A hybridized ANFIS-ANN based queueing model with orbital search, service interruptions during working vacation

Abstract

Queueing models are widely used to analyze and optimize service systems in which customer arrivals, service times, and system dynamics are stochastic. This paper presents an unreliable Markovian single-server retrial queueing model with impatient customers and breakdowns, under a working-vacation policy. The proposed model accounts for various server states, including busy, breakdown, orbital search, and working vacation. Customers arrive according to a Poisson process and may either enter service, join an orbit, or abandon the system due to impatience. The server operates under an adaptive vacation policy, offering reduced service during vacations, and is subject to breakdowns that require repair. To improve predictive accuracy and system performance evaluation, we employ adaptive neuro-fuzzy inference system and artificial neural network models. These intelligent computational techniques provide robust approximations for system parameters, enhancing decision-making in queue management. The effectiveness of the proposed model is demonstrated through numerical simulations, offering valuable insights into the impact of system parameters on overall performance.

Keywords

• Adaptive-network-based fuzzy inference system
• artificial neural network
• breakdown
• matrix geometric method
• orbit search
• single server
• working vacation

References

1. [1] A. Ahuja, A. Jain and M. Jain, Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation, Math. Comput. Simul. 192, 464–490, 2022.
2. [2] R. Aniyeri and C.R. Nadar, A multiphase queuing system with assorted servers by using matrix geometric method, Int. J. Appl. Eng. 382, 12052–12059, 2017.
3. [3] G.I. Falin, Model of coupled switching in presence of recurrent calls, Eng. Cybern. Rev. 17, 53–59, 1979.
4. [4] B.D. Choi and Y. Chang, Single server retrial queues with priority calls, Math. Comput. Modell. 30 (3–4), 7–32, 1999.
5. [5] A. Aissani and J.R. Artalejo, On the single server retrial queue subject to breakdowns, Queueing Syst. 30, 309–321, 1998.
6. [6] A.N. Dudin, R. Manzo and R. Piscopo, Single server retrial queue with group admission of customers, Comput. Oper. Res. 61, 89–99, 2015.
7. [7] I. Dimitriou, A single server retrial queue with event-dependent arrival rates, Ann. Oper. Res. 331 (2), 1053–1088, 2023.
8. [8] D. Shajin, A.N. Dudin, O. Dudina and A. Krishnamoorthy, A two-priority single server retrial queue with additional items, J. Ind. Manag. Optim. 16 (6), 2891–2912, 2020.

