Batch arrivals to a tandem queue without an intermediate buffer

Abstract

In this paper we study a system with two stations in tandem.There is an infinite buffer in front of the first station and no buffer between the two stations. The customers come in batches; the batches contain random numbers of customers and arrive according to a Poisson process. Assuming arbitrary service time distributions at the two stations, we derive an expression for the expected time in system and discuss various properties of the expression.