Multiple Access (CDMA).

To understand the basic principle for each of these multiple-access methods see Figure 2.6 In the case of FDMA,users in the system share the frequency spectrum, and a user is allocated a part of the frequency band called the voice channel. The user´s signal power is concentrated in this relatively narrow band in the frequency domain, and different users are assigned different voice (frequency) channels based on demand. Interference from adjacent channels is limited by the use of guard bands and bandpass filters that maintain separation

f signals associated with different users. The Analog Systems or First Generation (1G)

all use FDMA techniques. In TDMA systems, the available spectrum is partitioned into narrow frequency bands

r channels (as in FDMA), which in turn are divided into a number of time slots. An

individual user is assigned a time slot that allows access to the frequency channel for the duration of the time slot. Thus, the voice channel in case of TDMA consist of a time slot

SLIDE 31

2.2. QUALITY OF SERVICE IN CELLULAR NETWORKS, [?] 11 Figure 2.6: Access Technologies. in a periodic train of time slots that make up a frame. TDMA techniques are utilized in many digital cellular systems or Second Generation (2G) The CDMA systems utilizes the spread spectrum technique, where a spreading code (called a pseudo-random noise or PN code) is used to allow multiple users to share a block of frequency spectrum. In CDMA cellular systems that use direct sequence spread spectrum techniques, the digital information from an user is modulated by means of the unique PN code assigned to each user. All the PN-code-modulated signals from different users are then transmitted over the entire CDMA frequency channel. At the receiving end, the desired signal is recovered by despreading the signal with a copy of the PN code for the individual

user. All the other signals whose PN codes do not match that of the desired signal, are

not despread are perceived as noise. Since the signals in the case of CDMA use the entire block of spectrum, no guard bands are necessary within the allocated block.

2.2 Quality of Service in Cellular Networks, [17]

With the increasing demand and penetration of services provided by cellular networks, the emerging innovations in radio technology, and the evolution of the market, users of wireless networks now expect Quality of Service (QoS) and performance comparable to what is available from fixed networks.

SLIDE 32

12 CHAPTER 2. BACKGROUND The QoS in wireless networks is influenced by a number of factors that are inherent to the use of radio access and support of terminal mobility. Some of the key factors are:

Available frequency spectrum: scarce and expensive resource allocated by regulatory

agencies.

Multiplexing and channel assignment methods: tradeoff between system design and

management to increase capacity.

Speech encoding and decoding techniques: main goal is to transmit speech with the

highest possible quality using the least possible channel capacity.

Network and signaling architecture for mobility management: maintain subscriber

data, location information and detect fraudulent users.

Handoff requirements: the process must be successful and transparent to the user.
Authentication and privacy requirements: allow mobility of users between systems

and avoid subscribing frauds. Standards that address performance QoS for wireless communication networks and network elements are now emerging in such international, regional and national standards forums as the International Telecommunications Union (ITU) or the Telecommunications Industry Association (TIA).

2.2.1 Traffic Performance at Network Level

The network-level performance address performance parameters that relate to end-to-end performance, which may directly influence the quality of service perceived by the final user. Current cellular network standards primarily focus on traffic and transmission performance. The following traffic performance parameters have been specified by the ITU-T for public land mobile networks [7]:

Post Selection Delay: time interval from the instant of the initial setup message to

access the signaling network is sent until the message indicating call disposition has been received.

Answer Signal Delay: time interval from the instant at which the called MS passes

the connect message to its access signaling network until the connect message has been received by the calling MS.

SLIDE 33

2.3. NETWORKING CELLULAR CONCEPTS 13

Call Release Delay: time interval from the instant the disconnect message is passed,

by the MS that terminated the call to the access signaling network, until receipt of the release message by the same terminal and hence initiate or receive a new call.

Probability of Handoff Blocking: probability that a handoff attempt will fail, either

because of lack of resources in the cell or because necessary network resources for establishing the new connection were lacking .

Probability of End-to-End Blocking: probability that a call originated-terminated

from any MS will be blocked because lack of necessary resources. where end-to-end blocking is an aggregate representation of blocking on radio links, blocking on BS to MSC links and blocking on the fixed network.

2.3 Networking Cellular Concepts

In this section we will define some notation and concepts related to Queuing Theory and Networks of Queues [3] that will be required along the present work because is related to the networking of wireless communications systems.

2.3.1 Application of Networks of Queues

Using Queuing Theory many networks can be modelled by a set of queues where users arrive with a certain rate and leave the network with another rate. When there is only

ne server and users arrive to request service according to a Poisson Process, and the

probability distribution of the service time is exponential, by Kendall notation, we will refer to an M/M/1 system. When we have many M/M/1 systems interconnected between them as shown in Figure 2.7, they cannot be modelled now as M/M/1. The reason is that the interarrival times at the queues are strongly correlated with the arrival rates. It turns out that if somehow this correlation were eliminated and randomization were used to divide traffic among different routes, then the average arrival rate in the system can be derived as if each queue in the network was an M/M/1. This important result is known as Jackson´s Theorem [3]. Consider K single server queues in which customers arrive from outside the network at each queue i in accordance with independent Poisson processes at rate ri. Once a customer is served at queue i, it proceeds to join each queue j with probability qij or to exit the network with probability 1 −

j=1 qij. The total customer arrival rate at queue j, denoted

λj satisfies:

SLIDE 34

14 CHAPTER 2. BACKGROUND Figure 2.7: Network of Queues. λj = rj +

λiqij, j = 1, 2, ....K. (2.1) These equations represent a system of linear equations in which the total rates λj, j = 1, 2....K, constitute a set of K unknowns. We assume that they can be solved uniquely to yield λj, j = 1, 2....K in terms of rj, qij, i, j = 1, 2....K. It can be shown that uniqueness is guaranteed under very general assumptions. Jackson´s Theorem states that the number of customers in the queues at a time t, for different queues is an independent random variable. Also states that the steady state probabilities of the individual queues are those of an M/M/ck system. This is an amazing result because in general the input process to a queue within the network is not Poisson as demonstrated at the beginning of this section. In the particular case of our study of wireless networks with cells, we can model the arrival rate of each cell i by considering the external arrival and the handoffs from adjacent cells that moves into cell i with certain probability. But cells in the cellular systems have a finite number of channels, so if no channel is available in the cell, arriving users will be

blocked. Due to this, each cell cannot be modelled by an M/M/1 system but a better

approach is obtained with an M/M/C/C system. In cellular communication systems, there are calls that are initiated in a particular cell, say cell i, these calls are considered New Calls and the total number of new calls

ffered to cell i per time unit it the New Call Arrival Rate of cell i, λi.

Since cells have adjacent cells, users that have a call in progress can move and cross a cell boundary producing a handoff event. In this case the user call in progress is offered to an adjacent cell and is considered to be a Handoff Call. The total number of handoffs

SLIDE 35

2.4. METHODOLOGY FOR PERFORMANCE ANALYSIS 15 calls offered to cell i per time unit is the Handoff Call Arrival Rate of cell i, νi. The proportion of new calls that are rejected and blocked in cell i is denoted as Bi, and the proportion of handoffs calls that are blocked in cell i is denoted as Bhi. The arrival process of new calls will be determined by a Poisson process with mean λi for cell i. The dwell time of cell i is the time that an user stays within cell i as an active user, and it can be finished by a call drop, a hang up or a handoff to an adjacent cell, and it is considered as an exponential random variable with mean 1/µi for cell i.

