ABSTRACT
This monograph presents a concise mathematical approach for modeling and analyzing the perfor-
mance of communication networks with the aim of understanding the phenomenon of statistical
multiplexing.The novelty of the monograph is the fresh approach and insights provided by a sample-
path methodology for queueing models that highlights the important ideas of Palm distributions
associated with traffic models and their role in performance measures. Also presented are recent
ideas of large buffer, and many sources asymptotics that play an important role in understanding
statistical multiplexing. In particular, the important concept of effective bandwidths as mappings
from queueing level phenomena to loss network models is clearly presented along with a detailed
presentation of loss network models and accurate approximations for large networks.
KEYWORDS
communication networks, performance modeling, point process, fluid inputs, queues,
Palm distributions, loss networks, effective bandwiths, statistical multiplexing
à ma famille
ix
Contents
Preface .....................................................................xiii
1
Introduction to Traffic Models and Analysis ....................................1
1.1 Introduction ...............................................................1
1.1.1 Quantitative Tools 2
1.2 Traffic Arrival Models .......................................................3
1.2.1 Non-homogeneous Poisson Process 12
1.3 Residual Life and the Inspection Paradox ....................................15
1.4 Event and Time Averages (EATA) ..........................................18
1.5 Fluid Traffic Arrival Models ................................................25
Notes and Probing Further .................................................28
Book References 28
Journal Articles 29
2
Queues and Perfor mance Analysis ............................................31
2.1 Preliminaries ..............................................................31
2.1.1 Applications of the RCL 34
2.2 Queueing Models .........................................................36
2.2.1 Queues Viewed from Congestion Process Viewpoint 39
2.2.2 Queues from a Workload Viewpoint 42
2.3 Waiting Times and Workload in Queues .....................................46
2.4 From Means to Distributions ...............................................50
2.4.1 Equilibrium Distributions 50
2.4.2 Workload and Busy Period Distributions 51
2.4.3 Stationary Distributions of GI /M/1 Queues 53
2.4.4 Output Processes of Queues 56
x CONTENTS
2.5 Fluid Queues .............................................................57
Notes and Probing Further .................................................63
Book References 63
Journal Articles 65
3
Loss Models for Networks ...................................................67
3.1 Introduction ..............................................................67
3.2 Mathematical Preliminaries ................................................67
3.3 Erlang Loss System ........................................................70
3.4 Multi-rate Erlang Loss Systems ............................................73
3.5 The General Network Case.................................................77
3.6 Large Loss Systems ........................................................82
3.7 Loss Network Models in Wireless Communication Networks..................89
3.8 Some Properties of Large Multi-Rate Systems ...............................90
Notes and Probing Further .................................................93
Book References 94
Journal Articles 94
4
Statistic al Multiplexing ......................................................97
4.1 Performance Metrics for Quality of Service (QoS) ............................99
4.2 Multiplexing and Effective Bandwidths-Motivation .........................100
4.3 Multiplexing Fluid Inputs .................................................102
4.4 QoS-Packet Loss and Effective Bandwidths ................................107
4.5 Estimating Buffer Overflow Probabilities ...................................109
4.5.1 Large Buffer Asymptotics 110
4.5.2 Many Sources Asymptotics 112
4.6 Effective Bandwidths Revisited ............................................115
Notes and Probing Further ................................................118
Book References 118
Journal Articles 118
A
Review of Probability and Markov Chains ...................................121

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