Queueing analysis of a VoIP call center under retrial policy with re-service, server maintenance, and service disruptions

Document Type : Research Article

Authors

Preena R. ¹

Sumitha D. ²

¹ Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamil Nadu, India.

² Department of Science and Humanities, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamil Nadu, India.

10.22067/ijnao.2026.96253.1768

Abstract

This paper develops a retrial queueing framework for a Voice over Internet Protocol (VoIP) call center server with two obligatory service phases. Incoming voice packets arrive according to the Poisson process. The model captures caller behavior involving potential re-service requests based on satisfaction after the first phase, introducing dynamic retrial effects. It integrates operational uncertainties such as service disruptions due to malware attacks and immediate repair processes. Additionally, server maintenance activities and post maintenance buffer searches are integrated to reflect realistic system operations. The supplementary variable technique is employed to derive steady state solutions for performance evaluation. Numerical analysis highlights the influence of key parameters on system performance. To enhance the study, cost optimization is performed using the Particle Swarm Optimization (PSO) technique, offering effective strategies to balance service quality and operational cost.

Keywords

Retrial

Queue

Repair

Server

Re-service

Subjects

• Operations Research

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References

[1] Abdollahi, S. and Salehi Rad, M.R. Analysis of a batch arrival retrial queue with two-phase
services, feedback and admission, Bull. Iran. Math. Soc. (2022), 1–14.
[2] Arivudainambi, D. and Gowsalya, M. A single server non-Markovian retrial queue with two
types of service and Bernoulli vacation, Int. J. Oper. Res. 33(1) (2018), 55–81.
[3] Artalejo, J.R. Accessible bibliography on retrial queues: Progress in 2000–2009, Math. Com-
put. Model. 51(9–10) (2010), 1071–1081.
[4] Boualem, M., Bouchentouf, A.A., Bareche, A. and Cherfaoui, M. Stochastic interpretation
for a single server retrial queue with Bernoulli feedback and negative customers, Appl. Math.
J. Chin. Univ. 40(1) (2025), 1–19.
[5] Boussaha, Z., Oukid, N., Zeghdoudi, H., Soualhi, S. and Djellab, N. On the M/G/1 feedback
retrial queuing with orbital search of customers, Adv. Math. Sci. J. 11(8) (2022), 723–739.
[6] Chandrika, K.U. and Sumitha, D. Performance measures of feedback batch arrival retrial
queue with optional second service and orbital search, Adv. Appl. Res. 3(2) (2011), 179–186.
[7] Chang, F.M., Liu, T.H. and Ke, J.C. On an unreliable-server retrial queue with customer
feedback and impatience, Appl. Math. Model. 55 (2018), 171–182.
[8] Choudhury, G. A two phase batch arrival retrial queuing system with Bernoulli vacation
schedule, Appl. Math. Comput. 188(2) (2007), 1455–1466.
[9] Cooper, R.B. Introduction to Queueing Theory, Elsevier (North-Holland), Amsterdam, 1981.
[10] Dimitriou, I. A single server retrial queue with event-dependent arrival rates, Ann. Oper.
Res. 331(2) (2023), 1053–1088.
[11] Eberhart, R. and Kennedy, J. Particle swarm optimization, Proc. IEEE Int. Conf. Neural
Netw. 4 (1995), 1942–1948.
[12] Falin, G.I. A survey of retrial queues, Queueing Syst. 7 (1990), 127–167.
[13] Gelenbe, E. Random neural networks with negative and positive signals and product form
solution, Neural Comput. 1(4) (1989), 502–510.
[14] Gómez-Corral, A. Stochastic analysis of a single server retrial queue with general retrial
times, Naval Res. Logist. 46(5) (1999), 561–581.
[15] Hu, K., Allon, G. and Bassamboo, A. Understanding customer retrials in call centers:
Preferences for service quality and service speed, Manuf. Serv. Oper. Manag. 24(2) (2022),
1002–1020.
[16] Jain, M., Sharma, G.C. and Sharma, R. A batch arrival retrial queuing system for essential
and optional services with server breakdown and Bernoulli vacation, Int. J. Internet Enterp.
Manag. 8 (2012), 16–45.
[17] Keerthiga, S. and Indhira, K. Analysis of single server feedback retrial queue with Bernoulli
working vacation and starting failure, Reliab. Theory Appl. 19(3(79)) (2024), 310–326.
[18] Krishnamoorthy, A., Deepak, T.G. and Joshua, V.C. An M/G/1 retrial queue with non-
persistent customers and orbital search, Stoch. Anal. Appl. 23(5) (2005), 975–997.
[19] Kumar, B. A retrial queuing system with negative arrival under Bernoulli vacation schedule
and optional repair, (2024) PREPRINT (Version 1) available at Research Square https:
//doi.org/10.21203/rs.3.rs-4591933/v1
[20] Micheal, M.N.G. and Indhira, K. A literature review on retrial queuing system with Bernoulli
vacation, Yugosl. J. Oper. Res. 34(1) (2024), 109–134.
[21] Mokaddis, G.S., Metwally, S.A. and Zaki, B.M. A feedback retrial queuing system with
starting failures and single vacation, J. Appl. Sci. Eng. 10(3) (2007), 183–192.
[22] Radha, J., Indhira, K. and Chandrasekaran, V.M. A repairable M[X]/Gk/1 feedback retrial
G-queue, balking and reneging, search of customers with vacation, Int. J. Knowl. Manag.
Tour. Hosp. 1(4) (2017), 457–476.
[23] Rajadurai, P., Saravanarajan, M.C. and Chandrasekaran, V.M. Analysis of an M/G/1 feed-
back retrial queue with unreliable server, non-persistent customers, single working vacation
and vacation interruption, Int. J. Serv. Oper. Manag. 24(2) (2016), 235–266.
[24] Rusilko, T.V. and Pankov, A.V. Queuing network model of a call center with customer
retrials and impatient customers, Izv. Saratov Univ. Math. Mech. Inform. 24(2) (2024),
287–297.
[25] Seenivasan, M., Ramesh, R., Chandralekha, S. and Pandisaranya, S. Single server retrial
queuing system with reneging, feedback and balking customers, Proc. 1st Int. Conf. Innov.
Commun. Electr. Comput. Eng. (ICICEC) (2024), 1–7.
[26] Singla, N. and Kaur, H. A two-state retrial queuing model with feedback and balking, Reliab.
Theory Appl. 16(SI 2(64)) (2021), 142–155.
[27] Van Do, T. Bibliography on G-networks, negative customers and applications, Math. Com-
put. Model. 53(1–2) (2011), 205–212