On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times

Details On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times On the exact asymptotics for the stationary sojourn time distribution in a tandem of queues with light-tailed service times

2009-09-03

arxiv.org/abs/0909.0725v1

Problems of Information Transmission, 43 (2007), No.4, 93--108

Mathematics

Probability

15 pages; published in "Problems of Information Transmission" in December 2007

Scientific paper

We study the asymptotics of the stationary sojourn time Z of a "typical customer" in a tandem of single-server queues. It is shown that, in a certain "intermediate" region of light-tailed service time distributions, Z may take a large value mostly due to a large value of a single service time of one of customers. Arguments used in the paper allow us to obtain also an elementary proof of the logarithmic asymptotics for the tail distribution of the stationary sojourn time in the whole class of light-tailed distributions.

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