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A Result on Networks of Queues with Customer Coalescence and State-Dependent Signaling

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Xiuli Chao  and
Shaohui Zheng
Xiuli Chao*
Affiliation:
New Jersey Institute of Technology
Shaohui Zheng*
Affiliation:
Hong Kong University of Science and Technology
*
∗Postal address: Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA
∗∗Postal address: Department of Information and Systems Management, School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
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Abstract

In this paper we consider a network of queues with batch services, customer coalescence and state-dependent signaling. That is, customers are served in batches at each node, and coalesce into a single unit upon service completion. There are signals circulating in the network and, when a signal arrives at a node, a batch of customers is either deleted or triggered to move as a single unit within the network. The transition rates for both customers and signals are quite general and can depend on the state of the whole system. We show that this network possesses a product form solution. The existence of a steady state distribution is also discussed. This result generalizes some recent results of Henderson et al. (1994), as well as those of Chao et al. (1996).

Keywords

Networks of queuessignalspartial balancecustomer coalescenceproduct form solution

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 151 - 164
Copyright
Copyright © Applied Probability Trust 1998 

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References

Boucherie, R.J., and van Dijk, N.M. (1991). Product form for queueing networks with state dependent multiple job transitions. Adv. Appl. Prob. 23, 152–187.CrossRefGoogle Scholar
Chao, X., and Pinedo, M. (1993). On generalized networks of queues with positive and negative arrivals. Prob. Eng. Inf. Sci. 7, 301–334.Google Scholar
Chao, X., Pinedo, M., and Shaw, D. (1996). Networks of queues with batch services and customer coalescence. J. Appl. Prob. 33, 858–869.Google Scholar
Gelenbe, E. (1991). Product form networks with negative and positive customers. J. Appl. Prob. 28, 656–663.CrossRefGoogle Scholar
Henderson, W. (1993). Queueing networks with negative customers and negative queue lengths. J. Appl. Prob. 30, 931–942.CrossRefGoogle Scholar
Henderson, W., Northcote, B.S., and Taylor, P.G. (1994). State dependent signalling in queueing networks. Adv. Appl. Prob. 26, 436–455.Google Scholar
Henderson, W., and Taylor, P.G. (1989). Insensitivity of processes with interruptions. J. Appl. Prob. 26, 242–258.CrossRefGoogle Scholar
Henderson, W., and Taylor, P.G. (1990). Product form in networks of queues with batch arrivals and batch services. QUESTA 6, 71–88.Google Scholar
Miyazawa, M., and Wolff, R. (1996). Symmetric queues with batch departures and their networks. Adv. Appl. Prob. 28, 308–326.Google Scholar
Schauder, J. (1930). Der Fixpunktsatz in Funktionalraumen. Studia Math. 2, 171–180.CrossRefGoogle Scholar
Serfozo, R. (1989). Markovian network processes: congestion dependent routing and processing. QUESTA 5, 5–36.Google Scholar