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Fuzzy modeling of single server double orbit retrial queue

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Abstract

This paper investigates the single server double orbit retrial queueing model with customer’s discouragement in a fuzzy environment. The arriving customers in the system may be categorized into two classes, namely, ordinary customers and premium customers. The provision of double orbits (i) ordinary orbit and (ii) premium orbit, for the different class of customers, is made along with the realistic feature of balking and feedback behavior of the ordinary customers. On arrival, if both types of customers find the server busy and intend to join the system, then they are forced to shift their respective orbits. It is assumed that high (less) paying customers can be accommodated in a premium (ordinary) orbit. Further, based on Zadeh’s extension principle, \(\alpha\)-cut approach is implemented to construct a set of parametric nonlinear programming for performance indices, which is then solved by using concepts of calculus. Various performance indices including a mean number of customers and mean waiting time in the system are established for both in the crisp and fuzzy environment. Illustration examples are also explained by taking a triangular fuzzy number for input parameters.

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References

  • Arivudainambi D, Godhandaraman P (2015) Retrial queueing system with balking, optional service and vacation. Ann Oper Res 229:67–84

    Article  MathSciNet  Google Scholar 

  • Artalejo JR, Li Q-L (2010) Performance analysis of a block-structured discrete-time retrial queue with state-dependent arrivals. Discret Event Dyn Syst 20:325–347. https://doi.org/10.1007/s10626-009-0075-6

    Article  MathSciNet  MATH  Google Scholar 

  • Artalejo JR, Lopez-Herrero MJ (2000) On the single server retrial queue with balking. INFOR Inf Syst Oper Res 38:33–50

    Google Scholar 

  • Bagherinejad J, Pishkenari SB (2016) Analysis of FM/FM/c queuing system: using fuzzy approach and parametric nonlinear programming. Int J Ind Syst Eng 23:125–140

    Google Scholar 

  • Bhardwaj R, Singh T, Kumar V (2018) Mathematical study of queue system with impatient customers under fuzzy environment. In: Soft computing: theories and applications, pp 679–688

  • Bouazzi I, Bhar J, Atri M (2017) Priority-based queuing and transmission rate management using a fuzzy logic controller in WSNs. ICT Express 3:101–105

    Article  Google Scholar 

  • Buckley JJ (2004) Fuzzy probabilities and fuzzy sets for web planning, 1st edn. Springer-Verlag, Berlin

    Book  Google Scholar 

  • 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 

  • D’Arienzo MP, Dudin AN, Dudin SA, Manzo R (2020) Analysis of a retrial queue with group service of impatient customers. J Ambient Intell Humaniz Comput 11:2591–2599

    Article  Google Scholar 

  • Gal T (1979) Postoptimal analysis, parametric programming, and related topics, 2nd edn. McGraw-Hill, New York

    MATH  Google Scholar 

  • Gao S, Niu X, Li T (2017) Analysis of a constant retrial queue with joining strategy and impatient retrial customers. Math Probl Eng 2017:1–8

    MathSciNet  Google Scholar 

  • González García C, Núñez-Valdez E, García-Díaz V et al (2019) A review of artificial intelligence in the internet of things. Int J Interact Multimed Artif Intell 5:9–20

    Google Scholar 

  • Gross D, Shortle JF, Thompson JM, Harris CM (2008) Fundamentals of queueing theory, 4th edn. John Wiley & Sons, Inc., New Jersey

    Book  Google Scholar 

  • Houck DJ, Lai WS (1998) Traffic modeling and analysis of hybrid fiber-coax systems. Comput Netw ISDN Syst 30:821–834

    Article  Google Scholar 

  • Jain M, Bhagat A (2013) Transient analysis of retrial queues with double orbits and priority customers. In: 8th International conference on queuing theory and network applications, Taichung, Taiwan, pp 235–240

  • Jain M, Sanga SS (2017a) 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, Patiala, India, pp 248–258

  • Jain M, Sanga SS (2017b) Control F-policy for fault tolerance machining system with general retrial attempts. Natl Acad Sci Lett 40:359–364

