Throughput analysis of simple closed timed Petri net models

Zuberek, W.M.

Proc. 36-th Midwest Symposium on Circuits and Systems; Detroit, MI, 1993, pp.930-933.

Abstract:

It is shown that for some classes of closed timed Petri net models the steady-state behavior can be determined on the basis of structural properties only (i.e., without reachability analysis), using the concept of throughput and simple rules of operational analysis. Throughput analysis is based on the average values of firing times rather than firing time distribution functions, so the same approach can be used to a variety of net models. Bounded as well as unbounded (but ergodic) net models can be analyzed by the proposed approach.

Keywords:

Timed Petri nets, steady-state behavior, throughput, operational analysis. performance analysis.

References:

• M. Ajmone Marsan, G. Conte, G. Balbo, "A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems"; ACM Trans. on Computer Systems, vol.2, no.2, pp.93-122, 1984.
• S.C. Bruell, S. Ghanta, "Throughput bounds for generalized stochastic Petri net models"; Proc. Int. Workshop on Timed Petri Nets, Torino, Italy, pp.250-261, 1985.
• J.P. Buzen, "Fundamental operational laws of computer system performance"; Acta Informatica, vol.7, no.2, pp.167-182, 1976.
• J. Campos, G. Chiola, J.M. Colom, M. Silva, "Tight polynomial bounds for steady-state performance of marked graphs"; Proc. Int. Workshop on Petri Nets and Performance Models, Kyoto, Japan, pp.200-209, 1989.
• G. Ciardo, J. Muppala, K. Trivedi, "SPNP - stochastic Petri net package"; Proc. Int. Workshop on Petri Nets and Performance Models, Kyoto, Japan, pp.142-151, 1989;
• P.J. Denning, J.P. Buzen, "The operational analysis of queueing network models"; ACM Computing Surveys, vol.10, no.3, pp.225-261, 1978.
• J.B. Dugan, A. Bobbio, G. Ciardo, K. Trivedi, "The design of a unified package for the solution of stochastic Petri net models"; Proc. Int. Workshop on Timed Petri Nets, Torino, Italy, pp.6-13, 1985.
• D. Ferrari, G. Serazzi, A. Zeigner, Measurement and tuning of computer systems; Prentice-Hall 1983.
• M.A. Holliday, "Deterministic time and analytical models of parallel architectures"; Ph.D. Thesis, Computer Science Department, University of Wisconsin - Madison, Technical Report #652, 1986.
• P.J.B. King, Computer and communication systems performance modelling; Prentice-Hall 1990.
• T. Murata, "Petri nets: properties, analysis and applications"; Proceedings of IEEE, vol.77, no.4, pp.541-580, 1989.
• S. Natkin, "Les reseaux de Petri stochastique"; These de Docteur Ingenieur, CNAM, Paris, France, 1980.
• C. Ramchandani, "Analysis of asynchronous concurrent systems by timed Petri nets"; Project MAC Technical Report MAC-TR-120, Massachusetts Institute of Technology, Cambridge MA, 1974.
• W. Reisig, Petri nets - an introduction; Springer-Verlag 1985.
• J. Sifakis, "Use of Petri nets for performance evaluation"; in Measuring, modelling and evaluating computer systems, pp.75-93, North-Holland 1977.
• W.M. Zuberek, "M-timed Petri nets, priorities, preemptions, and performance evaluation of systems"; in Advances in Petri Nets 1985 (Lecture Notes in Computer Science 222), G. Rozenberg (ed.), pp.478-498, Springer-Verlag 1986.
• W.M. Zuberek, "D-timed Petri nets and modelling of timeouts and protocols"; Transactions of the Society for Computer Simulation, vol.4, no.4, pp.331-357, 1988.
• W.M. Zuberek, "Throughput analysis in timed Petri nets"; Proc. Midwest Symp. on Circuits and Systems, Washington DC, pp.1576-1580, 1992.