Response time densities in generalised stochastic petri net models

Generalised Stochastic Petri nets (GSPNs) have been widely used to analyse the performance of hardware and software systems. This paper presents a novel technique for the numerical determination of response time densities in GSPN models. The technique places no structural restrictions on the models that can be analysed, and allows for the high-level specification of multiple source and destination markings, including any combination of tangible and vanishing markings. The technique is implemented using a scalable parallel Laplace transform inverter that employs a modified Laguerre inversion technique. We present numerical results, including a study of the full distribution of end-to-end response time in a GSPN model of the Courier communication protocol software. The numerical results are validated against simulation.

[1]  William T. Weeks,et al.  Numerical Inversion of Laplace Transforms Using Laguerre Functions , 1966, JACM.

[2]  Marco Ajmone Marsan,et al.  A class of generalised stochastic petri nets for the performance evaluation of multiprocessor systems , 1983, SIGMETRICS '83.

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

[4]  Yao Li,et al.  Performance Petri net analysis of communications protocol software by delay-equivalent aggregation , 1991, Proceedings of the Fourth International Workshop on Petri Nets and Performance Models PNPM91.

[5]  Ward Whitt,et al.  The Fourier-series method for inverting transforms of probability distributions , 1992, Queueing Syst. Theory Appl..

[6]  Wolfgang Reisig,et al.  A Primer in Petri Net Design , 1992, Springer Compass International.

[7]  William Gropp,et al.  Skjellum using mpi: portable parallel programming with the message-passing interface , 1994 .

[8]  Ward Whitt,et al.  On the Laguerre Method for Numerically Inverting Laplace Transforms , 1996, INFORMS J. Comput..

[9]  William J. Knottenbelt,et al.  Generalised Markovian analysis of timed transition systems , 1996 .

[10]  William H. Sanders,et al.  An Efficient Disk-Based Tool for Solving Very Large Markov Models , 1997, Computer Performance Evaluation.

[11]  William John Knottenbelt,et al.  Parallel performance analysis of large Markov models , 1999 .

[12]  Gianfranco Ciardo,et al.  A data structure for the efficient Kronecker solution of GSPNs , 1999, Proceedings 8th International Workshop on Petri Nets and Performance Models (Cat. No.PR00331).

[13]  N. Dingle.  Production of the Extensible Petr i Net Editor / Animator “ Medusa ” , 2001 .

[14]  Peter G. Harrison,et al.  Passage time distributions in large Markov chains , 2002, SIGMETRICS '02.

[15]  Ekkart Kindler,et al.  The Petri Net Kernel , 2003, Petri Net Technology for Communication-Based Systems.