    Article  MathSciNet  Google Scholar 

  • Jain M, Sanga SS (2019) F-policy for M/M/1/K retrial queueing model with state-dependent rates. In: Performance prediction and analytics of fuzzy, reliability and queuing models, Asset analytics (performance and safety management), pp 127–138

  • Jain M, Sanga SS (2020) Fuzzy cost optimization and admission control for machine interference problem with general retrial. J Test Eval 48:4488–4502

    Article  Google Scholar 

  • Jain M, Sanga SS, Meena RK (2016) Control F-policy for Markovian retrial queue with server breakdowns. In: 1st International conference on power electronics, intelligent control and energy systems (ICPEICES), New Delhi, India, pp 1–5

  • Jain M, Kumar P, Meena RK (2020) Fuzzy metrics and cost optimization of a fault-tolerant system with vacationing and unreliable server. J Ambient Intell Humaniz Comput 11:5755–5770

    Article  Google Scholar 

  • Jain M, Kumar P, Sanga SS (2021) Fuzzy Markovian modeling of machining system with imperfect coverage, spare provisioning and reboot. J Ambient Intell Humaniz Comput 12:7935–7947

    Article  Google Scholar 

  • Ke J-C, Chang F-M (2009) Modified vacation policy for M/G/1 retrial queue with balking and feedback. Comput Ind Eng 57:433–443

    Article  Google Scholar 

  • Ke J-C, Huang H-I, Lin C-H (2006) Parametric programming approach for batch arrival queues with vacation policies and fuzzy parameters. Appl Math Comput 180:217–232

    MathSciNet  MATH  Google Scholar 

  • Ke J-C, Huang H-I, Lin C-H (2007) On retrial queueing model with fuzzy parameters. Phys A Stat Mech Appl 374:272–280

    Article  Google Scholar 

  • Ke J-C, Chang F-M, Liu T-H (2019) M/M/c balking retrial queue with vacation. Qual Technol Quant Manag 16:54–66

    Article  Google Scholar 

  • Kumar R, Sharma SK (2014) A multi-server Markovian feedback queue with balking reneging and retention of reneged customers. Adv Model Optim 16:395–406

    MATH  Google Scholar 

  • Kumar S, Kumar-Solanki V, Choudhary SK et al (2020) Comparative study on ant colony optimization (ACO) and K-means clustering approaches for jobs scheduling and energy optimization model in internet of things (IoT). Int J Interact Multimed Artif Intell 6:107–116

    Google Scholar 

  • Mueen Z, Ramli R, Zaibidi N (2017) Parametric nonlinear programming approach with fuzzy queues using hexagonal membership functions. J Comput Theor Nanosci 14:4979–4985

    Article  Google Scholar 

  • Sanga SS, Jain M (2019) FM/FM/1 double orbit retrial queue with customers’ joining strategy: a parametric nonlinear programing approach. Appl Math Comput 362:124542

    MathSciNet  MATH  Google Scholar 

  • Singh CJ, Kaur S, Jain M (2017) Waiting time of bulk arrival unreliable queue with balking and Bernoulli feedback using maximum entropy principle. J Stat Theory Pract 11:41–62

    Article  MathSciNet  Google Scholar 

  • 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 

  • Tran-Gia P, Mandjes M (1997) Modeling of customer retrial phenomenon in cellular mobile networks. IEEE J Sel Areas Commun 15:1406–1414

    Article  Google Scholar 

  • Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24:143–161

    Article  MathSciNet  Google Scholar 

  • Yang D-Y, Chang P-K (2015) A parametric programming solution to the F -policy queue with fuzzy parameters. Int J Syst Sci 46:590–598

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:61–72

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Humanities, SV National Institute of Technology Surat, Surat, India

    Sudeep Singh Sanga

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

    Madhu Jain

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  1. Sudeep Singh Sanga
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  2. Madhu Jain
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Correspondence to Sudeep Singh Sanga.

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Sanga, S.S., Jain, M. Fuzzy modeling of single server double orbit retrial queue. J Ambient Intell Human Comput 13, 4223–4234 (2022). https://doi.org/10.1007/s12652-022-03705-3

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