9. [9] J.E.A. Bagyam, P. Suganthi and P. Visali, Unreliable single server retrial queueing model with repeated vacation, Int. J. Math. Oper. Res. 26 (3), 357–372, 2023.
10. [10] V. Saravanan, V. Poongothai and P. Godhandaraman, Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model, Math. Comput. Simul. 214, 204–226, 2023.
11. [11] M.F. Neuts and M.F. Ramalhoto, A service model in which the server is required to search for customers, J. Appl. Probab. 21, 157–166, 1984.
12. [12] A. Krishnamoorthy, T.G. Deepak and V.C. Joshua, An $M/G/1$ retrial queue with non-persistent customers and orbital search, Stoch. Anal. Appl. 23, 975–997, 2005.
13. [13] S.R. Chakravarthy, A. Krishnamoorthy and V.C. Joshua, Analysis of a multi server retrial queue with search of customers from the orbit, Perform. Eval. 63, 776–798, 2006.
14. [14] T.G. Deepak, A.N. Dudin, V.C. Joshua and A. Krishnamoorthy, On an $M[X]/G/1$ retrial system with two types of search of customers from the orbit, Stoch. Anal. Appl. 31, 92–107, 2013.
15. [15] S. Gao and J. Wang, Performance and reliability analysis of an $M/G/1 − G$ retrial queue with orbital search and non-persistent customers, Eur. J. Oper. Res. 236, 561– 572, 2014.
16. [16] S. Rani, M. Jain and S. Dhibar, Analysis of Markovian retrial queue with double orbits, vacation, orbital search, and disaster using ANFIS approach, Iran. J. Sci. 47 (5), 1751–1764, 2023.
17. [17] B.K. Kumar, R. Sankar, R.N. Krishnan and R. Rukmani, Multiserver call center retrial queue under Bernoulli vacation schedule with two-way communication and orbital search, Telecommun. Syst. 84 (1), 23–51, 2023.
18. [18] S. Keerthiga and K. Indhira, Cost optimization for system stability and orbital search under working vacation and starting failure by using the ANFIS soft computing, Ain Shams Eng. J. 15 (8), 102847, 2024.
19. [19] L.D. Servi and S.G. Finn, $M/M/1$ queues with working vacations $(M/M/1/WV )$, Perform. Eval. 50 (1), 41–52, 2002.
20. [20] R. Sudhesh and A. Azhagappan, Transient analysis of an $M/M/1$ queue with variant impatient behavior and working vacations, OPSEARCH 55 (3), 787–806, 2018.
21. [21] K.V. Vijayashree and A. Anjuka, Stationary analysis of a fluid queue driven by an M/M/1 queue with working vacation, Qual. Technol. Quant. Manag. 15 (2), 187–208.
22. [22] D.A. Wu and H. Takagi, $M/G/1$ queue with multiple working vacations, Perform. Eval. 63 (7), 654–681, 2006.
23. [23] H. Zhang and G. Zhou, $M/M/1$ queue with m kinds of differentiated working vacations, J. Appl. Math. Comput. 54 (1–2), 213.
24. [24] V.M. Chandrasekaran, K. Indhira, M.C. Saravanarajan and P. Rajadurai, A survey on working vacation queueing models, Int. J. Pure Appl. Math. 106 (6), 33–41, 2016.
25. [25] K. Divya and K. Indhira, A literature survey on queueing model with working vacation, Reliab.: Theory Appl. 19 (1(77)), 40–49, 2024.
26. [26] P. Gupta and N. Kumar, Performance analysis of retrial queueing model with working vacation, interruption, waiting server, breakdown and repair, J. Sci. Res. 13 (3), 833– 844, 2021.
27. [27] K. Divya and K. Indhira, Performance analysis and ANFIS computing of a Markovian queuing model with intermittently accessible server under a hybrid vacation policy, RAIRO Oper. Res. 58 (2), 1257–1279, 2024.
28. [28] N. Singh, M. Jain and S. Dhibar, ANFIS computing for $M/M/\infty$ queue with two types of service interruption and balking, Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 94 (1), 63–73, 2024.
29. [29] S. Thakur, A. Jain and M. Jain, ANFIS and cost optimization for Markovian queue with operational vacation, Int. J. Math. Eng. Manag. Sci. 6 (3), 894–910, 2021.
30. [30] A. Dehmi, M. Boualem, S. Kahla and L. Berdjoudj, ANFIS computing and cost optimization of an M/M/c/M queue with feedback and balking customers under a hybrid hiatus policy, Croat. Oper. Res. Rev. 15 (2), 159–170, 2024.
31. [31] K. Divya and K. Indhira, Performance analysis and ANFIS computing of an unreliable Markovian feedback queueing model under a hybrid vacation policy, Math. Comput. Simul. 218, 403–419, 2024.
32. [32] M. Sivakami Sundari and S. Palaniammal, An ANN simulation of single server with infinite capacity queuing system, Int. J. Innov. Technol. Explor. Eng. 8 (12), 4067– 4071, 2019.
33. [33] S. Ghosh-Dastidar and H. Adeli, Neural network-wavelet microsimulation model for delay and queue length estimation at freeway work zones, J. Transp. Eng. 132 (4), 331–341, 2006.
34. [34] M. Hosoz and H.M. Ertunc, Artificial neural network analysis of an automobile air conditioning system, Energy Convers. Manag. 47, 1574–1587, 2006.
35. [35] M.O. Sigo, M. Selvam, B. Maniam, D. Kannaiah, C. Kathiravan and T. Vadivel, Big data analytics-application of artificial neural network in forecasting stock price trends in India, AAFSJ 22 (3).
36. [36] A.B.M. Al Islam and V. Raghunathan, iTCP: An intelligent TCP with neural network based end-to-end congestion control for adhoc multi-hop wireless mesh networks, Wireless Netw. 21, 581.
37. [37] I. Maqsood, M.R. Khan and A. Abraham, An ensemble of neural networks for weather forecasting, Neural Comput. Appl. 13, 112, 2004.
38. [38] S.A. Kalogirou, Application of artificial neural-networks for energy systems, Appl. Energy 67, 17–35, 2000.
39. [39] Y. Levy and U. Yechiali, Utilization of idle time in an $M/G/1$ queueing system, MNSC 22 (2), 202–211, 1975.
40. [40] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inform. Sci. 8 (3), 199–249.
41. [41] S. Dhibar and M. Jain, Metaheuristic optimization and strategic behavior of Markovian vacation queue with retrial policy: Application to virtual call center, Evol. Intell. 18 (1), 13, 2025.
42. [42] J. Sathiyavathy, A mathematical model for the double orbital queue with recurrent customers under working vacation and its optimal control analysis, Hacet. J. Math. Stat. 54 (5), 2139–2167, 2025.
43. [43] J. Kalaiselvi and M.C. Saravanarajan, Particle swarm optimization of a single server retrial queue with delayed repair under working vacation from optional service to reservice, Contemp. Math. 6 (1), 743–771, 2025.
44. [44] K. Divya and K. Indhira, ANFIS-based validation of a matrix geometric approach for an M/M/1 queue with two-kind of disaster under hybrid vacation, RAIRO Oper. Res. 60 (2), 809–829, 2026.
45. [45] T. Aghalya and R. Tamizharasi, Modeling of magnetohydrodynamic Casson nanofluid flow with nonlinear thermal radiation in a stretching porous channel using ANN and Levenberg Marquardt optimization, Indian J. Chem. Technol. 32 (4), 466–477, 2025.