2.4 Methodology for Performance Analysis

There are many different performance evaluation algorithms, most of which are based on Markov Process to describe qualitatively the schemes.

2.4.1 Erlang Fixed Point Approximation

This method is the most used to compute the blocking probability of a link in telecommunications networks. The approximation was first applied to the problem of finding the proportion of blocked calls in a link with finite capacity. Figure 2.8: Link with Capacity C and offered Poisson Traffic with mean λ. Assume a link with capacity C < ∞ is offered Poisson traffic with arrival rate λ. See Figure 2.8. A call will be blocked and lost if all C circuits are busy, otherwise the call is accepted and occupies one circuit for its holding time which is exponentially distributed with mean 1/µ and independent of other holding times and earlier arrivals. Defining ρ = λ/µ the Erlang´s B formula is:

SLIDE 36

16 CHAPTER 2. BACKGROUND E(ρ, C) = (ρ)C C!

(ρ)n n!

−1

. (2.2) Erlang´s B formula gives the proportion of calls that are lost in the link. Also the stationary probability that all C circuits are busy.

2.4.2 Analysis of a Cellular Network with the Fixed Point Ap- proximation

Consider a cell in a cellular network, where the channels are numbered 1, 2, ...C and being C the capacity of the cell. Calls arrive following a Poisson process with mean λ requesting service, consider no mobility between adjacent cells, i.e. no handoffs. A call will be blocked and lost if there is no free channel in the cell. Assume that call holding times are exponentially distributed with unit mean (µ = 1). Define the state of a cell as n, where n is the number of calls present on that cell, then the stationary distribution for this process is the same as that of an M/M/C/C system, and it is given by: π(n) = (λ)n n!

(λ)i i!

−1

, n = 0, 1, ...., C. (2.3) Define the offered traffic to a cell as ρ, in this case ρ = λ, and the total carried traffic to a cell as η, given by: η = (1 − B)λ, (2.4) where B is the blocking probability of the cell, and is defined as the probability that all C channels are busy. The blocking probability can be defined by Equation (2.2) as follows: B = E(ρ, C). (2.5) Now to extend the model of the network to include mobility between cells, there is a new arrival rate to each cell caused by handoffs. This new arrival rate is independent of the new call arrival rate, and is a Poisson process with mean ν. Hence the offered traffic to cell i is given by: ρi = λi +

νji,

(2.6)

SLIDE 37

2.4. METHODOLOGY FOR PERFORMANCE ANALYSIS 17 then νji is the amount of traffic out of cell j that goes into cell i; and it depends on its acceptance or blocking probability in cell j, and similarly for all the cells in the network. Then the offered traffic, ρ, depends on the blocking probabilities and new call arrival rates of other cells. Equation (2.5) and Equation (2.6) define a set of fixed point equations for the blocking probability: B = E(ρ(B), C). (2.7) The equations define a mapping from [0, 1] to [0, 1] and so, by the Brouwer fixed point theorem [20], a fixed point exist. In practice, the blocking values can be found iteratively by choosing an initial value for the blocking an then, using fixed point iteration of Equation (2.7).

SLIDE 38

18 CHAPTER 2. BACKGROUND

SLIDE 39

Chapter 3

Model Description

This chapter introduces the description of the original multicarrier network model used in [14]. The notation is defined together with the mathematical equations derived from the network for random and sequential strategies. Also a model with state dependent routing named (LLR) to optimize the network performance is presented. At the end, performance measures for both models are defined.

3.1 Model for a Multicarrier Cellular Network, [14]

This section contains the explanation of the network, the arrival process and call charac-

teristics. The particular notation for the model is also presented.

Let M be the set of service providers, each one with only one carrier to serve a wireless network and coexisting. So their networks coincide in the number and position of

cells. Let M be the total number of carriers, i.e., M = M, where the operator •

is the cardinality of a set. Each cell in the networks has a fixed number of channels. The service providers will be also referred as operators. Let N W be the set of cells of operator W and N W = N W be the total number of cells of operator W. Each cell i of operator W has CW

channels assigned to it. Let AW be the set of cells adjacent to cell i of operator

W. Let GW be the set of alternate operators and GW = GW be the total number of

alternate operators to which operator W can send handoffs when they are blocked in its

wn network due to fully occupancy of the cell to which is moving into.

The new call arrival process to cell i of operator W is a Poisson Process with mean λW

independent of other new call arrival processes. The dwell time of cell i is an exponential random variable with mean 1/µW

and independent of earlier arrival times, call duration and elapsed times of other users. At the end of a dwell time a call may undergo one of the three events: attempt a handoff to an adjacent cell, leave the network or stay using the channel assigned for other period of time. As mentioned, there are three possible events once the dwell time has expired. Each 19

SLIDE 40

20 CHAPTER 3. MODEL DESCRIPTION

f these events has a probability. Define qW

ij as the probability that a new call in progress in

cell i of operator W after completing its dwell time goes to cell j within the same operator. qW

ii , as the probability that a user stays using the same channel within cell i of the same

perator W after completing the dwell time of cell i.

And qW

iT as the probability of a

departure from the network from cell i from operator W. The sum of these probabilities must add to one, that is qW

iT + qW ii +

j∈AW

ij = 1.

(3.1) Cell i of operator W has a reservation parameter T W

i . The reservation parameter is

policy intended to give priority to handoff calls with respect to new calls as follows. Let n be the number of calls present in cell i of operator W. When n < CW

− T W

the cell will accept new and handoff calls, otherwise only handoff calls are accepted. Let us consider that the occupancy of a cell evolves according to a birth-death process independent of other cells. The offered traffic to cell i of operator W is ρW

i for the unreserved

states, i.e, states n such that n < CW

− T W

i , and αW i

for the reserved states, i.e., states n such that n ≥ CW

i . The departure rates when cell i of operator W are in state n is nµW i .

The birth-death process for cell i of operator W can be seen in Figure 3.1. Figure 3.1: Birth-Death process for cell i of operator W. Using the balance equations of the process, we can obtain the stationary probability that cell i of operator W is in state n defined as P W

i (n), as follows

P W

i (n) =

(ρW

i )n

n!(µW

i (1 − qW ii ))nP W i (0),

n ≤ CW

− T W

i ,

(3.2) P W

i (n) = (ρW i )CW

i −T W i (αW

i )n−CW

i +T W i

n!(µW

i (1 − qW ii ))n

P W

i (0),

> n > CW

− T W

i ,

(3.3)

SLIDE 41

3.1. MODEL FOR A MULTICARRIER CELLULAR NETWORK, [?] 21 P W

i (0) =

    

i −T W i

1 n!

µW

i (1 − qW ii )

n=CW

i −T W i

(ρW

i )CW

i −T W i (αW

i )n−CW

i +T W i

n!(µW

i (1 − qW ii ))n

    

−1

, (3.4) where the stationary distribution for the states of cell i of operator W must satisfy

P W

i (n) = 1.

(3.5) Now, define νW

ji as the handoff rate of cell j of operator W offered to cell i of operator

W, for adjacent cells i and j. The handoff traffic that can be offered from a neighboring cell j to an adjacent cell i both of operator W depends on the new calls accepted in cell j

f operator W that go to cell i

λW

j (1 − BW j )qW ji .

