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

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