Validity of heavy-traffic steady-state approximations in many-server queues with abandonment
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AbstractWe 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.
All Author(s) ListDai JG, Dieker AB, Gao XF
Journal nameQueueing Systems
Year2014
Month9
Day1
Volume Number78
Issue Number1
PublisherSPRINGER
Pages1 - 29
ISSN0257-0130
eISSN1572-9443
LanguagesEnglish-United Kingdom
KeywordsCustomer abandonment; Diffusion approximations; Geometric Lyapunov function; Halfin-Whitt regime; Multi-server queues; Phase-type distribution; Piecewise OU processes; Stationary distribution; Weak convergence
Web of Science Subject CategoriesComputer Science; Computer Science, Interdisciplinary Applications; Operations Research & Management Science
