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On the $$M_t/M_t/K_t+M_t$$ queue in heavy traffic

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  • Anatolii Puhalskii

Abstract

The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers processes under the fluid and diffusion scalings. Other results concern limits for general time-dependent queues and for time-homogeneous queues in steady state. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Anatolii Puhalskii, 2013. "On the $$M_t/M_t/K_t+M_t$$ queue in heavy traffic," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 119-148, August.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:1:p:119-148
    DOI: 10.1007/s00186-013-0435-8
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    References listed on IDEAS

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    1. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    2. Ward Whitt, 2004. "Efficiency-Driven Heavy-Traffic Approximations for Many-Server Queues with Abandonments," Management Science, INFORMS, vol. 50(10), pages 1449-1461, October.
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    Cited by:

    1. Xu Sun & Yunan Liu, 2021. "Staffing many‐server queues with autoregressive inputs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 312-326, April.
    2. Pang, Guodong & Zhou, Yuhang, 2017. "Two-parameter process limits for an infinite-server queue with arrival dependent service times," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1375-1416.

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