(3.6) The handoff calls accepted in cell j of operator W that go into adjacent cell i of

perator W are obtained as follows
k∈AW

νW

kj (1 − BW hj )qW ji ,

(3.7) and the handoff calls from operator Z = W that are offered to cell j of operator W with probability SZ

jW and accepted, and go into cell i of operator W are given as

Z∈GW
x∈AZ

νZ

xjSZ jW(1 − BW hj )qW ji .

(3.8) Thus with Equations (3.6), (3.7) and (3.8), the total handoff rate out of cell j offered to cell i of operator W is given by νW

ji = λW j (1 − BW j )qW ji +

k∈AW

νW

kj (1 − BW hj )qW ji +

Z∈GW
x∈AZ

νZ

xjSZ jW(1 − BW hj )qW ji .

(3.9) To have a better understanding of the terms involved in Equation (3.9) see Figure 3.2, where only cells adjacent to cell i and operators with agreements are shown.

SLIDE 42

22 CHAPTER 3. MODEL DESCRIPTION Figure 3.2: Handoff rate offered from adjacent cells and operators with agreement. The set of linear simultaneous equations defined by Equation (3.9), in νW

ji , ∀j, ∀i and

∀W can be solved to find the handoff rate into each cell of each operator. The solution of Equation (3.9) and the new call arrival rates, λW

i , will be used to

calculate the total offered traffic to every cell within the multicarrier system. When the occupancy of cell i of operator W is in the unreserved states the total traffic offered is ρW

i , and for the reserved states is αW i , as shown in the birth-death process

in Figure 3.1. These offered traffics are given by ρW

= λW

i +

j∈AW

νW

ji +

Z∈GW
x∈AZ

νZ

xiSZ iW,

n ≤ CW

− T W

i ,

(3.10) αW

j∈AW

νW

ji +

Z∈GW
x∈AZ

νZ

xiSZ iW,

n > CW

− T W

i .

(3.11) In [8], [21], it is shown that the Equations (3.9), (3.10) and (3.11) have a unique solution νW

ji , ρW i

and αW

for given values of blocking probabilities and reservation parameters.

3.2 Strategies for Carrier Assignment

When an active user need a handoff and is going to be blocked due to the lack of available channels in the cell, this call could be allocated with another operator, which the operator

SLIDE 43

3.2. STRATEGIES FOR CARRIER ASSIGNMENT 23

riginator has an agreement with to carry the calls. This could be seen as routing overflow

traffic on alternate routes in circuit-switched networks.

3.2.1 Routing, [19]

The main goal of routing in communication networks is to direct and re-direct if required user traffic from source to destination according to service requirements and the network’s service restrictions. Objectives include maximizing network performance while minimizing the implied cost of the network itself. Restrictions are imposed by the technology and dynamics of the switching network, user traffic and services provided by the operator.

3.2.2 Circuit-Switched Routing

The routing methods for circuit-switched networks can be grouped in three classes:

1. Fixed Routing: The call acceptance is made using defined (fixed) paths, ignoring

the previous and the current conditions of the network, do not change under any circumstance.

2. Alternative Routing: Centralized method where the routes are selected using a

set of fixed paths between two nodes. The routing decisions are made in a centralized way depending on some network conditions. The set of paths is ordered in a sequence

f potential choices.
3. Adaptive Routing: Identifies the best path and routes the traffic around the net-

work, also reduces cost by efficiently using network bandwidth and resources while eliminating needless management of static routes. The choice of the path is based

n a value placed on each path, usually obtained from observations of some of the

network components.

3.2.3 Alternative Routing Strategies

As mentioned in Chapter 1, [14], [15], attacked the problem of choosing operator with basic schemes. The schemes presented and evaluated were: a fixed sequence of alternate

perators, a uniform probability selection within the set of operators and a modified version
f the last one.

Sequential Scheme Each operator considers a sequence of alternate operators as shown in Figure 3.3 for a system with 5 operators.

SLIDE 44

24 CHAPTER 3. MODEL DESCRIPTION Figure 3.3: Sequences for alternate carrier assignment. Let us consider a call in progress in cell i of operator Z. Suppose that user moves into cell j of operator Z, where j ∈ AZ

i and this cell cannot accept the call because all

its channels are busy, then the call is offered to operator Z + 1, the first operator in the sequence of operator Z. If cell j of operator Z + 1 has free channels then the call will be accepted, otherwise the call will be blocked and will be offered to cell j of operator Z + 2, the second operator in the sequence of operator Z and so on. The call will be completely blocked in the the system when the end of the sequence is reached and no operator accepts the call. The sequential strategy defines the probability with which an operator will be chosen in case a blocked call in another operator needs to be offered to a sequence. Considering the situation described above, the probability of offering a handoff call from cell i to cell j in operator Z to the first in its sequence is SZ

j(Z+1) = BZ hj, the probability that the call

will be offered to the second operator in the sequence because the original operator and the first one in the sequence have blocked it, is SZ

j(Z+2) = BZ hjBZ+1 hj

and so on until the end

f the sequence is reached which is

j(Z−1) = BZ hj

X∈GZ/(Z−1)

hj.

(3.12)

SLIDE 45

3.3. MODEL WITH STATE-DEPENDENT ROUTING 25 Random Assignment In this scheme of selection, when operator Z needs to offer a handoff call to another operator, this is chosen with a uniform distribution. Operator Z can choose among operators to offer a handoff call already blocked in Z, to each operator, the call will be offered with probability 1/GZ. The probability of a call from operator Z being offered to cell j of operator W when GZ operators have agreement with operator Z is SZ

iW = BZ hi

GZ . (3.13) If the call is being offered to another operator, which has been chosen randomly, and is blocked due to full occupancy of the channels, then the call will be blocked from the system.

3.2.4 Adaptive Routing Strategies

The state-dependent routing algorithm suggested in the present work is the Least Load Routing (LLR) [4]. This because has been probed to be significantly more accurate than other approximation schemes like Dynamic Call Routing (DCR) [5], or other state- dependent schemes [11]. In circuit-switched networks, the LLR algorithm tries to route new calls over the less

ccupied portions of the network. If the call can not be setup over the direct route, the

two-link alternative route with the largest point-to-point free circuits is chosen. If none of the alternative routes is origin-destiny permissible, the call is blocked. For the particular case of the multicarrier system, where a decision to select an operator to accept the handoff call has to be took, the LLR algorithm will chose the operator with more free channels. The fixed point model of multicarrier system [14] have to be modified to allow us a state-dependent evaluation with Least Loaded Routing. To do so, the Erlang Fixed Point Approximation for State-Dependent Routing [9], [4], have to be used.

3.3 Model with State-Dependent Routing

Using the notation defined before for the multicarrier system we now consider that the free

ccupancy of a cell evolves according to a birth-death process independent of other cells.

The arrival process to each cell and the dwell time of a call remains the same as defined in Section 3.1. Let n be the number of free channels present in cell i of operator W and T W

SLIDE 46

26 CHAPTER 3. MODEL DESCRIPTION the reservation parameter of that cell. The reservation policy is the same where handoff calls have higher priority with respect of new calls. When n > T, the cell accepts new calls and handoff calls, otherwise only handoff calls are accepted. The process evolves according to a birth-death process with birth rate (CW

i −n)µW i (1−

ii ) in cell i of operator W in state n and death rate αW i (n). The birth-death process for

cell i of operator W can be seen in Figure 3.4. Figure 3.4: Birth-Death process for cell i of operator W. As mentioned, there are three possible events once the dwell time has expired. Each

f these events has a probability and are defined in Section 3.1.

