Abstract
In this paper a hierarchical evaluation procedure for Generalized Stochastic Petri Nets (GSPN) is presented which is based on aggregation algorithms that are extensions of Flow Equivalent Aggregation (FEA) and that use transient analysis of Markov Chains. In order to aggregate a subnetwork to a substitute network we consider, as criterion for the similarity of the networks, the Subnetwork Time Distribution (STD) defined as the distribution of the time a token X needs to proceed through a subnetwork conditioned on the token distribution at the epoch of arrival of X and the context into which the net is embedded just for the experiment of determining a characteristic sojourn time distribution for token X in the subnetwork. The consideration of the second condition may be regarded as the major extension to previous work. The substitute network with the least discrepancy in Subnetwork Time Distribution to the original subnetwork is chosen as the aggregate. Several variants of the aggregation algorithm called FEAD (FEA based on Subnetwork Time Distribution) have been implemented and tested. Their performance is discussed by means of an example and they are shown to outperform Flow Equivalent Aggregation when applied to GSPN.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S.C. Agrawal, J.P. Buzen, A.W. Shum, Response Time Preservation: A General Technique for Developing Approximate Algorithms for Qeueing Networks, Performance evaluation review, vol 12, no 3, pp 63–77 1984.
S.C. Agrawal, Metamodeling: A Study of Approximations in Queuing Models, MIT Press 1985.
G. Balbo, S.C. Bruell and S. Ghanta, Combining queueing networks and generalized stochastic Petri nets for the solution of complex models of system behaviour, IEEE Trans, on Computers, vol. 37, no. 10, pp. 1251- 1268, 1988.
F. Baskett, K.M. Chandy, R.R. Müntz, F. Palacios, Open, Closed and Mixed Networks of Queues with Different Classes of Customers, Journal ACM 22(2) pp.248–260 1975.
H. Beilner, P. Buchholz and B. Müller-Clostermann, Experimente mit Ersatzdarstellungen unter Berücksichtigung der Verweilzeitverteilung, 4. GI/NTG Fachtagung, 29.9–1.10.87, Erlangen, “Messung, Modellierung u. Bewertung von Rechensystemen”.
H. Beilner, Structured Modelling — Heterogeneous Modelling, European Simulation Multiconference, Rome, Juni 1989.
K.M. Chandy, U. Herzog, L. Woo, Parametric Analysis of Qeueing Networks, IBM Journal of R. and D. 19(1) pp.36–42 1975.
J. Giglmayr, Analysis of Stochastic Petri Nets by the Decomposition of the Transition Rate Matrix, ntz Archiv, 1987, Part I: vol. 9, no. 5, pp. 115–120, Part II: vol.9, no. 6, pp. 147–151.
D. Gross, D. Miller,The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes, Operations Research Vol.32 No.2 pp. 343–361 1984.
D. Gross and C.M. Harris,Fundamentals of Queueing Theory, John Wiley & Sons, N.Y., 1985.
B.R. Haverkort and I.G. Niemegeers, Using Dynamic Queueing Networks for Performability Modelling, Proceedings of the European Simulation Multiconference, June 10–13, 1990 Nuremberg, Germany.
K. Jensen, Coloured Petri Nets and the Invariant Method, Theoretical Computer Science 14, 1981, pp.317–336.
R. Lepold, PENPET: A New Approach to Performability Modeling Using Stochastic Petri Nets, Proc. of First Int. Workshop on Performability Modelling of Computer and Communication Systems, pp. 4–19, Enschede, February 1991.
R. Marie, A. Reibman, K. Trivedi,Transient Analysis of Acyclic Markov Chains, Performance Evaluation 7(1987) pp.175–194.
M. Ajmone Marsan, G. Balbo, G. Conte, A Class of Generalized Stochastic Petri Nets for the Performance Evaluation of Multiprocessor - systems, ACM Transaction on Computer Systems, 2(2) 1984, pp.93–122.
M. Ajmone Marsan, G. Chiola, On Petri Nets with Deterministic and Exponentially Distributed Firing Times, Advances of Petri Nets 1987, ed. G. Rozenberg LNCS 266 pp.132–145, Springer 1987.
M.K. Molloy, On the Integration of Delay and Throughput Measures in Distributed Processing Models, Ph.D. Thesis, University of California, Los Angeles, 1981.
S. Natkin, Reseaux de Petri Stochastique, Ph. D. thesis CNAM-Paris, June 1980.
J. Stoer, Einführung in die Numerische Mathematik I, Springer, 4.Edition 1983.
H. Szczerbicka,A Combined Queueing Networks and Stochastic Petri Nets Approach for Evaluating the Performability of Fault-Tolerant Computer Systems, 1st Int. Workshop on Performability Modelling of Computers and Computing Systems, Feb. 7–8, 1991, Univ. Twente, The Netherlands.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Matuschka, R., Klas, G. (1991). Hierarchical Evaluation of Generalized Stochastic Petri Nets based on Subnetwork Time Distribution. In: Lehmann, A., Lehmann, F. (eds) Messung, Modellierung und Bewertung von Rechensystemen. Informatik-Fachberichte, vol 286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76934-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-76934-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54550-7
Online ISBN: 978-3-642-76934-4
eBook Packages: Springer Book Archive