Validity of heavy-traffic steady-state approximations in many-server queues with abandonment

J. G. Dai; A. B. Dieker; Xuefeng Gao

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arXiv · 1306.5346

Validity of heavy-traffic steady-state approximations in many-server queues with abandonment

J. G. Dai·A. B. Dieker·Xuefeng Gao

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Abstract

We consider GI/Ph/n+M parallel-server systems with a renewal arrival process, a phase-type service time distribution, n homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin-Whitt regime, the sequence of stationary distributions corresponding to the normalized state processes is tight. As a consequence, we establish an interchange of heavy traffic and steady state limits for GI/Ph/n+M queues.

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J. G. Dai, A. B. Dieker, Xuefeng Gao. 2013-06-22. Validity of heavy-traffic steady-state approximations in many-server queues with abandonment. https://arxiv.org/abs/1306.5346

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