Controlling the GI/M/1 queue by conditional acceptance of customers

Haim Mendelson, Uri Yechiali

Research output: Contribution to journalArticlepeer-review


In this paper we consider the problem of controlling the arrival of customers into a GI/M/1 service station. It is known that when the decisions controlling the system are made only at arrival epochs, the optimal acceptance strategy is of a control-limit type, i.e., an arrival is accepted if and only if fewer than n customers are present in the system. The question is whether exercising conditional acceptance can further increase the expected long run average profit of a firm which operates the system. To reveal the relevance of conditional acceptance we consider an extension of the control-limit rule in which the nth customer is conditionally admitted to the queue. This customer may later be rejected if neither service completion nor arrival has occurred within a given time period since the last arrival epoch. We model the system as a semi-Markov decision process, and develop conditions under which such a policy is preferable to the simple control-limit rule.

Original languageEnglish
Pages (from-to)77-85
Number of pages9
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - May 1981


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