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

Guodong Pang, Yuhang Zhou

Research output: Contribution to journalArticle

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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.

Original languageEnglish (US)
Pages (from-to)1375-1416
Number of pages42
JournalStochastic Processes and their Applications
Volume127
Issue number5
DOIs
StatePublished - May 1 2017

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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