Many-server heavy-traffic limit for queues with time-varying parameters

By Yunan Liu, Ward Whitt. 2014

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+GI queueing model, having time-varying arrival rate and staffing, ageneral arrival process satisfying a FCLT, exponential service timesand customer abandonment according to a general probability dis-tribution. The FCLT provides theoretical support for the approxi-mating deterministic fluid model the authors analyzed in a previouspaper and a refined Gaussian process approximation, using varianceformulas given here. The model is assumed to alternate between un-derloaded and overloaded intervals, with critical loading only at theisolated switching points. The proof is based on a recursive analy-sis of the system over these successive intervals, drawing heavily onprevious results for infinite-server models. The FCLT requires carefultreatment of the initial conditions for each interval.

Subfields: Management Information Systems, Management Science and Operations Research, Safety, Risk, Reliability and Quality

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