Optimal service allocation among two heterogeneous traffic types with no queueing

Two communication traffic streams with Poisson statistics arrive at a network node. These are to be transmitted across a channel with a total bandwidth capacity of C frequency slots. Messages not accepted at the node are assumed to be lost. Under the assumption of exponential service time distributions, we study the problem of dynamic allocation of available channel bandwidth among the two traffic types so as to minimize a weighted sum of blocking probabilities. Modeling the system as a two-dimensional Markov chain, we show by an application of dynamic programming principles that the optimal policy has the form of a "switching curve."