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Order restoration in queues

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Abstract

We examine a class of problems in queueing networks which arise when customers enter a bank of parallel servers in a given order and lose their place in the sequence due to passing resulting from variations in service times. The original sequence is required before service can take place at the next station in the network. These problems arise naturally in flexible manufacturing systems. The result is that the next station beyond the parallel bank of servers can be approximated by a non-Markovian bulk arrival system. This station sees batch arrivals of customers that are eligible to receive service. The size of the arriving batches is shown to depend on the inter-arrival times. Several fundamental results are established for this class of problems including the distribution of batch inter-arrival times, batch sizes, and an approximate method for determining the distribution of the number of eligible and an exact method for determining the distribution of the number of ineligible customers in the system.

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Authors and Affiliations

  1. American Airlines Decision Technologies, MD 4462, P.O. Box 619616, 75261-9616, Dallas/Fort Worth Airport, TX, USA

    N. Venkatasubramanyan

  2. Department of Industrial Engineering, University of Wisconsin-Madison, 1513 University Avenue, 53706, Madison, WI, USA

    J. L. Sanders

Authors
  1. N. Venkatasubramanyan
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  2. J. L. Sanders
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Venkatasubramanyan, N., Sanders, J.L. Order restoration in queues. Queueing Syst 12, 409–429 (1992). https://doi.org/10.1007/BF01158811

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  • DOI: https://doi.org/10.1007/BF01158811

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