Two-parameter process limits for an infinite-server queue with arrival dependent service times

Guodong Pang and Yuhang Zhou

Stochastic Processes and their Applications, 2017, vol. 127, issue 5, 1375-1416

Abstract: We study an infinite-server queue with a general arrival process and a large class of general time-varying service time distributions. Specifically, customers’ service times are conditionally independent given their arrival times, and each customer’s service time, conditional on her arrival time, has a general distribution function. We prove functional limit theorems for the two-parameter processes Xe(t,y) and Xr(t,y) that represent the numbers of customers in the system at time t that have received an amount of service less than or equal to y, and that have a residual amount of service strictly greater than y, respectively. When the arrival process and the initial content process both have continuous Gaussian limits, we show that the two-parameter limit processes are continuous Gaussian random fields. In the proofs, we introduce a new class of sequential empirical processes with conditionally independent variables of non-stationary distributions, and employ the moment bounds resulting from the method of chaining for the two-parameter stochastic processes.

Keywords: Gt/Gt/∞ queues; Arrival dependent services; Two-parameter processes; Functional limit theorems; Gaussian random fields; Method of chaining (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:5:p:1375-1416

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DOI: 10.1016/j.spa.2016.08.003

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