Comparative Fuzzy and Intuitionistic Fuzzy Study of a Retrial Queue with Negative Arrivals, Breakdown and Delayed Repairs

Main Article Content

Vinod Kumar Srivastava
Sandeep Rawat
S S Mishra

Abstract

In this paper, comparative study of the steady state retrial system under fuzzy and Intuitionistic fuzzy environments has been made by us. The retrial system has negative arrivals, and breakdown with delayed repair. Triangular fuzzy and triangular intuitionistic fuzzy mathematics have been used as our tools. To validate the stability condition, a ranking method (for fuzzy number) and a magnitude method (for intuitionistic fuzzy number) have been applied. Various system probabilities together with multitude of performance measures under both the environments have been evaluated. We have supported the important effectiveness measures by relevant graphs.

Downloads

Download data is not yet available.

Article Details

Section

Articles

How to Cite

1.
Comparative Fuzzy and Intuitionistic Fuzzy Study of a Retrial Queue with Negative Arrivals, Breakdown and Delayed Repairs. J. Int. Acad. Phys. Sci. [Internet]. 2024 Sep. 15 [cited 2026 Oct. 23];28(3):223-40. Available from: http://www.iaps.org.in/journal/index.php/journaliaps/article/view/1019

References

Y. Han, R.Tian, X. Wu and L. He, On a Retrial Queue with Negative Customers, Passive Breakdown, and Delayed Repairs, Probability in the Engineering and Informational Sciences, 38(2), (2024), 428-447. https://doi:10.1017/S0269964823000219

L. Kosten, On the Influence of Repeated Calls in the Theory of Probabilities of Blocking, De Ingenieur, 59(1), (1947), 1-25.

J. W. Cohen, Basic Problems of Telephone Traffic Theory and Influence of Repeated Calls, Phillips Telecommunication Review, 18(2), (1957), 49-104.

G. I. Falin and J. G. Templeton, Retrial Queues (First ed.), Springer-Science+Business Media, (1997), https://doi:10.1007/978-1-4899-2977-8

J. R. Artalezo and A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach. Springer, Berlin, 2008.

J. R. Artalejo, Accessible Bibliography on Retrial Queues: Progress in 2000-2009. Mathematical and Computer Modelling, 51, (2010), 1071-1081, https://doi:10.1016/j.mcm.2009.12.011

H. White, L. S. Christie, Queueing with Preemptive Priorities or with Breakdowns. Operations Research, 6(1), (1958), 79-96, https://dx.doi.org/10.1287/opre.6.1.79

V. G. Kulkarni and B. D. Choi, Retrial Queues with Server Subject to Breakdowns and Repairs. Queueing Systems, 7, (1990), 191-208, https://doi:10.1007/BF01158474

R. Tian, X. Wu, L. He and Y. Han, Strategic Analysis of Retrial Queues with Setup Times, Breakdown and Repairs. Discrete Dynamics in Nature and Society, 2023, Article ID4930414, (2023), 1-19, https://doi.org/10.1155/2023/4930414

S. Upadhyay, D. Agarwal, R. Agarwal, I. Ahmad, A. H. Ibrahim and S. Al-homidan, Queueing and Reliability Analysis of Unreliable Multi-Server Retrial Queue with Bernouilly Feedback, Carapathian Journal of Mathemtics, 39(3), (2023), 745-758. https://doi:10.37193/CJM.2023.03.13

V. Poongothai, V. Saravanan, M. Kannan and P. Godhandaraman, An M/M/2 Retrial Queueing System with Discouragement, Breakdowns and Repairs, AIP Con. Proc. 2516, 360010. AIP Publishing. (2022), https://doi:10.1063/5.0109027

P. Gupta, Study of Feedback Retrial Queueing System with Working Vacation, Setup Time and Perfect Repair, Ratio Mathematica, 41, (2021), 291-307. https://doi:10.23755/rm.v41i0.655

E. Gelenbe, Random Neural Network Networks with Negative and Positive Signals and Product Form Solution, Neural Computation, 1(4), (1989), 502-510. https://doi:10.1162/neco.1989.1.4.502

Y. W. Shin, Multi-server Retrial Queue with Negative Customers and Disasters, Queueing Systems, 55, (2007), 223-237. https://doi:10.1007/s11134-007-9018-9

J. Wang and P. Zhang, A Discrete-time Retrial Queue with Negative Customers and Unreliable Server, Computers and Industrial Engineering, 4, (2009) 1216-1222. https://doi:10.1016/j.cie.2008.07.010

I. Dimitriou, A Mixed Priority Retrial Queue with Negative Arrivals, Unreliable Server and Multiple Vacations, Applied Mathematical Modelling, 37(3), (2013), 1295-1309. https://doi:10.1016/j.apm.2012.04.011

G. Malik, S. Upadhyay and R. Sharma, A Study on Retrial g-Queues under Different Scenarios: A Review. Proceedings of Industrial Conference on Scientific and Natural Computing: Proceedings of SNC 2021, (2021), (pp. 211-220). https://doi:10.1007/978-981-16-1528-3_18

J. Bharathi, S. Nandhini and N. Fataf, Bulk Arrival Retrial Queue with G-Queue and Reneging Clients, Reliability: Theory & Applications, 19(2(78)), (2024), 314-323.

