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Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds

Author

Listed:
  • Guodong Pang

    (Pennsylvania State University)

  • Yuhang Zhou

    (Pennsylvania State University)

Abstract

We prove two-parameter process limits for infinite-server queues with weakly dependent service times satisfying the $$\rho $$ ρ -mixing condition. The two-parameter processes keep track of the elapsed or residual service times of customers in the system. We use the new methodology developed in Pang and Zhou (Stoch Process Appl 127(5):1375–1416, 2017) to prove weak convergence of two-parameter stochastic processes. Specifically, we employ the maximal inequalities for two-parameter queueing processes resulting from the method of chaining. This new methodology requires a weaker mixing condition on the service times than the $$\phi $$ ϕ -mixing condition in Pang and Whitt (Queueing Syst 73(2):119–146, 2013), as well as fewer regularity conditions on the service time distribution function.

Suggested Citation

  • Guodong Pang & Yuhang Zhou, 2018. "Two-parameter process limits for infinite-server queues with dependent service times via chaining bounds," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 1-25, February.
    • Handle: RePEc:spr:queues:v:88:y:2018:i:1:d:10.1007_s11134-017-9550-1
    DOI: 10.1007/s11134-017-9550-1
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    References listed on IDEAS

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    1. Avishai Mandelbaum & Petar Momčilović, 2012. "Queues with Many Servers and Impatient Customers," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 41-65, February.
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    3. Guodong Pang & Ward Whitt, 2012. "The Impact of Dependent Service Times on Large-Scale Service Systems," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 262-278, April.
    4. Junfei Huang & Avishai Mandelbaum & Hanqin Zhang & Jiheng Zhang, 2017. "Refined Models for Efficiency-Driven Queues with Applications to Delay Announcements and Staffing," Operations Research, INFORMS, vol. 65(5), pages 1380-1397, October.
    5. Berkes, István & Hörmann, Siegfried & Schauer, Johannes, 2009. "Asymptotic results for the empirical process of stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1298-1324, April.
    6. 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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