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Networks of queues with batch services and customer coalescence

  • Xiuli Chao (a1), Michael Pinedo (a2) and Dequan Shaw (a3)

Abstract

Consider a queueing network with batch services at each node. The service time of a batch is exponential and the batch size at each node is arbitrarily distributed. At a service completion the entire batch coalesces into a single unit, and it either leaves the system or goes to another node according to given routing probabilities. When the batch sizes are identical to one, the network reduces to a classical Jackson network. Our main result is that this network possesses a product form solution with a special type of traffic equations which depend on the batch size distribution at each node. The product form solution satisfies a particular type of partial balance equation. The result is further generalized to the non-ergodic case. For this case the bottleneck nodes and the maximal subnetwork that achieves steady state are determined. The existence of a unique solution is shown and stability conditions are established. Our results can be used, for example, in the analysis of production systems with assembly and subassembly processes.

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Corresponding author

Postal address: Division of Industrial and Management Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA.
∗∗ Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA.
∗∗∗ Postal address: GTE Laboratories, 40 Sylvan Road, Waltham, MA 02254, USA.

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Research partially supported by the NSF under grant DDM-9209526.

Research partially supported by the NSF under grant ECS 91–14689.

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References

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