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Queues with superposition arrival processes in heavy traffic

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  • Whitt, Ward

Abstract

To help provide a theoretical basis for approximating queues with superposition arrival processes, we prove limit theorems for the queue-length process in a [Sigma] GIi/G/s model, in which the arrival process is the superposition of n independent and identically distributed stationary renewal processes each with rate n-1. The traffic intensity [rho] is allowed to approach the critical value one as n increases. If n(1-[rho])2 --> c, 0 0 and c --> [infinity].

Suggested Citation

  • Whitt, Ward, 1985. "Queues with superposition arrival processes in heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 81-91, December.
    • Handle: RePEc:eee:spapps:v:21:y:1985:i:1:p:81-91
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    Cited by:

    1. Ward Whitt & Wei You, 2018. "Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues," Operations Research, INFORMS, vol. 66(1), pages 184-199, January.
    2. Shuangchi He, 2020. "Diffusion Approximation for Efficiency-Driven Queues When Customers Are Patient," Operations Research, INFORMS, vol. 68(4), pages 1265-1284, July.
    3. A. Korhan Aras & Xinyun Chen & Yunan Liu, 2018. "Many-server Gaussian limits for overloaded non-Markovian queues with customer abandonment," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 81-125, June.

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