Using the balance equations of the process, we can obtain the stationary probability that cell i of operator W is in state n defined as QW

i (n), as follows

i (n) = [µW i (1 − qW ii )]n n

− m + 1 αW

i (m)

i (0),

n = 1, 2, 3, ...CW

i ,

(3.14) where we have for n = 0 QW

i (0) =

  1 +

[µW

i (1 − qW ii )]n n

− m + 1 αW

i (m)

  

−1

, (3.15) where the stationary distribution for the states of cell i of operator W must satisfy

i (n) = 1.

(3.16) In Equations (3.14) and (3.15), αW

i (n) is the traffic offered to cell i of operator W in

state n and is defined as

SLIDE 47

3.3. MODEL WITH STATE-DEPENDENT ROUTING 27 αW

i (n) =

              

0, n = 0;

j∈AW

νW

ji +

Z∈GW
x∈AW

ψZ

xiW(n),

0 < n ≤ T W

i ;

λW

i +

j∈AW

νW

ji +

Z∈GW
x∈AW

ψZ

xiW(n),

T W

< n ≤ CW

i ;

where ψZ

xiW(n), are the handoffs blocked in cell x of operator Z offered to cell i of

perator W, when cell i is in state n, and defined as

ψZ

xiW(n) = νZ xiSZ iW(n).

(3.17) Due to the dependence on the state of the cell, the total handoff rate out of cell j

ffered to cell i of operator W is given by the following Equations

νW

ji = λW j (1 − BW j )qW ji +

k∈AW

νW

kj (1 − BW hj )qW ji ,

(3.18) ψZ

xiW(n) = νZ xiSZ iW(n),

(3.19) where Equation (3.18) is the handoff traffic within operator W and Equation (3.19) is the handoff traffic shared by operators with agreement with operator W. Now, some further notation has to be introduced to calculate SZ

iW(n). Let GW be the

set of ordered alternate operators to which operator W can send handoffs. The operators are ordered according to the operator identification number, so GI= (II, III, IV, V ), GII= (III, IV, V, I) are sets of a system with 5 operators. Now let us define G

W(Z) as the set

f operators that precede operator Z in the sequence of alternate operators of operator
W. And G+

W(Z) the set of operators that succeed operator Z in the sequence of alternate

perators of operator W. See the explicit elements of next sample sets and its relation

according to Figure 3.5. These sets are considered so that ties are broken by a sequence when two or more operators have the same least loaded state. G

I (II)= (Ø),

G+

I (II)= (III, IV, V ),

I (IV)= (II, III),

G+

I (IV)= (V ).

SLIDE 48

28 CHAPTER 3. MODEL DESCRIPTION Figure 3.5: Sequences for LLR carrier assignment. In Equation (3.19), SZ

iW(n) is the contribution of traffic that operator Z gives to cell

i of operator operator W in state n and is obtained as SZ

iW(n) =

d∈G−

Z (W)

[1 −

i (m)]

d∈G+

Z(W)

[1 −

m=n+1

i (m)]QZ i (0).

(3.20)

3.4 Performance Measures

There are several useful performance measures in these models. At the cell level there are new call and handoff blocking probabilities. Also there are blocking probabilities at carrier level and the network blocking. These measures are obtained as follows. Using the stationary distribution P W

i (n) obtained in Equation (3.2), (3.3) and (3.4)

for the model evaluated with random and sequential schemes and the distribution QW

i (n)

btained in Equation (3.14) and (3.15) for the model with LLR scheme and according to

the blocked states of each cell, the new call blocking probability of cell i in operator W, BW

i , and handoff blocking probability of cell i in operator W, BW hi , can be obtained for the

model with random and sequential schemes as follows

SLIDE 49

3.4. PERFORMANCE MEASURES 29 BW

n=CW

i −T W i

P W

i (n),

(3.21) BW

hi = P W i (CW i ).

(3.22) Equations (3.21) and (3.22) were obtained from Equations (3.2) to (3.4) and the reservation parameter in each of the cells. Note that when no reservation is used in the cell, BW

and BW

hi are equal. Now for the model with LLR scheme we have

T W

i (n),

(3.23) BW

hi = QW i (0).

(3.24) Equations (3.23) and (3.24) were obtained from Equations (3.14), (3.15) and the reservation parameter in the cell. Also note that when no reservation is used in the cell, BW

and BW

hi are equal.

The blocking probability of each operator for the model with random and sequential schemes can be defined as the proportion of new calls and handoff calls from other operators blocked λW

i BW i

+ BW

Z∈GW
x∈AZ

νZ

xiSZ iW.

(3.25) to the total traffic load offered to the operator ρW

i −

j∈AW

νW

ji ,

(3.26) in all cells that correspond to the operator LW =

  λW

i BW i

+ BW

Z∈GW
x∈AZ

γZW

  

  ρW

i −

j∈AW

νW

  

, (3.27) where

SLIDE 50

30 CHAPTER 3. MODEL DESCRIPTION γZW

= νZ

xiSZ iW.

(3.28) The blocking probability of each operator for the model with LLR scheme can be defined as the proportion of new calls and handoff calls from other operators blocked λW

i BW i

+ BW

n
Z∈GW
x∈AZ

ψZ

xiW(n),

(3.29) to the total traffic load offered to the operator αW

i (n) −

j∈AW

νW

ji ,

(3.30) in all cells that correspond to the operator LW =

  λW

i BW i

+ BW

n
Z∈GW
x∈AZ

nψZ

xiW(n)QZ i (n)

  

  αW

i (n) −

j∈AW

νW

   nQW

i (n)

, (3.31) where ψZ

xiW(n) = νZ xiSZ iW(n).

(3.32) The network blocking or blocking probability in all the multicarrier system is defined as the proportion of the rate of new call arrivals that are blocked in the multicarrier system to the total new call arrival offered, to the system. L =

λW

i BW i

λW

. (3.33) Equation (3.33) is the same for the two models. The network rate of return of the system for the model with random and sequential schemes is the revenue generated by the new calls accepted λW

i (1 − BW i )wW i ,

(3.34)

SLIDE 51

3.4. PERFORMANCE MEASURES 31 minus the cost of all handoffs blocked cW

  

j∈AW

νW

ji +

Z∈GW
x∈AZ

νZ

xjSZ iW

   BW

hi ,

(3.35) added over all cells and all the carriers belonging to the multicarrier system, i.e., W =

  λW

i (1 − BW i )wW i

− cW

  

j∈AW

νW

ji +

Z∈GW
x∈AZ

νZ

xjSZ iW,

   BW

   ,

(3.36) where wW

is the revenue generated by accepting a call on cell i of operator W and cW

is the cost generated when a handoff is blocked in the system. The network rate of return of the system for the model with LLR scheme is the revenue generated by the new calls accepted λW

i (1 − BW i )wW i ,

(3.37) minus the cost of all handoffs blocked cW

  

j∈AW

νW

ji +

n
Z∈GW
x∈AZ

nψZ

xiW(n)QZ i (n)

   BW

hi ,

(3.38) added over all cells and all the carriers belonging to the multicarrier system, i.e., W =

  λW

i (1 − BW i )wW i

− cW

  

j∈AW

νW

ji +

n
Z∈GW
x∈AZ

nψZ

xiW(n)QZ i (n)

   BW

   ,

(3.39) where wW

is the revenue generated by accepting a call on cell i of operator W and cW

is the cost generated when a handoff is blocked in the system.

