Joining the right queue: A Markov decision-rule

The problem of assigning customers to one of several parallel queues so as to minimize the average time spent in the system (sojourn time) is studied as a Markov decision process. It is shown how the approach developed by Krishnan and Ott [7] to investigate state-dependent routing of voice-traffic for blocking minimization can also be used for sojourn-minimization for data traffic. For queues in parallel, this approach produces a rule, called the \´separable\´ rule, which is a generalization of "join the shortest queue" rule to the case of dissimilar queues, reducing to the shortest-queue rule when the queues are all alike - the case for which the shortest-queue rule is, in fact, optimum. Numerical results show that in cases where the queues are dissimilar in both the service rates and numbers of their servers, the \´separable\´ rule is strikingly superior to the shortest-queue rule; if the dissimilarities are limited to differences in the service rates, the \´separable\´ rule practically always is better than the shortest-queue rule; if the dissimilarities consist in the numbers of servers being different, with the individual servers all alike in the different queues, then the shortest-queue rule does better than the separable rule in most instances.