How big queues occur in multi-server system with heavy tails

Details How big queues occur in multi-server system with heavy tails How big queues occur in multi-server system with heavy tails

2011-04-16

arxiv.org/abs/1104.3192v1

Mathematics

Probability

Scientific paper

We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\rho$ which is the ratio of mean service and mean interarrival times. For service times with regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a `principle of $s-k$ big jumps' in this case (here $k$ is the integer part of $\rho$). As another corollary of the bounds obtained, we provide a new proof of necessity and sufficiency of conditions for existence of moments of the stationary waiting time.

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