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Queueing Systems

, Volume 91, Issue 1–2, pp 49–87 | Cite as

Diffusion approximations for double-ended queues with reneging in heavy traffic

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Abstract

We study a double-ended queue consisting of two classes of customers. Whenever there is a pair of customers from both classes, they are matched and leave the system. The matching is instantaneous following the first-come–first-match principle. If a customer cannot be matched immediately, he/she will stay in a queue. We also assume customers are impatient with generally distributed patience times. Under suitable heavy traffic conditions, we establish simple linear asymptotic relationships between the diffusion-scaled queue length process and the diffusion-scaled offered waiting time processes and show that the diffusion-scaled queue length process converges weakly to a diffusion process that admits a unique stationary distribution.

Keywords

Double-ended queues Matching systems First-come–first-serve Customer abandonment Generally distributed patience times Diffusion approximations Stationary distributions Heavy traffic 

Mathematics Subject Classification

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA

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