Stochastic Petri Nets
An Introduction to the Theory
2nd Edition
Published on 12. September 2002
Book
Paperback/Softback
218 pages
978-3-528-15535-3 (ISBN)
Description
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.
More details
Edition
2., Softcover reprint of the original 2nd ed. 2002
Language
English
Place of publication
Wiesbaden
Germany
Target group
Professional and scholarly
Upper undergraduate
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 21 cm
Width: 14.8 cm
Thickness: 12 mm
Weight
339 gr
ISBN-13
978-3-528-15535-3 (9783528155353)
DOI
10.1007/978-3-322-86501-4
Schweitzer Classification
Other editions
Previous edition
Book
01/1996
Vieweg & Teubner
€49.99
Article exhausted; check for reprint
Persons
Dr. rer. nat. Falko Bause has taught and done research work in the area of system engineering and has published several papers on Stochastic Petri Nets.Pieter Kritzinger is a full professor at the Department of Computer Science at the University of Cape Town.
Content
I Stochastic Theory.- 1 Random Variables.- 1.1 Probability Theory Refresher.- 1.2 Discrete Random Variables.- 1.3 Continuous Random Variables.- 1.4 Moments of a Random Variable.- 1.5 Joint Distributions of Random Variables.- 1.6 Stochastic Processes.- 2 Markov Processes.- 2.1 Discrete Time Markov Chains.- 2.1.1 Steady State Distribution.- 2.1.2 Absorbing Chains and Transient Behaviour.- 2.2 Semi-Markov Processes.- 2.2.1 Formal Model of a Semi-Markov Process.- 2.2.2 Interval Transition Probabilities.- 2.2.3 Steady State Behaviour.- 2.3 Continuous Time Markov Chains.- 2.3.1 Steady State Distribution.- 2.4 Embedded Markov Chains.- 3 General Queueing Systems.- 3.1 Little's Law.- 3.2 Birth-Death Processes.- 3.3 Poisson Process.- 3.4 M/M/1 Queue.- 3.5 M/M/m Queue.- 3.6 Queues with Processor Sharing Scheduling Strategy.- 3.7 Queues with Infinite Servers.- 3.8 Queues with Priority Service.- 4 Further Reading.- II Petri Nets.- 5 Place-Transit ion Nets.- 5.1 Structure of Place-Transition Nets.- 5.2 Dynamic Behaviour of Place-Transition Nets.- 5.3 Properties of Place-Transition Nets.- 5.4 Analysis of Place-Transit ion Nets.- 5.4.1 Analysis of the Reachability Set.- 5.4.2 Invariant Analysis.- 5.4.3 Analysis of Net Classes.- Analysis of State Machines.- Analysis of Marked Graphs.- Analysis of EFC-nets.- 5.4.4 Reduction and Synthesis Analysis.- 5.5 Further Remarks on Petri Nets.- 6 Coloured Petri Nets.- 7 Further Reading.- III Time-Augmented Petri Nets.- 8 Stochastic Petri Nets.- 9 Generalized Stochastic Petri Nets.- 9.1 Quantitative Analysis of GSPNs.- 9.2 Qualitative Analysis of GSPNs.- 9.2.1 Qualitative Analysis of EFC-GSPNs.- 9.3 Further Remarks on GSPNs.- 10 Queueing Petri Nets.- 10.1 Quantitative Analysis of QPNs.- 10.2 Qualitative Analysis of QPNs.- 10.2.1 Qualitative Analysis of EFC-QPNs.- 10.3 Some Remarks on Quantitative Analysis.- 11 Further Reading.- 12 Application Examples.- 12.1 Resource Sharing.- 12.2 Node of a DQDB network.- 13 Solutions to Selected Exercises.