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Heavy Traffic Scaling Limits for shortest remaining processing time queues with heavy tailed processing time distributions by Banerjee, Sayan; Budhiraja, Amarjit; Puha, Amber L. is a scholarly article available to read on EtoBox.

What is Heavy Traffic Scaling Limits for shortest remaining processing time queues with heavy tailed processing time distributions about?

We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. In this work we are interested in studying the asymptotic behavior of suitably scaled measure-valued state descriptors that describe the evolution of a sequence of SRPT queuing systems. Gromoll, Kruk, and Puha (2011) have studied this problem under diffusive scaling. In the setting where the processing time distributions have unbounded support, under suitable conditions, they show that the diffusion scaled measures converge in distribution to the process that is identically zero. In Puha (2015) for the setting where the processing time distributions have unbounded support and light tails, a non-standard scaling of the queue length process is shown to give rise to a form of state space collapse that results in a nonzero limit. In the current work we consider the case where processing time distributions have finite second moments and regularly varying tails. We show that the measure valued process, under a non-standard scaling, converges in distribution in the space of paths o

Author

Banerjee, Sayan; Budhiraja, Amarjit; Puha, Amber L.

Published

2020

Language

EN