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

Xin Liu ()
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Xin Liu: Clemson University

Queueing Systems: Theory and Applications, 2019, vol. 91, issue 1, No 3, 49-87

Abstract: 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; Primary: 60F05; 60K25; 90B22; Secondary: 60K05 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-018-9589-7

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