Stochastic Petri Nets (2nd edition)

Any developer of discrete event systems knows that the most important quality of the final system is that it be functionally correct by exhibiting certain functionaL or qualitative properties decided upon as being important. Once assured that the system behaves correctly, it is also important that it is efficient in that its running cost is minimal or that it executes in optimum time or whatever performance measure is chosen. While functional correctness is taken for granted, the latter quantitative properties will often decide the success, or otherwise, of the system. Ideally the developer must be able to specify, design and implement his system and test it for both functional correctness and performance using only one for malism. No such formalism exists as yet. In recent years the graphical version of the Specification and Description Language (SDL) has become very popular for the specification, design and partial implementation of discrete systems. The ability to test for functional correctness of systems specified in SDL is, however, limited to time consuming simulative executions of the specification and perfor mance analysis is not directly possible. Petri nets, although graphical in format are somewhat tedious for specifying large complex systems but, on the other hand were developed exactly to test discrete, distributed systems for functional correctness. With a Petri net specification one can test, e. g. , for deadlock, live ness and boundedness of the specified system. Preface......Page 5 Preface to the Second Edition......Page 7 Contents......Page 9 1.1 Probability Theory Refresher......Page 15 1.2 Discrete Random Variables......Page 18 1.3 Continuous Random Variables......Page 20 1.4 Moments of a Random Variable......Page 21 1.5 Joint Distributions of Random Variables......Page 22 1.6 Stochastic Processes......Page 23 2 Markov Processes......Page 25 2.1 Discrete Time Markov Chains......Page 27 2.2 Semi-Markov Processes......Page 43 2.3 Continuous Time Markov Chains......Page 49 2.4 Embedded Markov Chains......Page 56 3 General Queueing Systems......Page 58 3.1 Little’s Law......Page 61 3.2 Birth-Death Processes......Page 64 3.3 Poisson Process......Page 66 3.4 M/M/1 Queue......Page 68 3.5 M/M/m Queue......Page 71 3.6 Queues with Processor Sharing Scheduling Strategy......Page 72 3.8 Queues with Priority Service......Page 73 4 Further Reading......Page 75 5 Place-Transition Nets......Page 79 5.1 Structure of Place-Transition Nets......Page 83 5.2 Dynamic Behaviour of Place-Transition Nets......Page 86 5.3 Properties of Place-Transition Nets......Page 88 5.4 Analysis of Place-Transition Nets......Page 92 5.5 Further Remarks on Petri Nets......Page 115 6 Coloured Petri Nets......Page 119 7 Further Reading......Page 128 8 Stochastic Petri Nets......Page 135 9 Generalized Stochastic Petri Nets......Page 143 9.1 Quantitative Analysis of GSPNs......Page 145 9.2 Qualitative Analysis of GSPNs......Page 152 9.3 Further Remarks on GSPNs......Page 162 10 Queueing Petri Nets......Page 166 10.1 Quantitative Analysis of QPNs......Page 168 10.2 Qualitative Analysis of QPNs......Page 173 10.3 Some Remarks on Quantitative Analysis......Page 178 11 Further Reading......Page 180 12.1 Resource Sharing......Page 183 12.2 Node of a DQDB network......Page 184 13 Solutions to Selected Exercises......Page 189 Bibliography......Page 197 Index......Page 213 Falko Bause, Pieter S. Kritzinger. Includes Bibliographical References (p. 194-208) And Index.