Regeneration and Networks of Queues

ISBN-13: 9781461269977 / Angielski / Miękka / 2012 / 224 str.

Gerald S. Shedler; Gerald S. Shedler

Opis

Networks of queues arise frequently as models for a wide variety of congestion phenomena. Discrete event simulation is often the only available means for studying the behavior of complex networks and many such simulations are non- Markovian in the sense that the underlying stochastic process cannot be repre- sented as a continuous time Markov chain with countable state space. Based on representation of the underlying stochastic process of the simulation as a gen- eralized semi-Markov process, this book develops probabilistic and statistical methods for discrete event simulation of networks of queues. The emphasis is on the use of underlying regenerative stochastic process structure for the design of simulation experiments and the analysis of simulation output. The most obvious methodological advantage of simulation is that in principle it is applicable to stochastic systems of arbitrary complexity. In practice, however, it is often a decidedly nontrivial matter to obtain from a simulation information that is both useful and accurate, and to obtain it in an efficient manner. These difficulties arise primarily from the inherent variability in a stochastic system, and it is necessary to seek theoretically sound and computationally efficient methods for carrying out the simulation. Apart from implementation consider- ations, important concerns for simulation relate to efficient methods for generating sample paths of the underlying stochastic process. the design of simulation ex- periments, and the analysis of simulation output.

Spis treści

1 Discrete Event Simulation.- 1.1 Methodological Considerations l.- 1.2 The Generalized Semi-Markov Process Model.- 1.3 Specification of Discrete Event Simulations.- 2 Regenerative Simulation.- 2.1 Regenerative Stochastic Processes.- 2.2 Properties of Regenerative Processes.- 2.3 The Regenerative Method for Simulation Analysis.- 2.4 Implementation Considerations.- 2.5 Theoretical Values for Discrete Time Markov Chains.- 2.6 Theoretical Values for Continuous Time Markov Chains.- 2.7 Efficiency of Regenerative Simulation.- 2.8 Regenerative Generalized Semi-Markov Processes.- 3 Markovian Networks.- 3.1. Markovian Job Stack Processes.- 3.2. Augmented Job Stack Processes.- 3.3. Irreducible, Closed Sets of Recurrent States.- 3.4. The Marked Job Method.- 3.5. Fully Augmented Job Stack Processes.- 3.6. The Labelled Jobs Method.- 3.7. Sequences of Passage Times.- 3.8. Networks with Multiple Job Types.- 3.9. Simulation for Passage Times.- 4 Non-Markovian Networks.- 4.1 Networks with Single States.- 4.2 Regenerative Simulation of Non-Markovian Networks.- 4.3 Single States for Passage Times.- 4.4 Recurrence and Regeneration.- 4.5 The Marked Job Method.- 4.6 Finite Capacity Open Networks.- 4.7 Passage Through Subnetworks.- 4.8 The Underlying Stochastic Structure.- 4.9 The Labelled Jobs Method.- 4.10 Comparison of Methods.- Appendix 1 Limit Theorems for Stochastic Processes.- Appendix 2 Convergence of Passage Times.- Symbol Index.