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Queueing Analysis of Machine Repair Problem with Controlled Rates and Working Vacation Under F-Policy

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Abstract

This paper deals with the queueing characterization of a machine repair problem with single working vacation and controlled arrival of failed machines under F-policy. The server allows the failed machines to enter the system till full capacity K and thereafter the arrival of the failed machines is prohibited which continues till the queue length is reduced to the threshold value F. The server takes some time to start the repair of the failed machines. The life time of the machines, startup time and repair time of the server are exponentially distributed. When the system is empty, the server goes for a single vacation but it keeps on serving the failed units even during vacation at a different pace, and is said to be on working vacation. The matrix method has been used to obtain the steady state probabilities of the system states. Various performance characteristics have been derived. The numerical results have been obtained and shown in tables and graphs.

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References

  1. Borthakur A, Medhi J, Gohain R (1987) Poisson input queueing systems with startup time and under control operating policy. Comput Oper Res 14(1):33–40

    Article  MathSciNet  MATH  Google Scholar 

  2. Jain M, Rakhee SinghM (2004) Bilevel control of a degraded machining system with warm standbys, setup, and vacation. Appl Math Model 28(12):1015–1026

    Article  MATH  Google Scholar 

  3. Ke JC (2004) Bi level control for batch arrival queues with an early startup and unreliable server. Appl Math Model 28(5):469–485

    Article  MATH  Google Scholar 

  4. Ke JC (2007) Batch arrival queues under vacation policies with server breakdowns and startup/closedown times. Appl Math Model 31(70):1282–1292

    Article  MATH  Google Scholar 

  5. Dimitriou I, Langaris C (2010) A repairable queueing model with two-phase service, start-up times and retrial customers. Comput Oper Res 37(7):1181–1190

    Article  MathSciNet  MATH  Google Scholar 

  6. Jain M, Bhargava C (2009) Unreliable server M/G/1 queueing system with Bernoulli feedback, repeated attempts, modified vacation, phase repair and discouragement. J KAU Eng Sci 20(2):45–77

    Article  MathSciNet  Google Scholar 

  7. Yang DY, Wang KH, Ke JC (2008) Optimal randomized control policy of an unreliable server system with second optional service and startup. Eng Comput Int J Comput Aided Eng Softw 25(8):783–800

    Article  Google Scholar 

  8. Yang DY, Wang KH, Pearn WL (2011) Optimization on (N, p)-policy for an unreliable queue with second optional service and start-up. J Chin Inst Ind Eng 28(6):411–424

    Google Scholar 

  9. Tadj L, Choudhury G, Rekab K (2012) A two-phase quorum queueing system with Bernoulli vacation schedule, setup, and N-policy for an unreliable server with delaying repair. Int J Ser Oper Manag 12(2):139–164

    Google Scholar 

  10. Haridass M, Arumuganathan R (2012) A batch service queueing system with multiple vacations, setup time and server’s choice of admitting reservice. Int J Oper Res 14(2):156–186

    Article  MathSciNet  Google Scholar 

  11. Jain M, Upadhyaya S (2012) Optimal repairable Mx/G/1 queue with Bernoulli feedback and setup. Int J Math Oper Res 4(6):679–702

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  13. Goswami V, Mund GB (2011) Analysis of discrete-time batch service renewal input queue with multiple working vacations. Comput Ind Eng 61(3):629–636

    Article  Google Scholar 

  14. Jain M, Agarwal PK (2007) M/Ek/1 queueing system with working vacation. Int J Qual Technol Quant Manag 4(4):455–470

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Jain M, Upadhyaya S (2009) M/G/(a, b)/1/K queue with working vacation. Math Today 25(25):41–60

    Google Scholar 

  17. Jain M, Upadhyaya S (2011) Synchronous working vacation policy for finite-buffer. Appl Math Comput 217(24):9916–9932

    Article  MathSciNet  MATH  Google Scholar 

  18. Jain M, Sharma GC, Sharma R (2010) Matrix geometric method for working vacation queueing system with second optional service and vacation interruption. Math Today 26:14–27

    Google Scholar 

  19. Jain M, Sharma GC, Sharma R (2011) Working vacation queue with service interruption and multi optional repair. Int J Inform Manag Sci 22(2):157–175

    MathSciNet  MATH  Google Scholar 

  20. Li J, Tian N (2011) Performance analysis of a GI/M/1 queue with single working vacation. Appl Math Comput 217(10):4960–4971

