On the average optimality of circular assignment policy

We consider a parallel queueing system with identical exponential servers. Customers arrive according to a renewal process and upon arrival are immediately assigned to those queues. The problem is to find an optimal assignment policy minimizing the longrun average expected cost, without information about the current queue lengths, but with the initial queue-length distributions and information about the past arrival process and assignment of customers. In this paper, it is shown that the so-called circular assignment policy is optimal under mild conditions on the initial queue-length distributions and the holding cost.