Scaling Limits of a Tandem Retrial Queue with Common Orbit and Poisson Arrival Process

Nazarov, Anatoly; Paul, Svetlana; Phung-Duc, Tuan; Morozova, Mariya

doi:10.1007/978-3-030-92507-9_20

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2023

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Cited by 2 publications

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“…This motivated us to consider scaling limits for these models. In a recent series of work [7][8][9][10], we studied tandem queues with one orbit. In these papers, we studied an asymptotic regime where the retrial rate is extremely small, proving that in the transient regime, two scaled versions of the number of customers in orbit converge to a deterministic process and the diffusion process, respectively.…”

Section: Introductionmentioning

confidence: 99%

Scaling Limits of a Tandem Queue with Two Infinite Orbits

et al. 2023

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This paper considers a tandem queueing network with a Poisson arrival process of incoming calls, two servers, and two infinite orbits by the method of asymptotic analysis. The servers provide services for incoming calls for exponentially distributed random times. Blocked customers at each server join the orbit of that server and retry to enter the server again after an exponentially distributed time. Under the condition of low retrial rates, we prove that the joint stationary distribution of scaled numbers of calls in the orbits weakly converges to a two-variable Normal distribution.

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Section: Introductionmentioning

confidence: 99%