On Large Delays in Multi-Server Queues with Heavy Tails

Abstract

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 intermediate 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 $\rho$), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.

References in corpus (2)

• Moments and tails in monotone-separable stochastic networks
• Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows

Cited by in corpus (7)

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• Customer sojourn time in GI/G/1 feedback queue in the presence of heavy tails
• Tail Asymptotics for Delay in a Half-loaded GI/GI/2 Queue with Heavy-tailed Job Sizes
• Heavy-tailed queues in the Halfin-Whitt regime
• A unified approach for large queue asymptotics in a heterogeneous multiserver queue
• Sample-path large deviations for a class of heavy-tailed Markov additive processes