    Article  MathSciNet  MATH  Google Scholar 

  21. Li T, Wang Z, Liu Z (2012) Geo/Geo/1 retrial queue with working vacations and vacation interruption. J Appl Math Comput 39(1):131–143

    Article  MathSciNet  MATH  Google Scholar 

  22. Jain M, Chauhan D (2012) Working vacation queue with second optional service and unreliable server. Int J Eng 25(3):223–230

    Article  Google Scholar 

  23. Singh CJ, Jain M, Kumar B (2012) MX/G/1 queuing model with state dependent arrival and second optional vacation. Int J Math Oper Res. 4(1):78–96

    Article  MathSciNet  Google Scholar 

  24. Jain M, Sharma GC, Sharma R (2012) Maximum entropy approach for discrete time unreliable server Geox/Geo/1 queue with working vacation. Int J Math Oper Res 4(1):56–77

    Article  MathSciNet  Google Scholar 

  25. Dimitriou I (2013) A mixed priority retrial queue with negative arrivals, unreliable server and multiple vacations. Appl Math Model 37(3):1295–1309

    Article  MathSciNet  Google Scholar 

  26. Gupta SM (1995) Interrelationship between controlling arrival and service in queueing systems. Comput Oper Res 22(10):1005–1014

    Article  MATH  Google Scholar 

  27. Jain M, Sharma GC, Kumar N (2009) Controllable and interdependent MRP with additional repairman and mixed standbys. Rajasthan Acad Phys Sci 8(4):447–456

    MATH  Google Scholar 

  28. Karaesmen F, Gupta SM (1997) Control of arrivals in a finite buffered queue with setup costs. J Oper Res Soc 48(11):1113–1122

    Article  MATH  Google Scholar 

  29. Karaesmen F, Gupta SM (1997) Duality relations for queues with arrival and service control. Comput Oper Res 24(6):529–538

    Article  MathSciNet  MATH  Google Scholar 

  30. Mishra SS (2009) Optimum performance measures of interdependent queueing system with controllable arrival rates. Int J Eng Appl Sci 5(6):352–355

    Google Scholar 

  31. Wang KH, Yang DY (2009) Controlling arrivals for a queueing system with an unreliable server: Newton–Quasi method. Appl Math Comput 213(1):92–101

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang KH, Kuo CC, Pearn WL (2007) Optimal control of an M/G/1/K queueing system with combined F-policy and startup time. J Optim Theory Appl 135(2):285–299

    Article  MathSciNet  MATH  Google Scholar 

  33. Wang KH, Kuo CC, Pearn WL (2008) A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time. Appl Math Model 32(6):958–970

    Article  MathSciNet  MATH  Google Scholar 

  34. Jain M, Chauhan D (2010) Optimal control policy for state dependent queueing model with service interruption, setup and vacation. J Inform Math Sci 2(2):171–181

    Google Scholar 

  35. Yang DY, Wang KH, Wu CH (2010) Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation. J Comput Appl Math 234(2):545–556

    Article  MathSciNet  MATH  Google Scholar 

  36. Huang HI, Hsu PC, Ke JC (2011) Controlling arrival and service of a two-removable-server system using genetic algorithm. Expert Syst Appl 38(8):10054–10059

    Article  Google Scholar 

  37. Yang, DY, Wang KH, Liou CH (2011) Randomized controlling arrivals for a finite queue with startup. In: Proceedings of the fourth international joint conference on computational sciences and optimization, Yunnan, China, pp 122–126

  38. Jain M, Sharma GC, Sharma R (2012) Optimal control of (N, F) policy for unreliable server queue with multi-optional phase repair and start-up. Int J Math Oper Res 4(2):152–174

    Article  MathSciNet  Google Scholar 

  39. Jamil N (2013) A comparison of iterative methods for the solution of non-linear systems of equations. Int J Emerg Sci 3(2):119–130

    Google Scholar 

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Authors and Affiliations

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

    Madhu Jain

  2. Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Chandra Shekhar

  3. Department of Mathematics, D.A.V. (PG) College, Dehra Dun, Uttarakhand, 248001, India

    Shalini Shukla

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  1. Madhu Jain
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  2. Chandra Shekhar
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  3. Shalini Shukla
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Correspondence to Shalini Shukla.

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Jain, M., Shekhar, C. & Shukla, S. Queueing Analysis of Machine Repair Problem with Controlled Rates and Working Vacation Under F-Policy. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86, 21–31 (2016). https://doi.org/10.1007/s40010-015-0233-1

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  • DOI: https://doi.org/10.1007/s40010-015-0233-1

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