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Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue

P. Jelenkovi, P. Momilovi

Department of Electrical Engineering, Columbia University, New York, New York 10027
Department of Electrical Engineering, Columbia University, New York, New York 10027
predrag{at}ee.columbia.edu
petar{at}ee.columbia.edu

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^–x, it is shown that

Furthermore, we demonstrate that the preceding relationship does not hold if the service distribution has a lighter tail than e^–x.

Key Words: M/G/1 queue; processor sharing; waiting time distribution; large deviations; subexponential distributions
History: Received: September 29, 2001; revision received: November 1, 2002;

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