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On Flows in Stochastic Marked Graphs

Published online by Cambridge University Press:  27 July 2009

F. Baccelli ,
N. Bambos  and
J. Walrand
F. Baccelli
Affiliation:
INRIA Sophia Antipolis Valbonne 06565, France
N. Bambos
Affiliation:
Department of Electrical EngineeringUniversity of California, Los Angeles, California 90024
J. Walrand
Affiliation:
Department of Electrical Engineering and Computer ScienceUniversity of California, Berkeley, California 94720
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Abstract

In this work, the discrete event systems called Stochastic Marked Graphs (SMGs) are investigated from a stability point of view. Being a special class of Timed Petri Nets with stochastic firing times, they are studied under general assumptions of stationarity and ergodicity of the firing times and ergodicity of flows of their free strongly connected components. The values of the flows of tokens in an SMG are specified as functions of the intrinsic rates of its free strongly connected components, and various stability issues are discussed.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 2 , April 1991 , pp. 145 - 157
Copyright
Copyright © Cambridge University Press 1991

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References

Baccelli, F. (1989). Ergodic theory of stochastic Petri networks. Rapport INRIA No. 1037 (to appear in the Annals of Probability).Google Scholar
Baccelli, F. & Bremaud, P. (1987). Palm probabilities and stationary queues. Lecture Notes in Statistics, 41. New York: Springer-Verlag.Google Scholar
Commoner, F., Holt, A., Even, S. & Pnueli, A. (1971). Marked directed graphs. Journal of Computer and System Sciences, 5.CrossRefGoogle Scholar
Florin, G. & Natkin, S. (1985). On open synchronized queueing networks. International Workshop on Timed Petri Nets. Torino, Italy, 07.Google Scholar
Karp, R. & Miller, R. (1966). Properties of a model for parallel computations: Determinancy, termination, queueing. SIAM Journal of Applied Mathematics 14(6).CrossRefGoogle Scholar
Murata, T. (1977). Circuit theoretic analysis and synthesis of marked graphs. IEEE Transactions on Circuits and Systems, 24(17).Google Scholar
Peterson, J. (1977). Petri nets. Computing Surveys 9(3).Google Scholar
Ramamoorthy, C. & Ho, G. (1980). Performance evaluation of asynchronous concurrent systems using Petri nets. IEEE Transactions of Software Engineering 6(5).Google Scholar
Reiter, R. (1968). Scheduling parallel computations. Journal of the Association of Computing Machinery 15(4).CrossRefGoogle Scholar
Walrand, J. (1988). An introduction to queueing networks. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Baccelli, F., Bambos, N. & Walrand, J. (1989). Flow analysis of stochastic marked graphs. Proceedings of the IEEE Conference on Decision and Control, 12, Tampa, FL.Google Scholar