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ANFIS for Markovian Unreliable Retrial Queue with Differentiated Vacation

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Proceedings of the 12th International Conference on Soft Computing for Problem Solving (SocProS 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 995))

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Abstract

The performance analysis of an unreliable server Markovian retrial queueing system with balking and reneging of the customers has been proposed. The differentiated vacation policy has been considered which is a combination of \(k\) working vacation and complete vacation. To analyze the queueing system, Chapman-Kolmogorov equations are constructed and solved by implementing the matrix geometric method. The system metrics such as state probabilities, mean queue length, mean system length, mean waiting time in the queue, and total cost of the system are formulated. The sensitivity analysis of the system performance metrics has been done by taking illustrations. The hybrid soft computing approach Adaptive Neuro-Fuzzy Inference System (ANFIS) has also been implemented to explore the design of AI-based controller in order to control the traffic.

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References

  1. Falin G (1990) A survey of retrial queues. Queueing Syst 7(2):127–167

    Article  MathSciNet  Google Scholar 

  2. Artalejo JR (2010) Accessible bibliography on retrial queues: progress in 2000–2009. Math Comput Model 51(9–10):1071–1081

    Article  MathSciNet  Google Scholar 

  3. Kim J, Kim B (2016) A survey of retrial queueing systems. Ann Oper Res 247(1):3–36

    Article  MathSciNet  Google Scholar 

  4. Servi LD, Finn SG (2002) M/M/1 queues with working vacations (M/M/1/WV). Perform Eval 50(1):41–52

    Article  Google Scholar 

  5. Li K, Wang J, Ren Y, Chang J (2016) Equilibrium joining strategies in M/M/1 queues with working vacation and vacation interruptions. RAIRO-Operat Res 50(3):451–471

    Article  MathSciNet  Google Scholar 

  6. Yang DY, Wu CH (2019) Performance analysis and optimization of a retrial queue with working vacations and starting failures. Math Comput Model Dyn Syst 25(5):463–481

    Article  MathSciNet  Google Scholar 

  7. Jain M, Dhibar S, Sanga SS (2022) Markovian working vacation queue with imperfect service, balking and retrial. J Ambient Intell Humaniz Comput 13(4):1907–1923

    Article  Google Scholar 

  8. Doshi BT (1986) Queueing systems with vacations—a survey. Queueing Syst 1(1):29–66

    Article  MathSciNet  Google Scholar 

  9. Takagi H (1991) Queueing analysis: a foundation of performance evaluation. Finite Systems, North Holland, Amsterdam

    Google Scholar 

  10. Tian N, Zhang ZG (2006) Vacation queueing models: theory and applications, vol 93. Springer Science & Business Media

    Google Scholar 

  11. Ke JC, Chang FM, Liu TH (2019) M/M/c balking retrial queue with vacation. Qual Technol Quant Manag 16(1):54–66

    Article  Google Scholar 

  12. Kumar A, Jain M (2021) M/M/1 queue with bi-level network process and bi-level vacation policy with balking. Commun Stat Theory Methods 52(15):5502–5526

    Article  MathSciNet  Google Scholar 

  13. Ibe OC, Isijola OA (2014) M/M/1 multiple vacation queueing systems with differentiated vacations. Model Simul Eng 2014:18–24

    Google Scholar 

  14. Suranga Sampath MIG, Liu J (2018) Impact of customer’s impatience on an M/M/1 queueing system subject to differentiated vacations with a waiting server. Qual Technol Quant Manag 17(2):125–148

    Google Scholar 

  15. Gupta P, Kumar N (2021) Analysis of classical retrial queue with differentiated vacation and state dependent arrival rate. Ratio Math 40:47–66

    Google Scholar 

  16. Azhagappan A, Deepa T (2022) Transient analysis of various vacation interruption policies in a Markovian queue with differentiated multiple vacations. Int J Oper Res 45(4):492–510

