An alternative approach to heavy-traffic limits for finite-pool queues

G. Bet ()
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G. Bet: Università degli Studi di Firenze

Queueing Systems: Theory and Applications, 2020, vol. 95, issue 1, No 6, 144 pages

Abstract: Abstract We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $$\Delta _{(i)}/G/1$$Δ(i)/G/1 queue, the customers decide independently when to join the queue by sampling their arrival time from a common distribution. We prove that, when the queue satisfies a certain heavy-traffic condition and under the additional assumption that the second moment of the service time is finite, the rescaled queue length process converges to a reflected Brownian motion with parabolic drift. Our result holds for general arrival times, thus improving on an earlier result Bet et al. (Math Oper Res 2019, https://doi.org/10.1287/moor.2018.0947) which assumes exponential arrival times.

Keywords: Queueing theory; Transitory queueing systems; Heavy-traffic approximations; Continuous-mapping approach; Primary 60K25; 90B22; Secondary 68M20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11134-020-09653-z

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