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On the Improvement of the Operational Characteristics of Single‐Server Queues by the Use of a Queue‐Length‐Dependent Service Mechanism
Author(s) -
Hadidi N.,
Conolly B. W.
Publication year - 1969
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346583
Subject(s) - computer science , queue , service (business) , queueing theory , poisson distribution , interval (graph theory) , computer network , real time computing , state dependent , state (computer science) , algorithm , mathematics , statistics , economy , mathematical economics , combinatorics , economics
Summary 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 μσ n 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 σ n = 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.