SLIDE 52

32 CHAPTER 3. MODEL DESCRIPTION

SLIDE 53

Chapter 4

Numerical Results

This chapter presents results obtained with the performance measures derived in Chapter 3 from the solution of the stationary distribution for the states of occupancy of the cells carrying new call, inter-cell handoff and inter-carrier handoff traffic. Two main cases were evaluated:

Symmetric-Symmetric System Case (SSC): defines a set of symmetric operators and

also symmetric among them.

Asymmetric-Symmetric System Case (ASC): defines a set of symmetric operators

but asymmetric among them. A wireless network is symmetric when all the cells in the network have the same capacity and the same new call arrival rate.

4.1 Mobility

Recall that users decide what to do among three possible events with certain distribution

nce the dwell time expires. The events are: staying within the cell, moving to an adjacent

cell or terminating the call. The values of the probabilities of the distribution used to decide among the three possible events mentioned, are set by fixing the probability of terminating a call in cell i, qiT, and then defining qij = 1 − qiT − qii K , (4.1) where K is the number of neighbors of cell i. This procedure has to be done to each cell in the system. 33

SLIDE 54

34 CHAPTER 4. NUMERICAL RESULTS By fixing the value of qiT ∈ [0, 1] and satisfying Equation (3.1), three possible levels of mobility can be defined by qii. The proposed values are Low Mobility (LM) with qii = 0.37, Medium Mobility (MM) with qii = 0.25 and High Mobility (HM) with qii = 0.05 for every cell in every operator. The eventual case of No Mobility can also be evaluated, to do so, set qij = 0 and qii = 1 − qiT. (4.2) For all the cases analyzed, we considered the dwell time to have unit mean, µW

= 1 for all the cells in all the operators.

4.2 Symmetric-Symmetric System Case (SSC)

The scenario proposed for this case consists of 5 operators and 3 cells by operator, with all the cells having a capacity of 30 channels, CW

= 30. All the operators have agreement between them to share idle resources and use Fixed Channel Assignment (FCA). The new call arrival rate of each cell of all the operators has been chosen to be λW

= 10. The arrival rate will be called the base load. As mentioned in Section 4.1, the dwell time has been chosen to have unit mean, µW

= 1. All the parameters can be seen in Table 4.1. Table 4.1: Parameters for the SSC. Operator CW

λW

µW

T W

I 30 10 1 0/2 II 30 10 1 0/2 III 30 10 1 0/2 IV 30 10 1 0/2 V 30 10 1 0/2 Using Equation (4.1) and setting the values qiT = 0.6 and K = 2 for the scenario to be evaluated, Table 4.2 can be obtained. Thus for the case of interest (3-cell network) LM means that 40% of the users remain in the network with 37% staying within same cell and 3% moving towards adjacent cells. For MM, 25% stay within same cell and 15% move into adjacent cells. For the case HM, 5% stay within same cell and 35% move into adjacent cells. The parameter T or reservation was also varied during the numerical analysis. We present results for different values of T. T = 0 is the case with no reservation and T > 0

SLIDE 55

4.2. SYMMETRIC-SYMMETRIC SYSTEM CASE (SSC) 35 Table 4.2: Parameters for the mobility cases. Mobility qii qij LM 0.37 0.015 MM 0.25 0.075 HM 0.05 0.175 the cases with reservation. The main case of reservation evaluated was T = 2, with the same reservation parameter for all the cells in all the carriers.

4.2.1 Blocking Results

To obtain graphs of the performance of the multicarrier system, the arrival rate of a cell of

ne operator was varied. We kept constant the rest of the cells in the remaining operators

at the base load. The arrival rate was incremented from 0.25 to an overload of 30 on cell i

f carrier I.

In Figure 4.1 the new call blocking probability with no reservation T = 0 and with reservation parameter of T = 2 with low mobility for the cell in overload is shown for all the schemes. The performance of the random uniform and sequential scheme is almost the same as presented in [14]. As expected the LLR scheme improves the grade of service in both cases of reservation, because its state dependent nature and best selection criteria.

5 10 15 20 25 30 0.05 0.1 0.15 0.2 0.25 0.3 traffic load (calls per time unit) new call blocking probability random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.1: New Call Blocking Probability, Case LM. SSC. Also note in Figure 4.1, the little performance degradation of new call blocking prob-

SLIDE 56

36 CHAPTER 4. NUMERICAL RESULTS ability compared to the case with no reservation, this is part of a tradeoff that will be understood later. Thus, the reservation parameter becomes a very important issue on the design of a network and has to be used carefully. Remember that as stated in Section 3.4, when no reservation is used in the system, the new call blocking probability and handoff blocking probability are the same. See Equations (3.21) to (3.24). Due to this, we can see the behavior of handoff blocking probability with no reservation in the same Figure 4.1 In Figure 4.2 the handoff blocking probability for the same cell but with reservation parameter of T = 2 is shown. Note the considerable improvement of the system with the use of reservation to handoffs compared to Figure 4.1. Also note that the LLR scheme practically eliminates the risk of a handoff drop.

5 10 15 20 25 30 0.002 0.004 0.006 0.008 0.01 0.012 0.014 traffic load (calls per time unit) hand off blocking probability random T=2 sequence T=2 LLR T=2

Figure 4.2: Handoff Blocking Probability, Case LM, T = 2. SSC. In Figure 4.3 we can see the considerable improvement of the new call blocking probability with the use of LLR compared to the random and sequential schemes for the case

f medium mobility.

Handoff blocking probability for medium mobility and T = 2 can be seen in Figure 4.4 and for high mobility and T = 2 in Figure 4.5. Even in the extreme case of high mobility where 35% of the users move into adjacent cells generating handoffs, the LLR scheme maintains a handoff blocking probability far below 0.05. As shown in [14], when more users start moving among cells the scheme that performs worst is the sequential. And this behavior can be seen in Figure 4.5. This occurs since the overload carrier will be overloading the other carriers in a sequence, and causing high blocking status.

SLIDE 57

4.2. SYMMETRIC-SYMMETRIC SYSTEM CASE (SSC) 37

5 10 15 20 25 30 0.05 0.1 0.15 0.2 0.25 0.3 traffic load (calls per time unit) new call blocking probability random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.3: New Call Blocking Probability, Case MM. SSC.

5 10 15 20 25 30 0.002 0.004 0.006 0.008 0.01 0.012 0.014 traffic load (calls per time unit) hand off blocking probability random T=2 sequence T=2 LLR T=2

Figure 4.4: Handoff Blocking Probability, Case MM, T = 2. SSC. In Figure 4.6 the new call blocking probability of the overloaded cell can be seen for the case of no mobility. Note that because there are no handoffs the performance of the schemes is the same. Now to have a better view of the tradeoff between new call and handoff blocking probabilities take a look to Table 4.3 and Table 4.4. As shown in previous figures the use of reservation in the system worsens the new call blocking probability, but improves the handoff blocking probability. A positive sign in the “% of change” column means an increase in the blocking probability or degradation of the performance and a negative sign

SLIDE 58

38 CHAPTER 4. NUMERICAL RESULTS

5 10 15 20 25 30 0.05 0.1 0.15 0.2 0.25 traffic load (calls per time unit) hand off blocking probability random T=2 sequence T=2 LLR T=2

Figure 4.5: Handoff Blocking Probability, Case HM, T = 2. SSC.

