Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers

We investigate the stability condition of a multiserver queueing system. Each customer needs simultaneously a random number of servers to complete the service. The times taken by each server are independent. The input flow is assumed to be a regenerative one. The service time has an exponential, phase-type or hyper-exponential distribution. The stability criteria for the models are established. It turns out that the stability conditions do not depend on the structure of the input flow, but only on the rate of the process. However, the distribution of the service times is a very important factor. We give examples which show that the stability condition cannot be expressed only in terms of the mean of the service time.