HETEROGENEOUS MULTISERVER QUEUES WITH GENERAL INPUT

A queueing system with heterogeneous servers and general input is anal yzed. In particular, it is shown how to obtain the steady state probab ilities for such a system, both at random-times and at the times prece ding an arrival. If more than one server is idle, an arrival has the c hoice how to select one of the idle servers. The rules used to do the selection are part of the model description. The probabilities at arri val points are found as follows. First, one determines the probabiliti es for all states in which there is no queue, and then one calculates the probabilities in which customers are waiting. The probabilities at arrival epochs allow one to find the probability of no wait, the wait ing time distribution, and the distribution of the number in the syste m at random epochs. Heuristic arguments, supported by numerical calcul ations, show that the importance of selecting a server increases with decreasing traffic intensity, increasing number of servers, and decrea sing variation between interarrival times.