A level-crossing approach to the solution of the shortest-queue problem

We develop a two-dimensional extension of the standard level-crossing approach and apply it to the shortest-queue problem. Here, the criterion for selecting a queue to join is based on a comparison of the accumulated workload in each of the queues. In particular, we obtain a simple closed-form expression for the stationary waiting-time distribution for the asymmetric two-server shortest-queue system. This result is then generalized to the many server case. Analytical forms for characteristics such as moments of the waiting time and queue length are also obtained. We also compare our results with those of standard approaches in which the queue selection criterion is based on the number of customers in the various queues.