5 10 15 20 25 30 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 traffic load (calls per time unit) new call blocking probability random sequence LLR

Figure 4.6: New Call Blocking Probability, Case NM. SSC. means a decrease in the blocking probability or improvement in the performance of the system. Table 4.3 and Table 4.4 show the change of performance in cell i of carrier I and cell i of carrier III due to the use of reservation at a load of λI

i = 15 in cell i of carrier

I for low and medium mobility, respectively. For all the schemes and all the mobilities evaluated, handoff blocking probability of Carrier I and Carrier III benefits from the use

f reservation, because we take the resources from the carriers less loaded to give attention

to the lack of free channels on the overloaded carrier.

SLIDE 59

4.2. SYMMETRIC-SYMMETRIC SYSTEM CASE (SSC) 39 Table 4.3: Blocking probabilities for cell i in carriers I and III with LM. New Call Blocking Handoff Blocking Scheme Carrier T = 0 T = 2 % change T = 0 T = 2 % change I 0.070506 0.113047 +60.33 0.070506 0.000711

98.99

Random III 0.001657 0.005056 +205.12 0.001657 0.000012

99.27

I 0.070507 0.113047 +60.33 0.070507 0.000711

98.99

Sequence III 0.001657 0.005056 +205.12 0.001657 0.000013

99.27

I 0.043830 0.072511 +65.43 0.043830 0.000020

99.95

LLR III 0.000770 0.002548 +230.90 0.000770 0.000001

99.87

Table 4.4: Blocking probabilities for cell i in carriers I and III with MM. New Call Blocking Handoff Blocking Scheme Carrier T = 0 T = 2 % change T = 0 T = 2 % change I 0.160288 0.276005 +72.19 0.160288 0.026429

83.51

Random III 0.010091 0.027408 +171.60 0.010091 0.001181

88.29

I 0.160416 0.276036 +72.07 0.160416 0.026435

83.52

Sequence III 0.010096 0.027408 +171.47 0.010096 0.001181

88.30

I 0.024239 0.047818 +97.27 0.024239 0.000295

98.78

LLR III 0.000426 0.001636 +284.03 0.000426 0.000010

97.65

Note something interesting on the tables for LLR, for low mobility cell i of carrier I has a new call blocking probability of 4.3% with no reservation and 7.2% with reservation in contrast with the same cell and carrier, but with medium mobility has 2.4% with no reservation and 4.7% with reservation. One could expect the opposite!, low mobility blocking probabilities to be lower than medium mobility blocking probabilities. This because due to the increase in mobility more handoffs occur in the system and LLR tends to connect all this users in the least loaded carriers and for hence decreasing blocking probability. In Table 4.5, we can see the change of performance in cell i of carrier I and cell i of carrier III due to the use of reservation at a load of λI

i = 15 in cell i of carrier I for high

mobility. Note that LLR scheme always performs best among them even with the higher

degradation in new call blocking probability. This because LLR scheme tends to allocate the handoff in cell i of the best carrier, in this case, the best carrier means the one with more free channels in its cell. In Figure 4.7 we can see the performance of Carrier I with low mobility for the case

SLIDE 60

40 CHAPTER 4. NUMERICAL RESULTS Table 4.5: Blocking probabilities for cell i in carriers I and III with HM. New Call Blocking Handoff Blocking Scheme Carrier T = 0 T = 2 % change T = 0 T = 2 % change I 0.308014 0.526759 +71.01 0.308014 0.131213

57.40

Random III 0.077649 0.173176 +123.02 0.077649 0.026761

65.53

I 0.314919 0.538703 +71.06 0.314919 0.137353

56.38

Sequence III 0.078159 0.173443 +121.91 0.078159 0.026821

65.68

I 0.019528 0.045103 +130.96 0.019528 0.001499

92.32

LLR III 0.000665 0.002700 +306.01 0.000665 0.000081

87.81
f no reservation T = 0 and reservation parameter T = 2. Remember that the overloaded

cell belongs to Carrier I. And in Figure 4.8 the case with medium mobility for the same reservation parameters is shown. Seeing previous figures it is easy to see the considerably improvement on the performance of the carrier with the use of LLR algorithm to select the carrier to which we need to offer the handoff call.

5 10 15 20 25 30 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 traffic load (calls per time unit) carrier blocking probability random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.7: Carrier Blocking Probability, Case LM. SSC. Figure 4.9 to Figure 4.11 show a big picture of the schemes evaluated. On surface plots we can see the behavior of Carrier I with different reservation parameters to have a better understanding of the tradeoff between new call versus handoff blocking probabilities. This because as shown on [14], the use of reservation to give priority to handoffs over new calls have to be used wisely. It needs to be determined beforehand if the use of reservation will improve performance for the system when using specific carrier assignment, besides, it

SLIDE 61

4.2. SYMMETRIC-SYMMETRIC SYSTEM CASE (SSC) 41

5 10 15 20 25 30 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 traffic load (calls per time unit) carrier blocking probability random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.8: Carrier Blocking Probability, Case MM. SSC. might be possible to use reservation only on some carriers.

1 2 3 4 5 5 10 15 20 25 30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 reservation traffic load (calls per time unit) carrier blocking probability HM MM LM

Figure 4.9: Carrier Blocking Probability. Random Scheme. SSC. The behavior of the carrier performance for the sequential and random schemes is as expected, but with the LLR scheme something different happens. In Figure 4.11 we can confirm that the LLR scheme performs better with higher mobilities of users as seen on previous Tables. In Figure 4.12 we can see carrier blocking probability of carrier I with LLR scheme and reservations parameters T = 0 and T = 2 varying traffic load and mobility. To obtain

SLIDE 62

42 CHAPTER 4. NUMERICAL RESULTS

1 2 3 4 5 5 10 15 20 25 30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 reservation traffic load (calls per time unit) carrier blocking probability HM MM LM

Figure 4.10: Carrier Blocking Probability. Sequence Scheme. SSC.

1 2 3 4 5 5 10 15 20 25 30 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 reservation traffic load (calls per time unit) carrier blocking probability LM MM HM

Figure 4.11: Carrier Blocking Probability. LLR Scheme. SSC. the surface plot an additional mobility case was considered with qii = 0.15 between medium and high mobilities. Note how blocking probability decrease when mobility of users increase in the network. Also here the use of reservation improve performance.

4.2.2 Revenue Results

In Figure 4.13 the network rate of return of the multicarrier system with low mobility for no reservation and reservation parameter T = 2 can be seen. The revenue generated

SLIDE 63

4.2. SYMMETRIC-SYMMETRIC SYSTEM CASE (SSC) 43

10 20 30 40 10 20 30 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 % mobility traffic load carrier blocking probability 10 20 30 40 10 20 30 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 % mobility traffic load carrier blocking probability T=0 T=2 a) b)

Figure 4.12: Carrier Blocking Probability. LLR Scheme. SSC. by accepting a call on cell i was chosen to be 1, i.e., wW

= 1, and the cost of a forced termination of a call due to a handoff blocked was chosen to be 5, i.e., cW

= 5.