    Article  MathSciNet  Google Scholar 

  17. Sherman NP, Kharoufeh JP (2006) An M/M/1 retrial queue with unreliable server. Oper Res Lett 34(6):697–705

    Article  MathSciNet  Google Scholar 

  18. Jain M, Jain A (2010) Working vacations queueing model with multiple types of server breakdowns. Appl Math Model 34(1):1–13

    Article  MathSciNet  Google Scholar 

  19. Chang FM, Liu TH, Ke JC (2018) On an unreliable-server retrial queue with customer feedback and impatience. Appl Math Model 55:171–182

    Article  MathSciNet  Google Scholar 

  20. Choudhary A, Sharma DC (2022) Analysis of Markovian queue model with unreliable service station and a vacation after fixed services. Int J Math Oper Res 21(3):411–428

    Article  MathSciNet  Google Scholar 

  21. Jain M, Mehta P (2023) Markovian unreliable server retrial queue with double orbit, imperfect repair and balking. Natl Acad Sci Lett 1–7. https://doi.org/10.1007/s40009-023-01250-x

  22. Neuts MF (1981) Matrix geometric solutions in stochastic models: an algorithmic approach. Johns Hopkins University Press, Baltimore, MD

    Google Scholar 

  23. Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modeling. ASA-SIAM series on applied probability, Philadelphia PA

    Google Scholar 

  24. Tian NS, Li JH, Zhang ZG (2009) Matrix analytic method and working vacation queues—a survey. Int J Inf Manag Sci 20(4):603–633

    MathSciNet  Google Scholar 

  25. Gómez-Corral A (2006) A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Ann Oper Res 141(1):163–191

    Article  MathSciNet  Google Scholar 

  26. Zhang ZJ, Xu XL (2008) Analysis for the M/M/1 queue with multiple working vacations and N-policy. Int J Inf Manag Sci 19(3):495–506

    MathSciNet  Google Scholar 

  27. Tao L, Zhang L, Gao S (2014) M/M/1 retrial queue with working vacation interruption and feedback under N-policy. J Appl Math 2014:1–9

    Article  MathSciNet  Google Scholar 

  28. Jain A, Raychaudhuri C (2022) Cost optimization using genetic algorithm in customers intolerance Markovian model with working vacation and multiple working breakdowns. Int J Math Eng Manag Sci 7(5):656–669

    Google Scholar 

  29. Jang JS (1993) ANFIS: Adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Article  Google Scholar 

  30. Jain M, Sanga SS. Performance modeling and ANFIS computing for finite buffer retrial queue under F-policy. In: Proceedings of sixth international conference on soft computing for problem solving. Advances in intelligent systems and computing, vol. 547. Springer, Singapore

    Google Scholar 

  31. Sanga SS, Jain M (2019) Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement. Appl Math Comput 363:124624

    MathSciNet  Google Scholar 

  32. Sethi R, Jain M, Meena RK, Garg D (2020) Cost optimization and ANFIS computing of an unreliable M/M/1 queueing system with customers’ impatience under N-policy. Int J Appl Comput Math 6(2):1–14

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Indian Institute of Technology Roorkee, Roorkee, 247667, Uttarakhand, India

    Palak Mehta

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, Uttarakhand, India

    Madhu Jain

  3. Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    Anamika Jain

Authors
  1. Palak Mehta
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  2. Madhu Jain
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  3. Anamika Jain
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Corresponding author

Correspondence to Palak Mehta .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Scientific Computing, IIT Roorkee, Roorkee, Uttarakhand, India

    Millie Pant

  2. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Kusum Deep

  3. School of Mathematics, Computer Science and Engineering, Liverpool Hope University, LIVERPOOL, UK

    Atulya Nagar

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Mehta, P., Jain, M., Jain, A. (2024). ANFIS for Markovian Unreliable Retrial Queue with Differentiated Vacation. In: Pant, M., Deep, K., Nagar, A. (eds) Proceedings of the 12th International Conference on Soft Computing for Problem Solving. SocProS 2023. Lecture Notes in Networks and Systems, vol 995. Springer, Singapore. https://doi.org/10.1007/978-981-97-3292-0_50

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