This paper is concerned with the computation of asymptotic blocking probabilities for a generalized Erlangian system which results when M independent Poisson streams of traffic with rates access a trunk group of C circuits with traffic from stream k requiring Ak circuits which are simultaneously held and released after a time which is randomly distributed with unit mean and independent of earlier arrivals and holding times. A call from stream k is lost if on arrival less than Ak circuits are available. Although exact expressions for the blocking probabilities are known, their computation is unwieldy for even moderate-sized switches. It is shown that as the size of the switch increases in that both the traffic rates and trunk capacity are scaled together, simple asymptotic expressions for the blocking probabilities are obtained. In particular the expression is different for light, moderate and heavy loads. The approach is via exponential centering and large deviations and provides a unified framework for the analysis.

Particles may be removed from a lattice by murder, coalescence, mutual annihilation and simple death. If the particle system is not to die out, the removed particles must be replaced by births. This letter shows that coalescence can be counteracted by arbitrarily small birth-rates and contrasts this with the situations for annihilation and pure death where there are critical phenomena. The problem is unresolved for murder.