Remarks on the hypercube model

Abstract

Consider a generalization of the Hypercube queueing model for exponential queueing systems which allows for distinguishable servers and multiple types of customers. The determination of the assignment policy which minimizes the long-run average number of lost customers and the expected discounted cost (if a cost structure is imposed in the model) is always formulated as a Markov decision problem. It is natural to conjecture that the full-service policy (the policy always using the highest effective service rate) is optimal. Some authors intend to prove the optimality of the full-service policy by analyzing a Markov decision chain. In this paper, we propose some modifications about this. Also, a new proof of the full-service policy which minimizes the long-run average number of lost customers in the system is presented.