Abstract
A birth-death queueing system with asingle server, first-come first-served discipline, Poisson arrivals and mean service rate which depends linearly on the number of customers in the system, is considered. Explicit expressions are derived for the equilibrium densities of the sojourn and waiting times. Simple approximations to the densities, including the first order correction terms, are obtained in a heavy-traffic situation.
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J.A. Morrison, Sojourn and waiting times in a single-server system with state-dependent mean service rate, Queueing Systems 4 (1989) 211–234.
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Morrison, J.A. Single server with linear state-dependent mean rate. Queueing Syst 4, 237–248 (1989). https://doi.org/10.1007/BF02100268
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DOI: https://doi.org/10.1007/BF02100268