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2015 Diffusion models for double-ended queues with renewal arrival processes
Xin Liu, Qi Gong, Vidyadhar G. Kulkarni
Stoch. Syst. 5(1): 1-61 (2015). DOI: 10.1214/13-SSY113

Abstract

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be a non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits.

Citation

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Xin Liu. Qi Gong. Vidyadhar G. Kulkarni. "Diffusion models for double-ended queues with renewal arrival processes." Stoch. Syst. 5 (1) 1 - 61, 2015. https://doi.org/10.1214/13-SSY113

Information

Received: 1 June 2013; Published: 2015
First available in Project Euclid: 23 December 2015

zbMATH: 1331.60177
MathSciNet: MR3442388
Digital Object Identifier: 10.1214/13-SSY113

Subjects:
Primary: 60F05, 60K25, 90B22
Secondary: 60K05

Rights: Copyright © 2015 INFORMS Applied Probability Society

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