Finite capacity assembly-like queues

In assembly lines, service involves assembling units coming from more than one source. In queue terminology, we may consider this situation as one in which service is rendered only to groups of customers — one from each class. In this paper we give procedures to determine response time characteristics of such a system under Markovian assumptions when a finite capacity restriction is imposed. This restriction is imposed to reflect reality as well as to make analysis tractable. In the course of this study, we also give a recursive technique to determine the distribution of the time taken for a specific number of departures in a Poisson queue from an arbitrary initial state. We demonstrate that this distribution is related to the response time distribution of the assembly-like queue. We believe that this procedure will also be of independent interest.