Extended Vacation Systems and the Universality of the M/G/1/K Blocking Formula

Abstract

A simple blocking formula B(K) = (1 - p)EK [1 - pEK]- 1 relates the probability of blocking for the finite capacity M/G/1/K to EK, the steady state occupancy tail probability of the same system with infinite capacity. The validity of this formula is demonstrated for M/G/1 vacation systems augmented by an idle state, an umbrella for a host of priority systems and vacation systems related to M/G/1. A class of occupancy level dependent vacation systems introduced are shown to require a variant of this blocking formula.