Control Policies for the M X /G/1 Queueing System

Hyo-Seong Lee and Mandyam M. Srinivasan
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Mandyam M. Srinivasan: Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2117

Management Science, 1989, vol. 35, issue 6, 708-721

Abstract: The M X /G/1 queueing system is studied under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the length of the queue every time an arrival occurs. When the queue length reaches, or exceeds, a pre-specified value m for the first time, the server is turned on and serves the system until it is empty. (2) At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length is greater than, or equal to, a pre-specified value m at this time, he begins to serve the system until it is empty. For both cases, the mean waiting time of an arbitrary customer for a given value of m is derived, and the procedure to find the stationary optimal policy under a linear cost structure is presented.

Keywords: batch arrival queueing systems; optimal control; server vacation models (search for similar items in EconPapers)
Date: 1989
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