On the Improvement of the Operational Characteristics of Single‐Server Queues by the Use of a Queue‐Length‐Dependent Service Mechanism

N. Hadidi and B. W. Conolly

Journal of the Royal Statistical Society Series C, 1969, vol. 18, issue 3, 229-240

Abstract: Complementing our earlier work (Conolly and Hadidi, 1969a, b) which showed that operational improvements could be achieved in single‐server queueing systems by correlating arrival and service patterns, this paper considers a state‐dependent service mechanism such that the probability differential of a service completion is μσn dt when the queue contains n. Arrivals occur in a Poisson stream with parameter A. Formulae are found for transient and stationary state probabilities. The waiting time process is also investigated and for σn = n +1 a comparison is made with the system previously considered, where service time is allotted to a customer in proportion to the inter‐arrival interval between him and his predecessor.

Date: 1969
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