Heterogeneous multiserver queues with general input

A queueing system with heterogeneous servers and general input is analyzed. In particular, it is shown how to obtain the steady state probabilities for such a system, both at random–times and at the times preceding an arrival. If more than one server is idle, an arrival has the choice how to select one of the idle servers. The rules used to do the selection are part of the model description. The probabilities at arrival points are found as follows. First, one determines the probabilities 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 waiting time distribution, and the distribution of the number in the system at random epochs. Heuristic arguments, supported by numerical calculations, show that the importance of selecting a server increases with decreasing traffic intensity, increasing number of servers, and decreasing variation between interarrival times.