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

Guodong Pang () and Yuhang Zhou ()
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Guodong Pang: Pennsylvania State University
Yuhang Zhou: Pennsylvania State University

Queueing Systems: Theory and Applications, 2018, vol. 88, issue 1, No 1, 25 pages

Abstract: 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.

Keywords: Infinite-server queue; Dependent service times; $$\rho $$ ρ -Mixing; Two-parameter processes; Functional limit theorems; Maximal inequalities; The method of chaining; 60F05; 60F17; 60K25; 60G15 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11134-017-9550-1

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