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1 results

  • Heavy-Traffic Limits for Nearly Deterministic Queues

  • Part of
  • Karl Sigman, Ward Whitt
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 3 / September 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 657-678
    Print publication:
    September 2011
    • Article
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  • 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.