Chernoff bounds for mean overflow rates

A number of independent traffic streams arrive at a queueing node which provides a finite buffer and a non-idling service at constant rate. Customers which arrive when the buffer is full are dropped and counted as overflows. We present Chernoff type bounds for mean overflow rates in the form of finite-dimensional minimization problems. The results are based on bounds for moment generating functions of buffer and bandwidth usage of the individual streams in an infinite buffer with constant service rate. We calculate these functions for regulated, Poisson and certain on/off sources. The achievable statistical multiplexing gain and the tightness of the bounds are demonstrated by several numerical examples.