Tandem queue with group arrivals and no intermediate buffer

The paper studies a system with two single-server stations in series. There is an infinite buffer in front of the first station and no buffer between the two stations. The customers come in groups; the groups contain random numbers of customers and arrive according to a Poisson process. Assuming general service time distributions at the two stations, the paper derives the Laplace transform and the recursive formula for the moments of the total time spent in the tandem system (waiting time in the system) by an arbitrary customer. From the Laplace transform, it concludes that the optimal order of the servers for minimizing the waiting time in the system does not depend on the group size.