Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue
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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.
author list (cited authors)
Jelenković, P., & Momčilović, P.