Heavy-traffic limits for nearly deterministic queues

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) (1 − ρn)n → β as n → ∞, where ρn is the traffic intensity in model n. The nearly deterministic feature leads to interesting nonstandard scaling.

• Type: Journal
• Year: 2010
• Where: SIGMETRICS
• Authors: Karl Sigman, Ward Whitt
• Keywords: Gn Interarrival Times, Hardware, Interarrival Times, Model, SIGMETRICS 2010