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Simple bounds for a transient queue

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2 Author(s)
Osogami, T. ; IBM Res. - Tokyo, Yamato, Japan ; Raymond, R.

Bounds on performance of a queueing model can provide useful information to guarantee quality of service for communication networks. We study the bounds on the mean delay in a transient GI/GI/1 queue given the first two moments of the service time and the inter-arrival time, respectively. We establish a simple upper-bound, which then is used to show that the true transient mean-delay is at most four times larger than an asymptotic diffusion-approximation. We also prove that the tight lower-bound is zero as long as the service time and the inter-arrival time have finite variance and the load is below one. Tightness of the trivial lower-bound is in contrast to the stationary mean-delay, which has strictly positive lower-bound when the service time is sufficiently variable. We also show how our results can be applied to analyze the transient mean delay of packets in the real-world Internet.

Published in:

Dependable Systems & Networks (DSN), 2011 IEEE/IFIP 41st International Conference on

Date of Conference:

27-30 June 2011