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Networks of queues with batch services and customer coalescence

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


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.


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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