Accession Number : ADA322409

Title :   Discrete Deterministic and Stochastic Petri Nets.

Descriptive Note : Contractor rept.,

Corporate Author : INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA

Personal Author(s) : Zijal, Robert ; Ciardo, Gianfranco

PDF Url : ADA322409

Report Date : DEC 1996

Pagination or Media Count : 26

Abstract : Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

Descriptors :   *MATHEMATICAL MODELS, *MARKOV PROCESSES, *STOCHASTIC CONTROL, ALGORITHMS, TIME DEPENDENCE, PROBABILITY DISTRIBUTION FUNCTIONS, SYSTEMS ANALYSIS, EXPONENTIAL FUNCTIONS, APPLIED MATHEMATICS, DETERMINANTS(MATHEMATICS).

Subject Categories : Statistics and Probability
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE