Teletraffic

1 Introduction.- 1.1 Features of Teletraffic Systems.- 1.2 Modeling of Teletraffic Systems.- 1.3 Fundamental Relations.- Exercises.- 2 Markovian Models.- 2.1 Markovian Loss Systems.- 2.2 Markovian Delay Systems.- 2.3 Extended Markovian Models.- Exercises.- 3 Non-Markovian Models.- 3.1 Renewal Process.- 3.2 Poisson Input General Service Time Models.- 3.3 Poisson Input Constant Service Time Model.- 3.4 Renewal Input Exponential Server Models.- 3.5 Renewal Input Single Server Models.- Exercises.- 4 Multi-Class Input Models.- 4.1 Batch Arrival Models.- 4.2 Priority Models.- 4.3 Multi-Dimensional Traffic Models.- 4.4 Mixed Loss and Delay Systems.- 4.5 Multi-Queue Models.- Exercises.- 5 Alternative Routing Systems.- 5.1 Overflow System.- 5.2 Approximate Methods for Overflow Systems.- 5.3 Optimum Design of Alternative Routing.- 5.4 Numerical Analysis of State Equations.- Exercises.- 6 Advanced Teletraffic Models.- 6.1 Renewal Input Multi-Server Model.- 6.2 PH-MRP Input Models.- 6.3 MMPP Input Model.- 6.4 Statistical Packet Multiplexer.- 6.5 Local Area Networks.- Exercises.- 7 Traffic Simulation.- 7.1 Introduction.- 7.2 Methods of Simulation.- 7.3 Generation of Random Numbers.- 7.4 Analysis of Output Result.- Exercises.- Appendices.- A Basic Teletraffic Formulas.- A.1 Notation.- A.2 Markovian Models.- A.3 Poisson Input Non-Markovian Models.- A.4 Renewal Input Non-Markovian Models.- A.5 Non-Renewal Input Models.- B Programs for Erlang B Formula.- B.1 Integer Number of Servers.- B.2 Real Number of Servers.- B.3 Derivatives of Erlang B Formula.- B.4 BASIC Program Lists.- C Basis of Probability Theory.- C.1 Events and Probability.- C.1.1 Events.- C.1.2 Probability.- C.1.3 Conditional Probability.- C.2 Distribution Functions.- C.2.1 Random Variables.- C.2.2 Joint Distribution Function.- C.2.3 Convolution.- C.3 Expectation and Transforms.- C.3.1 Expectation.- C.3.2 Laplace-Stieltjes Transform.- C.3.3 Probability Generating Function.- C.4 Examples of Probability Distributions.- C.4.1 Probability Distribution.- C.4.2 Discrete Distributions.- C.4.3 Continuous Distributions.- C.5 Stochastic Processes.- C.5.1 Markov Process.- C.5.2 Discrete-Time Markov Chain.- C.5.3 Continuous-Time Markov Chain.- C.5.4 Birth-Death Process.- D Solutions to Exercises.