Queues in Series

Abstract

It has been demonstrated in this paper how Lindley's analytical method of solving the integral equation for the waiting-time distribution in a queue with a single server can be extended to obtain the waiting-time distribution in different queues, when queues are in series and each queue has a single server. The input has been taken as Poisson, but the service time has been assumed to follow a gamma distribution in the first queue and an exponential distribution in the second queue.