Sojourn and Waiting Times in a Single-Server System with Service Rate depending Linearly on the Number of Customers
01 January 1988
A birth-death queueing system with a single server, first-come first-served discipline, unlimited queue size, Poisson arrivals and service rate mu sub i = (sigma + i) mu, where sigma > -1, when there are i> 1 customers in the system, is considered. Explicit expressions are derived for the equilibrium densities of the sojourn and waiting times.