A Monotonicity Result for the Blocking Probability in a G / GI / c / m Queueing System

We prove a slightly more general version of the following: In a G/GI/c/m queueing system where arriving customers are randomly deleted with probability 1 − p, the blocking probability of the remaining customers must be non-decreasing in p. In particular, we show that if more customers are accepted, even with a possibly different service time distribution, the blocking probability is at least as large.