5 10 15 20 25 30 140 142 144 146 148 150 152 154 156 158 160 traffic load (calls per time unit) network rate of return random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.13: Network Rate or Return. LM. SSC. Figure 4.14 shows the network rate of return of the multicarrier system with medium mobility for no reservation T = 0 and reservation parameter T = 2.

SLIDE 64

44 CHAPTER 4. NUMERICAL RESULTS

5 10 15 20 25 30 80 90 100 110 120 130 140 150 160 traffic load (calls per time unit) network rate of return random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.14: Network Rate or Return. MM. SSC.

4.3 Asymmetric-Symmetric System Case

As explained at the beginning of this chapter, the scenario proposed for this case has been ruled according Table 4.6. The rest of the parameters remain the same of the symmetric- symmetric case. Table 4.6: Parameters for the ASC. Operator CW

λW

µW

T W

I 30 10 1 0/2 II 40 14 1 0/2 III 50 17 1 0/2 IV 20 7 1 0/2 V 25 9 1 0/2

4.3.1 Blocking Results

The mobility cases will be the same, and were presented in Table 4.2. Again to obtain graphs the arrival rate of cell i of carrier I was incremented from 0.25 to an overload of 30 and obtained from the performance measures derived in Chapter 3. Figure 4.15 shows the new blocking probability of cell i of overloaded carrier with medium mobility for no reservation T = 0 and reservation parameter T = 2. Note that

SLIDE 65

4.3. ASYMMETRIC-SYMMETRIC SYSTEM CASE 45 as shown in the symmetric-symmetric case the LLR performs best among the schemes for both kinds of reservation. Figure 4.16 shows the handoff blocking probability of cell i of overloaded carrier with medium mobility for on reservation T = 0 and reservation parameter T = 2. Again as shown on the symmetric-symmetric case the use of LLR scheme practically eliminates the risk of a dropped handoff call.

5 10 15 20 25 30 0.05 0.1 0.15 0.2 0.25 0.3 traffic load (calls per time unit) new call blocking probability random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.15: New Call Blocking Probability, Case MM. ASC.

5 10 15 20 25 30 0.002 0.004 0.006 0.008 0.01 0.012 0.014 traffic load (calls per time unit) hand off blocking probability random T=2 sequence T=2 LLR T=2

Figure 4.16: Handoff Blocking Probability, Case MM, T = 2. ASC.

SLIDE 66

46 CHAPTER 4. NUMERICAL RESULTS Figure 4.17 shows blocking probability of carrier I with medium mobility for no reservation and reservation parameter T = 2.

5 10 15 20 25 30 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 traffic load (calls per time unit) carrirer blocking probability random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.17: Carrier Blocking Probability, Case MM. ASC. In Table 4.7 we can see the new call blocking probabilities and handoff blocking probabilities for the schemes evaluated and with low, medium and high mobility. The case with no reservation T = 0 and with reservation parameter of T = 2 are presented. See the benefit of the use of reservation in handoff blocking probabilities thanks to a degradation

f the new call blocking probability. Note that the performance of random and sequential

scheme is almost the same with low and medium mobility, only a little difference appear with high mobility. In Figure 4.18 we can see the surface plot of the carrier blocking probability with different reservation parameters for the LLR scheme. As seen in the symmetric-symmetric case the LLR scheme performs better with higher mobilities, this can also be noted in Figure 4.19.

4.3.2 Revenue Results

In Figure 4.20 the network rate of return of the multicarrier system with medium mobility for no reservation and reservation parameter T = 2 can be seen. Here the same values of revenue, wW

= 1, and cost, cW

= 5 were used. Figure 4.21 shows the network rate of return with LLR scheme for the 3 mobility cases proposed with no reservation and with reservation parameter T = 2.

SLIDE 67

4.3. ASYMMETRIC-SYMMETRIC SYSTEM CASE 47 Table 4.7: Blocking Probabilities for cell i on Carrier I. New Call Blocking Handoff Blocking Scheme T = 0 T = 2 % change T = 0 T = 2 % change Random 0.075680 0.120813 +59.63 0.075680 0.000971

98.71

LM Sequence 0.075681 0.120813 +59.63 0.075681 0.000971

98.71

LLR 0.043847 0.072511 +65.37 0.043847 0.000020

99.95

Random 0.188277 0.324027 +72.10 0.188277 0.037734

79.95

MM Sequence 0.188366 0.324043 +72.02 0.188366 0.037738

79.96

LLR 0.024267 0.047819 +97.05 0.024267 0.000295

98.78

Random 0.359770 0.616163 +71.26 0.359770 0.182071

49.39

HM Sequence 0.365099 0.625026 +71.19 0.365099 0.187786

48.56

LLR 0.019573 0.045111 +130.47 0.019573 0.001500

93.33

1 2 3 4 5 5 10 15 20 25 30 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 reservation traffic load (calls per time unit) carrier blocking probability LM MM HM

Figure 4.18: Carrier Blocking Probability. LLR Scheme. ASC.

SLIDE 68

48 CHAPTER 4. NUMERICAL RESULTS

Figure 4.19: Carrier Blocking Probability. LLR Scheme. ASC.

5 10 15 20 25 30 80 100 120 140 160 180 200 traffic load (calls per time unit) network rate of return random T=0 sequence T=0 LLR T=0 random T=2 sequence T=2 LLR T=2

Figure 4.20: Network Rate or Return. MM. ASC.

SLIDE 69

4.3. ASYMMETRIC-SYMMETRIC SYSTEM CASE 49

5 10 15 20 25 30 165 170 175 180 185 traffic load (calls per time unit) network rate of return LLR LM T=0 LLR LM T=2 LLR MM T=0 LLR MM T=2 LLR HM T=0 LLR HM T=2

Figure 4.21: Network Rate of Return, Case LM, MM and HM. ASC.

SLIDE 70

50 CHAPTER 4. NUMERICAL RESULTS

SLIDE 71

Chapter 5

Conclusions

In this chapter, general conclusions of this work are presented. Also some further research projects are suggested.

5.1 General Conclusions

The main goal of the multicarrier system can be understand as the organized integration of carriers to obtain benefit from all its idle resources, because the idle network infrastructure can not generate revenue. Independently of political and regulatory affairs between carriers and operators, all can play as a multi-system to obtain revenue and improve its grade of service. Remember that from the point of view of a user the indignation of losing a call in progress is bigger than the rejection of a new incoming call. Hence, from the point of view of the carrier its more expensive to lost an active call than refusing access a new one. So as a multi-sharing-system if an operator can not continue serving its user due to lack of free channels, the carrier with more free channels will accept the call. And the carrier with more free channels is also the carrier with lower blocking probability, so the degradation of its performance is less damaging to the system. With the evaluation of wireless networks with a state-dependent approach, we obtain considerably better results that with the previous performance evaluation. But remember that the use of reservation parameters have to be evaluated very carefully to obtain the tradeoff required. The use of Least Loaded Routing scheme guarantees that the lazy infrastructure within the multi-system will be used and will generate revenue with less damage in its blocking probability. Now with all the evolution in recent years of the PSTN where this kind of routing schemes have been implemented and perform very successfully, its now technologically feasible to monitor the occupancy levels of alternate routes and make routing decisions on 51

SLIDE 72

52 CHAPTER 5. CONCLUSIONS a call-by-call basis. Together with a robust and efficient signaling system this schemes tend to be implemented in all telecommunication networks.

