Sojourn And Waiting Times In A System In Which The Server Has Two Mean Rates

Earlier we considered a birth-death queueing system with a single server, first-come first-served discipline and Poisson arrivals. 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. A generating function for the Laplace transforms of the equilibrium densities of the sojourn and waiting times was derived. In this paper the generating function is used to obtain explicit expressions for the Laplace transforms of the densities of the sojourn and waiting times, and it is shown below to invert these Laplace transforms. It is also shown how to invert the Laplace transform of the generating function. Both procedures lead to explicit expressions for the densities of the sojourn and waiting times, and their relative merits are pointed out.