Heavy-tailed queues in the Halfin-Whitt regime
نویسندگان
چکیده
We consider the FCFS GI/GI/n queue in the Halfin-Whitt heavy traffic regime, in the presence of heavy-tailed distributions (i.e. infinite variance). We prove that under minimal assumptions, i.e. only that processing times have finite 1 + moment for some > 0 and inter-arrival times have finite second moment, the sequence of stationary queue length distributions, normalized by n 1 2 , is tight in the Halfin-Whitt regime. All previous tightness results for the stationary queue length required that processing times have finite 2 + moment. Furthermore, we develop simple and explicit bounds on the stationary queue length in that setting.
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