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Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

  • Xiuli Chao (a1) and Masakiyo Miyazawa (a2)


In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.


Corresponding author

Postal address: New Jersey Institute of Technology, Newark, NJ 07102, USA.
∗∗ Postal address: Science University of Tokyo Noda, Chiba 278, Japan.


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Boucherie, R. J. and van Dijk, N. M. (1994). Local balances in queueing networks with positive and negative customers. Ann. Operat. Res. 48, 463492.
Chao, X. (1994). A note on queueing networks with signals and random triggering times. Probability in the Engineering and Informational Sciences, 8, 213219.
Chao, X. (1995). Networks of queues with customers, signals and arbitrary service time distributions. Operat. Res. 43, 537544.
Chao, X. and Miyazawa, M. (1998). On quasi-reversibility and local balance: an alternative derivation of product form results. Operat. Res. 46, 927933. A probabilistic decomposition approach to quasi-reversibility and its applications in coupling of queues, preprint.
Chao, X. and Pinedo, M. (1993). On generalized networks of queues with positive and negative arrivals. Prob. Eng. Inf. Sci. 7, 301334.
Chao, X. and Pinedo, M. (1995). Networks of queues with batch services, signals, and product form solutions. Operat. Res. Lett. 17, 237242.
Chao, X., Miyazawa, M., Serfozo, R. and Takada, H. (1998). Markov network processes with product form stationary distributions. Queueing Systems 28, 377403.
Chao, X., Miyazawa, M. and Pinedo, M. (1999). Queueing Networks: Customers, Signals, and Product Form Solutions. John Wiley, Chichester, UK.
Dembo, A. and Zeitouni, O. (1993). Large Deviation Techniques and Applications. Jones and Bartlett, Boston, MA.
Gelenbe, E. (1991). Product-form queueing networks with negative and positive customers. J. Appl. Prob. 28, 656663.
Gelenbe, E. (1993). G-networks with triggered customer movement. J. Appl. Prob. 30, 742748.
Henderson, W. and Taylor, P. G. (1990) Product form in networks of queues with batch arrivals and batch services, Queueing Systems 6, 71–88.
Henderson, W. (1993). Queueing networks with negative customers and negative queueing lengths. J. Appl. Prob. 30, 931942.
Henderson, W. and Taylor, P. G. (1999). State-dependent coupling of quasireversible nodes. To appear in Queueing Systems.
Henderson, W., Northcote, B. S. and Taylor, P. G. (1994a). Geometric equilibrium distributions for queues with interactive batch departures. Ann. Operat. Res. 48, 463492.
Henderson, W., Northcote, B. S. and Taylor, P. G. (1994b). State-dependent signaling in queueing networks. Adv. Appl. Prob. 26, 436455.
Henderson, W., Pearce, C. E. M., Pollett, P. K. and Taylor, P. G. (1992). Connecting internally balanced quasireversible Markov processes. Adv. Appl. Prob. 24, 934959.
Kelly, F. P. (1979). Reversibility and Stochastic Networks. John Wiley, New York.
Kelly, F. P. (1982). Networks of quasi-reversible nodes. In Applied Probability–Computer Science: The Interface, Vol. I, eds Disney, R. L. and Ott, T. J., pp. 326. Birkhauser, Boston, MA.
Miyazawa, M. (1996). Stochastic bound and stability of discrete-time Jackson networks with batch movements. In Stochastic Networks: Stability and Rare Events, eds Glasserman, P., Sigman, K. and Yao, D. (Lecture Notes in Statist. 117). Springer, New York.
Miyazawa, M. and Taylor, P. G. (1997). A geometric product-form distribution for a queueing network with nonstandard batch arrivals and batch transfers. Adv. Appl. Prob. 29, 523544.
Serfozo, R. F. and Yang, B. (1998). Markov network processes with string transitions. Ann. Appl. Prob. 8, 793821.
Stoyan, D. (1983). Comparison Methods for Queues and Other Stochastic Models. John Wiley, New York.
Walrand, J. (1988). An Introduction to Queueing Networks. Prentice Hall, New Jersey.
Whittle, P. (1986). Systems in Stochastic Equilibrium. John Wiley, New York.


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