A two-dimensional Multiserver Queuing system with repeated attempts and impatience

Neelam Singla; Sonia Kalra

doi:10.17485/IJST/v14i17.820

Article

A two-dimensional Multiserver Queuing system with repeated attempts and impatience

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v14i17.820

Year: 2021, Volume: 14, Issue: 17, Pages: 1379-1391

Original Article

A two-dimensional Multiserver Queuing system with repeated attempts and impatience

Neelam Singla¹, Sonia Kalra^2*

¹ Assistant Professor, Department of Statistics, Punjabi University, Patiala, 147001, India
² Research Scholar, Department of Statistics, Punjabi University, Patiala, 147001, India

^*Corresponding author
Email: [email protected]

Received Date:04 June 2020, Accepted Date:26 April 2021, Published Date:15 May 2021

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: This study discusses a two-state multiserver retrial queueing system, where the customer may leave the system due to impatience. In this paper, we deal with the time dependent probabilities when all, some or none servers are busy. Method: For this model, we solved difference differential equations recursively and obtained the time dependent probabilities when all, some or none servers are busy. Findings: Time dependent probabilities of exact number of arrivals and exact number of departures at when all, some or none servers are busy are obtained. In this paper, some kind of verification and converting two state model into single state model are discussed. Some special cases of interest are also discussed. Novelty: In communication networks, multiple servers are used to reduce traffic congestion and improve system performance. The operation mode of a call center with repeated attempts provides an initial motivation for our study.

Keywords: Impatience; Multiserver; Probability; Queueing; Retrial

References

Artalejo JR. Accessible bibliography on retrial queues. Mathematical and Computer Modelling. 1999;30(3-4):1–6. Available from: https://dx.doi.org/10.1016/s0895-7177(99)00128-4
Falin G. A survey of retrial queues. Queueing Systems. 1990;7(2):127–167. Available from: https://dx.doi.org/10.1007/bf01158472
Kulkarni VG, Liang H. Retrial queues Revisited. In: Dshalalow JH., ed. Frontiers in Queueing. (pp. 19-34) CRC Press. 1998.
Yang T, Templeton JGC. A survey on retrial queues. Queueing Systems. 1987;2(3):201–233. Available from: https://dx.doi.org/10.1007/bf01158899
Palm C. Methods of judging the annoyance caused by congestion. Telecommunications. 1953;4:4–5. Available from: http://ie.technion.ac.il/serveng/Lectures/PalmAnnoyance.pdf
Cohen JW. Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommunication Review. 1957;18:49–100. Available from: https://ci.nii.ac.jp/naid/10000050792/
Baccelli F, Boyer P, Hebuterne G. Single-server queues with impatient customers. Advances in Applied Probability. 1984;16(4):887–905. Available from: https://doi.org/10.2307/1427345
Perel N, Yechiali U. Queues with slow servers and impatient customers. European Journal of Operational Research. 2010;201(1):247–258. Available from: https://dx.doi.org/10.1016/j.ejor.2009.02.024
Choudhury A, Medhi P. Balking and reneging in multiserver Markovian queuing system. International Journal of Mathematics in Operational Research. 2011;3(4):377–394. Available from: https://dx.doi.org/10.1504/ijmor.2011.040874
Pegden CD, Rosenshine M. Some New Results for theM/M/1 Queue. Management Science. 1982;28(7):821–828. Available from: https://dx.doi.org/10.1287/mnsc.28.7.821
Indra, R. Transient analysis of two- dimensional state Markovian queueing model with multiple working vacations and non-exhaustive service. International Journal of Computer Applications. 2010;11(7):1–7. Available from: https://www.ijcaonline.org/archives/volume11/number7/1598-2147
Garg PC, Kumar S. A Single Server Retrial Queue With Impatient Customers. Mathematical Journal of Interdisciplinary Sciences. 2012;1(1):67–82. Available from: https://dx.doi.org/10.15415/mjis.2012.11006
Falin GI, Templeton JGC. Retrial Queues (1). (p. 320) Chapman and Hall/CRC. 1997.
Singla N, Kalra S. A Two - State Retrial Queueing Model with Balking Customers. International Journal of Interdisciplinary Research and Innovations. 2018;6:528–539. Available from: https://researchpublish.com/journal-details/IJIRI
Singla N, Kalra S. A Two - State Retrial Queueing Model with Reneging Customers. International Journal of Management. 2018;8:2650–2663. Available from: http://ijamtes.org/VOL-8-ISSUE-10-2018-1/

Copyright

© 2021 Singla & Kalra. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)