System sizes in infinite server queues with constant service times

This paper gives explicit expressions for the generating functions of the continuous time and pre-arrival system size processes in an infinite server batch arrival system with a constant service time. By specifying the input processes, explicit distribution functions can be obtained for some special cases. The paper also discusses the relation between the two system size processes and makes some interesting observations. Transient behaviour and the speed at the system size processes approach steady state are discussed.