Large deviation analysis of subexponential waiting times in a processor-sharing queue

摘要

We investigate the distribution of the waiting time V in a stable M/G/1 processor-sharing queue with traffic intensity p < 1. When the distribution of a customer service request B belongs to a large class of subexponential distributions with tails heavier than e(-rootx), it is shown that P[V > x] = P[B > (1 - p)x](1 + o(1)) as x --> infinity. Furthermore, we demonstrate that the preceding relationship does not hold if the service distribution has a lighter tail than e(-rootx). [References: 45]