Large deviations for arrivals, departures, and overflow in some queues of interacting traffic

The theoretical relationship between the entropy of a source and the overflow probabilities in a single server queue is well understood in a great deal of generality. This paper applies such a `calculus of entropy´ to classes of queueing problems involving traffic of different priorities. The main new ingredient is that traffic with a lower service priority experiences a varying service rate: it takes the service unused by traffic of a higher service. The entropic techniques developed enable one to characterize the unused bandwidth available. An application shows how such low priority traffic can achieve very low loss ratios if buffered separately from a stream of comparatively high intensity. Such an arrangement could be used to transmit low volume traffic which is extremely sensitive to loss. The entropy of the output of such a stream from the buffer is also derived