Bounding the mean response time of the minimum expected delay routing policy: an algorithmic approach

Balancing loads in a multi-server system can have a significant impact on performance. In this paper, we model such a system as a heterogeneous multi-server queueing system. We study the behavior of such a system operating under the minimum expected delay (MED) routing policy, i.e., an arriving customer is assigned to the queue which has the minimal expected value of unfinished work. This routing discipline can be viewed as a generalization of the join-the-shortest queue (SQ) discipline for homogeneous servers. There is no closed-form solution for this class of queueing problem. In this paper, we provide a methodology to compute upper and lower bounds on the mean response time of the system. This methodology allows one to tradeoff the tightness of the bounds and computational cost. Applications and numerical examples are presented which show how to use this methodology for deriving performance measures and also illustrating that the excellent accuracy of the computational algorithm which is achievable with modest computational cost.