A minimax approach to a simple routing problem

A simple routing problem is considered in which there are two service stations. Subject to burstiness constraints on the arrival of work, the worst-case delay performance of dynamic routing algorithms is studied. Under a light loading condition, it is found that the well-known `route-to-shortest´ (RTS) rule is optimal in some sense. On the other, it is shown that under a heavy load condition, the RTS rule is not optimal. In addition, the performance of RTS routing is compared with fixed routing. Finally, the burstiness constraints are relaxed to obtain a result which bounds the average backlogs in the stations for the RTS rule under light loading