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G-Networks with Signals and Batch Removal

Published online by Cambridge University Press:  27 July 2009

Erol Gelenbe
Erol Gelenbe
Affiliation:
Duke University, Department of Electrical EngineeringDurham, North Carolina 27706
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Abstract

We consider queueing networks containing customers and signals that were recently introduced in Gelenbe [4]. Both customers and signals can be exogenous or can be obtained by a Markovian transition of a customer after service. A signal entering a queue forces a customer to move on to another queue according to a Markovian routing rule or to leave the network in batch mode. This synchronized or triggered motion is useful in representing the effect of tokens in Petri-nets, for systems in which customers and work can be instantaneously moved from one queue to the other on the arrival of a signal as well as for other network behaviors that are encountered in parallel computer system modelling. We show that this network has product form stationary solution and establish the non-linear customer flow equations that govern it. Network stability is discussed in this new context.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 3 , July 1993 , pp. 335 - 342
Copyright
Copyright © Cambridge University Press 1993

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References

1.Baskett, F., Chandy, K.M., Muntz, R.R., & Palacios, F.G. (1975). Open, closed and mixed networks of queues with product form. Journal of the Association for Computing Machines 22(2): 248–260.CrossRefGoogle Scholar
2.Gelenbe, E. (to appear). Non-linear resolvents for very large linear systems. In Proceedings of the Institute for Mathematics and Its Applications Workshop on Numerical Methods in Markov Chains, 01 1991, University of Minnesota, Minneapolis.Google Scholar
3.Gelenbe, E. (1991). Product form queueing networks with negative and positive customers. Journal of Applied Probability 28: 656–663.CrossRefGoogle Scholar
4.Gelenbe, E. (to appear). G-networks with triggered customer movement. Journal of Applied Probability, September 1993.CrossRefGoogle Scholar
5.Gelenbe, E., Glynn, P., & Sigman, K. (1991). Queues with negative arrivals. Journal of Applied Probability 28: 245–250.CrossRefGoogle Scholar
6.Gelenbe, E. & Mitrani, I. (1980). Analysis and synthesis of computer systems. London and New York: Academic Press.Google Scholar
7.Gelenbe, E. & Schassberger, R. (1992). Stability of G-networks. Probability in the Engineering and Informational Sciences 6: 271–276.CrossRefGoogle Scholar
8.Kemeny, J.G. & Snell, J.L. (1965). Finite Markov chains. Princeton, NJ: Van Nostrand.Google Scholar