BLOCKING PROBABILITIES FOR LARGE MULTIRATE ERLANG LOSS SYSTEMS

This paper is concerned with the computation of asymptotic blocking pr obabilities for a generalized Erlangian system which results when M in dependent Poisson streams of traffic with rates (lambda(i)}i=1M access a trunk group of C circuits with traffic from stream k requiring A(k) circuits which are simultaneously held and released after a time whic h is randomly distributed with unit mean and independent of earlier ar rivals and holding times. A call from stream k is lost if on arrival l ess than A(k) circuits are available. Although exact expressions for t he blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the swi tch increases in that both the traffic rates and trunk capacity are sc aled together, simple asymptotic expressions for the blocking probabil ities are obtained. In particular the expression is different for ligh t, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysi s.