Scaling Limits of a Tandem Queue with Two Infinite Orbits

Anatoly Nazarov, Tuan Phung-Duc (), Svetlana Paul and Mariya Morozova
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Anatoly Nazarov: Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., Tomsk 634050, Russia
Tuan Phung-Duc: Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan
Svetlana Paul: Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., Tomsk 634050, Russia
Mariya Morozova: Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 36 Lenina Ave., Tomsk 634050, Russia

Mathematics, 2023, vol. 11, issue 11, 1-14

Abstract: 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.

Keywords: tandem queueing networks; retrial; asymptotic analysis; two infinite orbits (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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