Characteristics of deterministic optimal routing for a simple traffic control problem

This paper deals with a routing problem for a pair of parallel paths connecting a source node and a destination node. The problem is to find the optimal routing that minimizes the average packet delay under the condition that all of the packets' arrival times at the source node as well as all of the packets' sizes are completely deterministic. The numerical solutions of the problem show that the optimal routing assigns most of the short packets to one path and most of the long packets to the other path when the input traffic intensity is high. This new routing assignment is called the fix-queue-based-on-size (FS) policy. It is shown mathematically that the expected average packet delay of the FS policy is smaller than that of the send-to-shortest-delay (SSD) policy if a large number of packets simultaneously arrive at the source node.