On the Waiting-Time Distribution for Queues in Series

Abstract

Suppose that customers leaving a queueM/E2/1 immediately join another single-server queue in which the service-time is negative exponential: it will be shown that in equilibrium (if it is possible) the characteristic function of the waiting-time in the second queue is not meromorphic. This is somewhat surprising, and disagrees with a result of Ghosal (1962). If the first queue is of the typeE2/M/1 a similar though weaker result is obtained.