Reduction Methods for Tandem Queuing Systems

Henry D. Friedman
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Henry D. Friedman: Sylvania Electronic Systems, Waltham, Massachusetts

Operations Research, 1965, vol. 13, issue 1, 121-131

Abstract: A tandem stage queuing system has n stages A 1 , A 2 , …, A n in series, where stage A i consists of m i parallel channels each having the same constant service time s i . In addition, one of the stages may be a single-channel stage A j having variable service times that are always ≧ s i / m i for i ≠ j . Customers arrive at the first stage and proceed through the stages, in order, on a first-come, first-served, unlimited queuing basis. For any sequence of customer arrival times, the time spent in the system by each customer is independent of the order of the stages. It follows that certain steady-state and time- and customer-dependent problems for the system and for its stages, involving waiting time, queue length, and busy period, can for any interarrival distribution be reduced to corresponding problems for a system of fewer stages, possibly a single stage.

Date: 1965
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