Control Policies for the MX/G/1 Queueing System

• Published in: Management science Vol. 35; no. 6; pp. 708 - 721
• Main Authors: Lee, Hyo-Seong, Srinivasan, Mandyam M
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.06.1989; Institute of Management Sciences; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Algebra; Applied sciences; batch arrival queueing systems; Cost efficiency; Cost structure; Exact sciences and technology; Mathematical moments; Minimization of cost; Network servers; Operational research and scientific management; Operational research. Management science; optimal control; Queuing theory. Traffic theory; Random variables; server vacation models; Start up firms; Unit costs; Vacations; Queue length; Batch mode; Control method; Server vacation; Poisson distribution; Queue; Waiting time; Optimization; Stationary condition; Queuing system
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.35.6.708

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.