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.
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