Deterministic Routing to Buffered Channels

Consider exponential transmission channels which transmit information with different rates. Every channel has a buffer which is capable of storing an unlimited number of messages. A new message first arrives at the controller, which immediately routes it to one of the channels according to an infinite deterministic routing sequence. A cost per unit of staying time is charged in each of the channels (channel dependent cost), and the long-run average staying cost is taken as the cost criterion. For every and a Poisson arrival process, a lower bound to the cost is found and a new routing policy, the golden ratio policy, is presented and its cost is evaluated. It is shown that for a variety of system parameters, the golden ratio routing policy has a cost close to the lower bound.