OPTIMAL BERNOULLI ROUTING IN AN UNRELIABLE M/G/1 RETRIAL QUEUE

Abstract

Recently, Sherman et al. [14] analyzed an M/G/1 retrial queuing model in which customers are forced to retry their service if interrupted by a server failure. Using classical techniques, they provided a stability analysis, queue length distributions, key performance parameters, and stochastic decomposition results. We analyze the system under a static Bernoulli routing policy that routes a proportion of arriving customers directly to the orbit when the server is busy or failed. In addition to providing the key performance parameters, we show that this system exhibits a dual stability structure, and we characterize the optimal Bernoulli routing policy that minimizes the total expected holding costs per unit time.