On the ergodic distribution of oscillating queueing systems (Q1430559)

The authors consider a single-server queueing system with infinite waiting room, in which the interarrival-time distributions and service-time distributions alternate between two types. The switching points are determined by the time points at which the number of customers in the system reaches a level \(b\) from below and a level \(a<b\) from above. Conditions are given under which the queue length process has a limit distribution. In the special case of exponentially distributed service times and a single interarrival-time distribution, the ergodic distribution is given explicitly.