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A Sequence of Service Stations with Arbitrary Input and Regular Service Times

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  • B. Avi-Itzhak

    (Cornell University, Ithaca, New York)

Abstract

In a queuing system with an ordered sequence of stations, the arrivals process is arbitrary and service times are regular at all stations. The case where each station consists of the same number of servers in parallel and the service times at all servers belonging to one station are the same is investigated and shown to possess the following properties: (a) The time spent in the system by any customer is independent of the order of the stations and of the allowable sizes of the intermediate queues; (b) The waiting time (not including service) of any customer equals the time the same customer would have been waiting in the queue of a single station system with regular service time, equaling the longest service time of the sequence (assuming the same arrivals process in both systems). These properties enable one to obtain waiting time distributions and other characteristics of such queuing processes.

Suggested Citation

  • B. Avi-Itzhak, 1965. "A Sequence of Service Stations with Arbitrary Input and Regular Service Times," Management Science, INFORMS, vol. 11(5), pages 565-571, March.
    • Handle: RePEc:inm:ormnsc:v:11:y:1965:i:5:p:565-571
    DOI: 10.1287/mnsc.11.5.565
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    Cited by:

    1. Rhee, Young & Perros, Harry G., 1996. "Analysis of an open tandem queueing network with population constraint and constant service times 1," European Journal of Operational Research, Elsevier, vol. 92(1), pages 99-111, July.
    2. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    3. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    4. Benjamin Avi-Itzhak & Hanoch Levy, 2001. "Buffer Requirements and Server Ordering in a Tandem Queue with Correlated Service Times," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 358-374, May.

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