Heavy Loads and Heavy Tails

2023/04/18 by Borst, Sem
#60K25 (primary) #68M20 #90B22 (secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2304.09279

Abstract

The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to some of the pioneering results of J.W. Cohen in this domain. We specifically demonstrate that reduced-load equivalence properties established for the tail asymptotics of the workload naturally extend to the heavy-traffic limit.

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