5.2 Future Work

There are some research projects that can continue this work, because there are a lot of new technologies and new business paradigms.

This work used Fixed Channel Assignment, but Dynamic Channel Assignment can

be considered or a combination of both.

Packing of channels and return to original channels in original carrier.
Further considerations between boundaries of cells from different carriers, such carrier-

to-cochannel interference.

There are more methods of state-dependent routing to be evaluated like DAR, or

RTNR.

An efficient approach can be considered with aggregated states, such as in ALBA.
A statistical study of the parameters SZ

iW and SZ iW(n) from the carriers coexisting in

some coverage area.

Extend the analysis to cover soft-handoffs, like the ones in CDMA.

SLIDE 73

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February 1993. [6] Hurley B.R., Seidl, C.J. and Sewel W.F., “A Survey of Dynamic Routing methods for circuit-switched traffic,” IEEE Communications Magazine, vol. 25, pp. 13-21, 1987. [7] ITU-T Recomendation E. 771, “Network Grade of Service Parameters and Target Values for Circuit Switched Public Land Mobile Services,” International Telecommu- nication Union, Geneva, 1996. [8] Kelly, Frank P., Reversibility and Stochastic Networks, Wiley Chichester, 1979. [9] Kelly, Frank P., “Routing and Capacity Allocation in Networks with Trunk Reserva- tion,” Math. of Operat. Res., vol. 15, pp. 771-792, 1990. [10] Krishnan, K.R. and Ott, T.J., “State-Dependent Routing for Telephone Traffic: The-

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1986, pp. 2124-2128, 1986. 53

SLIDE 74

54 BIBLIOGRAPHY [11] Krishnan, K.R., “Performance Evaluation of Networks under State-Dependent Rout- ing,” Proc. Bellcore Symp. Perform. Model, October 1990. [12] Lin, Yi-Bing, Chlamtac, Imrich, Wireless and Mobile Network Architectures, John Wiley and Sons Inc, 2001. [13] Mc Donald, V.H., “Advanced Mobile Phone Service: The Cellular Concept,” Bell System Technical Journal, vol. 58, pp. 15-41, January 1979. [14] Mora Zamorano, Jose Juan, “Multicarrier Wireless Network Evaluation,” ITESM Master Thesis, December 1997. [15] Mora Zamorano, Jose Juan and Vargas-Rosales, Cesar, “Handoff Routing Strategies and Mobility in Multicarrier Wireless Networks,” Global Telecommunications Confer- ence, 1998. IEEE GLOBECOM 1998. The Bridge to Global Integration., vol. 3, pp. 1402-1407, 1998. [16] Oliphant, Malcolm W., “The Mobile Phone meets the Internet,” IEEE Spectrum, vol. 36, pp. 20-28. August 1999. [17] Pandya, Raj, Mobile and Personal Communication Systems and Services, IEEE Press, 2000. [18] Rappaport, Theodore S., Wireless Communications Principles & Practice, Prentice Hall Inc., 1996. [19] Steenstrup, Martha E., Routing in Communications Networks, Prentice Hall Inc., 1995. [20] Vasile I., Istratescu, Fixed Point Theory, 1981. [21] Vargas, Cesar, “Communication Network Design and Evaluation using Shadow Prices,” Ph.D. Dissertation, Louisiana State University, 1996. [22] Wong, Eric W.M., Chan, Andy K.M., Yum and Tak-Shing Peter, “A Taxonomy of Rerouting in Circuit-Switched Networks,” IEEE Communications Magazine, vol. 37,

pp. 116-122, November 1999.

SLIDE 75

Vita

Enrique Stevens Navarro Hijo del Dr. Guillermo Enrique Stevens Amaro y de Maria Guadalupe Navarro de Stevens. Naci´

en la ciudad de San Luis Potos´

ı, San Luis Potos´ ı el 5 de julio de 1977. Realiz´

estudios profesionales en la Facultad de Ciencias de la Universidad Aut´

noma de San Luis

Potos´ ı como Ingeniero Electr´

nico con terminal en Comunicaciones de agosto de 1996 a

junio del 2000. Becario de la Fundaci´

n TELMEX desde 1997. Miembro Estudiante de la

IEEE desde 1998. Direcci´

n Permanente: 2a. Privada de Fray Jos´

e de Arlegui #180-1

Col. Las Aguilas C.P. 78240

San Luis Potos´ ı, S.L.P. M´ exico. estevens77@yahoo.com La presente tesis fue tipografiada con L

EX1 por Enrique Stevens Navarro.

1El paquete de macros, ITESMtesis.sty, utilizado en el formateo de esta tesis fue escrito por el Dr. Hora-

cio Mart´ ınez Alfaro <hma@campus.mty.itesm.mx>, Profesor Asociado del Centro de Inteligencia Artificial del Instituto Tecnol´

gico y de Estudios Superiores de Monterrey, Campus Monterrey.

Instituto Tecnol´

Monterrey

Campus Monterrey Divisi´

Comunicaciones

MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST LOADED ROUTING THESIS Presented as a partial fulfillment of the requeriments for the degree of Master of Science in Electronic Engineering Major in Telecommunications

Instituto Tecnol´

Monterrey

Campus Monterrey Divisi´

Comunicaciones

Approved

Enrique Stevens Navarro

MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST LOADED ROUTING

MULTICARRIER WIRELESS NETWORK EVALUATION WITH LEAST LOADED ROUTING

Contents

List of Figures

List of Tables

Chapter 1

Introduction

1.1 Previous Work

1.2 Objective

1.3 Justification

1.4 Contributions

1.5 Organization

Chapter 2

Background

2.1 The Cellular Concept

2.1.1 Elements of the Cellular Concept, [18], [12].

2.1.2 Frequency Reuse and Cell Splitting, [18].

2.1.3 Channel Assignment Strategies

2.1.4 Handoffs

2.1.5 Multiple Access Technologies

2.2 Quality of Service in Cellular Networks, [17]

2.2.1 Traffic Performance at Network Level

2.3 Networking Cellular Concepts

2.3.1 Application of Networks of Queues

2.4 Methodology for Performance Analysis

2.4.1 Erlang Fixed Point Approximation

2.4.2 Analysis of a Cellular Network with the Fixed Point Ap- proximation

Chapter 3

Model Description

3.1 Model for a Multicarrier Cellular Network, [14]

3.2 Strategies for Carrier Assignment

3.2.1 Routing, [19]

3.2.2 Circuit-Switched Routing

3.2.3 Alternative Routing Strategies

3.2.4 Adaptive Routing Strategies

3.3 Model with State-Dependent Routing

3.4 Performance Measures

Chapter 4

Numerical Results

4.1 Mobility

4.2 Symmetric-Symmetric System Case (SSC)

4.2.1 Blocking Results

4.2.2 Revenue Results

4.3 Asymmetric-Symmetric System Case

4.3.1 Blocking Results

4.3.2 Revenue Results

Chapter 5

Conclusions

5.1 General Conclusions

5.2 Future Work

Bibliography

Vita