Queues with Hyper-Poisson Input and Exponential Output with Finite Waiting Space

In this paper we consider the steady-state solution of the queuing system in which (i) units arrive according to the Hyper-Poisson distribution with n branches; (ii) the queue discipline is first-come, first-served; and (iii) the service time distribution is exponential. Assuming a finite waiting space, we derive the system-size distribution and the mean number of units therefrom. Results are also deduced when an infinite queue is allowed. Another interesting case is discussed when the over-all arrival rate for all the n branches is pre-assigned. Towards the end we study the simple case when no queue is allowed.