Multiple channel queues in heavy traffic. III: random server selection

Abstract

As in [4] and [5], we study service facilities with r arrival channels and s service channels. However, here we assume that customers, immediately upon arrival, randomly select one of the s service channels. Successive customers make this choice independently, choosing server i with probability pi, p1 + · · · + ps = 1. Customers are then served by the servers they select in order of their arrival without defections. The average processing rates as well as the server selection probabilities may vary from server to server, but again we assume the r arrival channels are independent and independent of the service channels. The service channels are not independent, however, because of the random server selection. For simplicity, we only consider a single queueing system; the extension to sequences follows immediately using the argument of [5].