Stochastic modeling of a retrial queue with server vacations and customer impatience in a multi-level environment
*C. T. Dora PravinaCorresponding authortdorapravinac@veltech.edu.inDepartment of MathematicsAvadiVel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyChennai, Tamil Nadu, 600062, IndiaView full profile → , G. Hemavathihemagovidh@gmail.comDepartment of MathematicsAvadiVel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and TechnologyChennai, Tamil Nadu, 600062, IndiaView full profile → , Sukumaran DamodaranSukumaran.d@velhightech.comDepartment of MathematicsAvadiVel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering CollegeChennai, Tamil Nadu, 600062, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2025
- Published Online:
- 11 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2175
- Pages:
- 2391–2400
Abstract
Keywords
Subject Classifications
References
[1] J. D. Cordeiro Jr., “Unreliable Retrial Queues in a Random Environment,” M.S. thesis, Air Force Institute of Technology (2007).
[2] J. D. Cordeiro and J. P. Kharoufeh, “The unreliable M/M/1 retrial queue in a random environment,” Stochastic Models, vol. 28, no. 1, pp. 29–48 (2012).
[3] S. Udayabaskaran and C. D. Pravina, “Transient analysis of an M/M/1 queue in a random environment subject to disasters,” Far East Journal of Mathematical Sciences, vol. 91, no. 2, pp. 157 (2014).
[4] Z. Liu and S. Yu, “The M/M/C queueing system in a random environment,” Journal of Mathematical Analysis and Applications, vol. 436, no. 1, pp. 556–567 (2016).
[5] H. Li and T. Yang, “A single-server retrial queue with server vacations and a finite number of input sources,” European Journal of Operational Research, vol. 85, no. 1, pp. 149–160 (1995).
[6] Z. Wenhui, “Analysis of a single-server retrial queue with FCFS orbit and Bernoulli vacation,” Applied Mathematics and Computation, vol. 161, no. 2, pp. 353–364 (2005).
[7] K. C. Madan, W. Abu-Dayyeh, and F. Taiyyan, “A two-server queue with Bernoulli schedules and a single vacation policy,” Applied Mathematics and Computation, vol. 145, no. 1, pp. 59–71 (2003).
[8] M. Haridass and R. Arumuganathan, “Analysis of a single server batch arrival retrial queueing system with modified vacations and N-policy,” RAIRO-Operations Research, vol. 49, no. 2, pp. 279–296 (2015).
[9] C. Raychaudhuri and A. Jain, “Efficiency of retrial queueing system under n threshold during vacation,” International Journal of Information Technology, vol. 17, no. 3, pp. 1419–1430 (2025).
[10] A. A. Bouchentouf, A. Guendouzi, M. Houalef, and S. Majid, “Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience,” Operations Research and Decisions, vol. 32, no. 2, pp. 16–33 (2022).
[11] C. D. Pravina, P. Kamala, and S. Sreelakshmi, “Analysis of a Markovian queue of single server performing in multi-phase subject to disaster, recovery and repair,” Contemporary Mathematics, pp. 5012–5026 (2024).
[12] A. Economou, A. Gómez-Corral, and S. Kanta, “Optimal balking strategies in single-server queues with general service and vacation times,” Performance Evaluation, vol. 68, no. 10, pp. 967–982 (2011).
[13] P. Guo and R. Hassin, “Strategic behavior and social optimization in Markovian vacation queues,” Operations Research, vol. 59, no. 4, pp. 986–997 (2011).
[14] P. Guo and R. Hassin, “Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers,” European Journal of Operational Research, vol. 222, no. 2, pp. 278–286 (2012).
[15] Y. Zhang, “Strategic behavior in the constant retrial queue with a single vacation,” RAIRO-Operations Research, vol. 54, no. 2, pp. 569–583 (2020).
[16] A. Nain, G. M. Upadhyay, N. Bohra, P. K. Soni, and L. Raja, “A mathematical approach to model signal variation in an aquatic robot’s environmental sensor using heavy-tailed distributions,” Journal of Interdisciplinary Mathematics, vol. 28, no. 2, pp. 597–606 (2025), doi: 10.47974/JIM-2103.
[17] S. Kale, J. Hase, S. Deshmukh, S. N. Ajani, P. K. Agrawal, and C. S. Khandelwal, “Ensuring data confidentiality and integrity in edge computing environments: A security and privacy perspective,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 421–430 (2024), doi: 10.47974/JDMSC-1898.
[18] S. M. Stefanov, “On the discrete and continuous Markov processes,” Journal of Interdisciplinary Mathematics, vol. 28, no. 5, pp. 1901–1908 (2025), doi: 10.47974/JIM-2160.
[19] K. Sivakumar, S. Kaliappan, and R. D. Ramasamy, “A lightweight fog assisted cloud model (FACM) for secure environment,” Journal of Information and Optimization Sciences, vol. 47, no. 2, pp. 777–792 (2026), doi: 10.47974/JIOS-2116.
