A heavy-traffic expansion for asymptotic decay rates of tail probabilities in multichannel queues

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Abstract

We establish a heavy-traffic asymptotic expansion (in powers of one minus the traffic intensity) for the asymptotic decay rates of queue-length and workload tail probabilities in stable infinite-capacity multichannel queues. The specific model has multiple independent heterogeneous servers, each with i.i.d. service times, that are independent of the arrival process, which is the superposition of independent nonidentical renewal processes. Customers are assigned to the first available server in the order of arrival. The heavy-traffic expansion yields relatively simple approximations for the tails of steady-state distributions and higher percentiles, yielding insight into the impact of the first three moments of the defining distributions.

References (23)

  • J. Abate et al.

    Asymptotics for steady-state tail probabilities in structured Markov queueing models

    Stochastic Models

    (1994)
  • J. Abate, G.L. Choudhury and W. Whitt, “Exponential approximations for tail probabilities in queues, I: waiting times”,...
  • J. Abate, G.L. Choudhury and W. Whitt, “Exponential approximations for tail probabilities in queues, II: sojourn time...
  • M. Abramowitz et al.
  • S. Asmussen et al.

    On cycle maxima, first passage problems and extreme value theory for queues

    Stochastic Models

    (1992)
  • S. Asmussen et al.

    Risk theory in a periodic environment: the Cramér-Lundberg approximation and Lundberg's inequality

    Math. Oper. Res.

    (1994)
  • C.S. Chang

    Stability, queue length and delay of deterministic and stochastic queueing networks

    IEEE Trans. Autom. Control

    (1994)
  • G.L. Choudhury et al.

    Squeezing the most out of ATM

    (1993)
  • G.L. Choudhury et al.

    Heavy-traffic asymptotic expansions for the asymptotic decay rates in the BMAP/G/1 queue

    Stochastic Models

    (1994)
  • A.I. Elwalid et al.

    Effective bandwidths of general Markovian traffic sources and admission control of high speed networks

    ACM/IEEE Trans. Networks

    (1993)
  • A.I. Elwalid et al.

    Markovian arrival and service communication systems: Spectral expansions, separability and Kronecker-product forms

    (1993)
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