M. Jain and A. Bhagat, Unreliable bulk Retrial Queues with Delayed Repairs and Modified Vacation Policy, Journal of Industrial Engineering International, 10(63), (2014), 1-19. https://doi:10.1007/s40092-014-0063-9

G. Chaudhary and J. C. Ke, An Unreliable Retrial Queue with Delaying Repair and General Retrial Times under Bernoulli Vacation Schedule, Applied Mathematics and Computation, 230, (2014), 436-450. https://doi:10.1016/j.amc.2013.12.108

G. Choudhary and J. C. Ke, A Batch Arrival Retrial Queue with General Retrial Times under Bernoulli Vacations Schedule for Unreliable Server and Delaying Repair, Applied Mathematical Modelling, 36(1), (2012), 255-269. https://doi:10.1016/j.apm.2011.05.047

S. Gao, J. Zhang and X. Wang, Analysis of Retrial Queue with Two Type Breakdowns and Delayed Repairs, IEEE Access, 8, (2020), 172428-172442. https://doi:10.1109/ACCESS.2020.3023191

C. J. Singh, S. Kaur and M. Jain, Unreliable Retrial G-Queue with Bulk Arrival, Optional Additional Service and Delayed Repair, International Journal of Operational Research, 38(1), (2020), 82-111. https://doi:10.1504/IJOR.2020.106362

T.-H. Liu, F.-M. Chang, J.-C. Ke and S.-H. Sheu, Optimization of Retrial Queue with Unreliable Servers Subject to Imperfect Coverage and Reboot Delay, Quality Technology and Quantitative Management, 19(4), (2022), 428-453. https://doi:10.1080/16843703.2021.2020952

J. Bharathi and S. Nandhini, Retrial G-Queue with Precipitous Breakdown and Non-Tenacious Customers, Yugoslav Journal of Operations Research. (2024), https://doi:10.2298/YJOR230915001B

L. A. Zadeh, Fuzzy Sets as a Basis for a Theory of Possibility, Information and Control, 8 (1965), 338-353. https://doi:10.1016/S0019-9958(65)90241-X

H. -J. Zimmerman, Fuzzy Set Theory and Its Applications, Springer Science and Business Media, 2001, https://doi:10.1007/978-94-010-0646-0

J. -C. Ke, H. -I. Huang and C. -H. Lin, On Retrial Queueing Model with Fuzzy Parameters, Physica A: Statistical Mechanics and Its Applications, 374(1), (2007), 272-280. https://doi:10.1016//j.physa.2006.05.057

J. P. Mukeba, Application of L-R Method to Single Server Fuzzy Retrial Queue with Patient Customers, Journal of Pure and Applied Mathematics:Advances and Applications, 16(1), (2016), 43-59. https://dx.doi.org/10.18642/jpamaa_7100121698

J. P. Kanyinda, Analysis of Retrial Fuzzy Queue with Single Server Subject to Breakdowns and Repairs by Flexible Alpha-Cuts Method, Journal of Pure and Applied Mathematics: Advances and Applications, 22(1), (2020), 41-58. https://dx.doi.org/10.18642/jpamaa_7100122109

G. Kannadasan and V. Padmavathi, Classical Fuzzy Retrial Queue with Working Vacation Using Hexagonal Fuzzy Numbers, Journal of Physics: Conference Series, 2070(1):012018, (2021), https://doi:10.1088/1742-6596/2070/1/012018

G. Kannadasan and V. Padmavathi, Analysis of FM/FM/1/N Finite Retrial Queue with Hexagonal Fuzzy Numbers, AIP Conference Proceedings 2516, 360001,(2022), https://doi.org/10.1063/5.0108636

L. Dymova and P. Sevastjanov, Operations on Intuitionistic Fuzzy Values in Multiple Criteria Decision Making, Scientific Research of the Institute of Mathematics and Computer Science, 10(1), (2011), 41-48.

K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3

D. Dubey and A. Mehra, Linear Programming with Triangular Intuitionistic Fuzzy Number, Proceedings of 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11), Series: Advances in Intelligent Systems Research. 1(1), (2011), 563-569. Atlantis Press. https://doi.org//10.2991/eusflat.2011.78

S. Aarathi; Comparison of Single Server Retrial Queueing Performance Using Fuzzy Queueing Model and Intuitionistic Fuzzy Queueing Model with Inffinite Capacity, RT&A, 19(2(78)), (2024) 218-231.

S. Aarthi, and M. Shanmugasundari, Comparison of Infinite Capacity FM/FEk/1 Queueing Performance using Fuzzy Queueing Model and Intuitionistic Fuzzy Queueing Model with Erlang Service Rates, Pakistan Journal of Statistics and Operations Research, 19(1), (2023), 187-202. https://dx.doi.org/18187/pjsor.v19i1.4055

S. Aarthi and M. Shanmugasundari, Comparison of Single Server Queueing Performance Measure using Fuzzy Queueing Model with Infinite Capacity, Journal of Intelligent and Fuzzy Systems, 44(3), (2023), 4733-4746. https://doi.org/10.3233/JIFS-221367

S. Chandrasekaran and V. R. Bindu Kumari, Performance Measure of Retrial Queues in Intuitionistic Fuzzy Environment, International Journal of Mechanical Engineering, 6(3), (2021), 2073-2077.

Most read articles by the same author(s)