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G-networks by triggered customer movement

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Erol Gelenbe
Erol Gelenbe*
Affiliation:
Duke University
*
∗ Postal address: Department of Electrical Engineering, Duke University, Durham, NC 27706, USA.
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Abstract

The generalized queueing networks (G-networks) which we introduce in this paper contain customers and signals. Both customers and signals can be exogenous, or can be obtained by a Markovian movement of a customer from one queue to another after service transforming itself into a signal or remaining a customer. A signal entering a queue forces a customer to move instantaneously to another queue according to a Markovian routing rule, or to leave the network, while customers request service. This synchronised or triggered motion is useful in representing the effect of tokens in Petri nets, in modelling systems in which customers and work can be instantaneously moved from one queue to the other upon certain events, and also for certain behaviours encountered in parallel computer system modelling. We show that this new class of network has product-form stationary solution, and establish the non-linear customer flow equations which govern it. Network stability is discussed in this new context.

Keywords

PRODUCT FORMINSTANTANEOUS CUSTOMER MOTIONSYNCHRONISED MOTION

MSC classification

Primary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 3 , September 1993 , pp. 742 - 748
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

This research was supported by the ESPRIT QMIPS Project, and by the Distributed Algorithms Section of C3-CNRS (French National Program on Parallelism and Concurrency).

References

Baskett, F., Chandy, K. M, Muntz, R. R. and Palacios, F. G. (1975) Open, closed and mixed networks of queues with product form. J. Assoc. Comput. Math. 22, 248–260.Google Scholar
Gelenbe, E. (1991) Product form queueing networks with negative and positive customers. J. Appl. Prob. 28, 656–663.Google Scholar
Gelenbe, E. and Mitrani, I. (1980) Analysis and Synthesis of Computer Systems. Academic Press, London.Google Scholar
Gelenbe, E. and Schassberger, R. (1992) Stability of G-networks. In Probability and its Applications in Engineering and the Information Sciences. Cambridge University Press.Google Scholar
Gelenbe, E., Glynn, P. and Sigman, K. (1991) Queues with negative arrivals. J. Appl. Prob. 28, 245–250.Google Scholar
Kemeny, J. G. and Snell, J. L. (1965) Finite Markov Chains. Van Nostrand, Princeton, NJ.Google Scholar