Abstract
We establish heavy-traffic limits for nearly deterministic queues, such as the G/D/n many-server queue. Since waiting times before starting service in the G/D/n queue are equivalent to waiting times in an associated Gn/D/1 model, where the Gn interarrival times are the sum of n consecutive interarrival times in the original model, we focus on the Gn/D/1 model and the generalization to Gn/Gn/1, where `cyclic thinning' is applied to both the arrival and service processes. We establish different limits in two cases: (i) when (1 - ρn)√n → β as n → ∞ and (ii) when (1 - ρn)n → β as n → ∞, where ρn is the traffic intensity in model n. The nearly deterministic feature leads to interesting nonstandard scaling.
Citation
Karl Sigman. Ward Whitt. "Heavy-traffic limits for nearly deterministic queues." J. Appl. Probab. 48 (3) 657 - 678, September 2011. https://doi.org/10.1239/jap/1316796905
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