Batch arrivals to a tandem queue without an intermediate buffer

In this paper the authors 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, the authors derive an expression for the expected time in system and discuss various properties of the expression.