Comparison of queueing systems with various rules of service and regenerative input flow
We study stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service time is the same on all occupied servers and equals a constant τ . Discipline is FIFO. We define an auxiliary service process Z(t) that is the number of completed services by all m servers during the time interval (0, t) under the assumption that there are always customers in the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. It allows us to deduce the stability condition of the model under consideration. We compare this stability condition with the stability conditions of the systems where service time has an exponential, phase-type or hyper-exponential distribution.