Sojourn and Waiting Times in a Single-Server System with State-Dependent Mean Service Rate
01 July 1989
A birth-death queueing system with a single server, first-come first-served discipline, Poisson arrivals and state-dependent mean service rate is considered. The problem of determining the equilibrium densities of the sojourn and waiting times is formulated, in general. The particular case in which the mean service rate has one of two values, depending on whether or not the number of customers in the system exceeds a prescribed threshold, is then investigated. A generating function for the Laplace transforms of the densities of the sojourn and waiting times is derived. Explicit expressions for the second moments of the sojourn and waiting times are obtained.