GSPM models: sensitivity analysis and applications

Sensitivity analysis of continuous time Markov chains has been considered recently by several re­ searchers. This is very useful in performing bottle­ neck analysis and optimization on systems especially during the design stage. However the construction of these large and complex Markov models is tedious and error-prone process. Generalized Stochastic Petri Nets (GSPN) provide a very useful high-level inter­ face for the automatic generation of the underlying Markov chain. This paper extends parametric sensi­ tivity analysis to GSPN models. The rates and proba­ bilities of the transitions of GSPN models are defined as functions of an independent variable. Equations for the sensitivity analysis of steady-state and transient measures of GSPN and GSPN reward models are de­ veloped and implemented in a software package. An example illustrating the use of sensitivity analysis is presented.

[1]  Kishor S. Trivedi,et al.  Reliability Modeling Using SHARPE , 1987, IEEE Transactions on Reliability.

[2]  Kishor S. Trivedi,et al.  Transient analysis of cumulative measures of markov model behavior , 1989 .

[3]  John F. Meyer,et al.  Closed-Form Solutions of Performability , 1982, IEEE Transactions on Computers.

[4]  Kishor S. Trivedi,et al.  Transient Analysis of Acyclic Markov Chains , 1987, Perform. Evaluation.

[5]  Philip Heidelberger,et al.  Sensitivity Analysis of Continuous Time Markov Chains Using Uniformization , 1987, Computer Performance and Reliability.

[6]  Kishor S. Trivedi,et al.  Numerical transient analysis of markov models , 1988, Comput. Oper. Res..

[7]  Michael K. Molloy.  Performance Analysis Using Stochastic Petri Nets , 1982, IEEE Transactions on Computers.

[8]  Mark Kelly Smotherman.  Parametric error analysis and coverage approximations in reliability modeling (sensitivity) , 1984 .

[9]  Ronald A. Howard,et al.  Dynamic Probabilistic Systems , 1971 .

[10]  Gregory K. Miller,et al.  Elements of Applied Stochastic Processes , 1972 .

[11]  K. Grace,et al.  Probabilistic Reliability: An Engineering Approach , 1968 .

[12]  Kishor S. Trivedi,et al.  Performability Analysis: Measures, an Algorithm, and a Case Study , 1988, IEEE Trans. Computers.

[13]  Kishor S. Trivedi,et al.  The hybrid automated reliability predictor , 1986 .

[14]  Kishor S. Trivedi,et al.  Sensitivity analysis of reliability and performability measures for multiprocessor systems , 1988, SIGMETRICS 1988.

[15]  Kishor S. Trivedi,et al.  SPNP: stochastic Petri net package , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.

[16]  Marco Ajmone Marsan,et al.  A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems , 1984, TOCS.

[17]  Stephen S. Lavenberg,et al.  Computer Performance Modeling Handbook , 1983, Int. CMG Conference.

[18]  Kishor S. Trivedi,et al.  Performability Modeling Based on Real Data: A Case Study , 1988, IEEE Trans. Computers.

[19]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[20]  Kishor S. Trivedi,et al.  Performance and Reliability Analysis Using Directed Acyclic Graphs , 1987, IEEE Transactions on Software Engineering.

[21]  J. C. Cluley,et al.  Probabilistic Reliability: an Engineering Approach , 1968 .