Keywords:-
Keywords:
Balking, Equilibrium threshold, Equilibrium social benefit, markovian queue, observable queue
Article Content:-
Abstract
Queueing system is one of the real applications which is used to establishing the relationship between customers and server for providing service facility. In Wang and zhang [9], The equilibrium threshold balking strategies are analyzed for fully observable and partially observable m/m/1 queue with server breakdown and delayed repair. By the observation and state of server, when customer arrive in the system, he/she decide whether to join or balk the queue. In this paper we consider equilibrium strategy markovian queue with presence of redundant server for condition of balking and delayed repair. By the redundant server, system can improve service quality. Customers may not lose their time for service. In this paper, we calculate the stationary distribution of queue size of queueing system. With the help of markove chain approach and system cast analysis. We calculated equilibrium threshold strategy and equilibrium social benefit for fully observable and partially observable with redundant server for server breakdown and delayed repair.
References:-
References
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2. Economou, A. Manou, Equilibrium balking strategies for a clearing queueing system in alternating environment, Ann. Oper. Res. 208 (1) (2013) 489–514.
3. Economou, S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs, Operations Research Letters 36 (2008) 696–699
4. Nellai Murugan, S. Vijayakumari Saradha "Queueing Systems – A Numerical Approach", International Journal of Mathematics Trends and Technology, 20(1) (2015).
5. Avi-Itzhak, P. Naor, Some queueing problems with the service station subject to breakdown, Operations Research 10 (1962) 303–320.
6. Doo Ho Lee, (2017) Optimal pricing strategies and customer’s equilibrium behaviour in an unobservable M/M/1 queuing system with negative customer and repair, Hindawi, Mathematical problem in Engineering, Volume (2017), Article ID 8910819,11page
7. G. Falin, The M / M / ∞ queue in a random environment, Queueing Syst. 58 (1) (2008) 65–76.
8. Gajendra k. Saraswat, Single Counter Markovian Queuing Model with Multiple Inputs International Journal of Mathematics Trends and Technology, 60(4) (2018), 205-219.
9. J. Wang, F. Zhang, Equilibrium analysis of the observable queues with balking and delayed repairs, Appl. Math. Compute. 218 (6) (2011) 2716–2729.
10. J. Wang, J. Cao, Q. Li, Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing Systems 38 (2001) 363–380
11. Kalidas, K., & Kasturi, R, A Queue with working breakdown, Computer & Industrial Engineer 63(4) (2012),779-783.
12. Kuo-Hsiung Wang and Ying-Chung Chang, cast analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns, Math Meth Oper Res 56 (2002) 169–180.
13. L. Li, J. Wang, F. Zhang, Equilibrium customer strategies in Markovian queues with partial breakdowns, Comput. Ind. Eng. 66 (4) (2013) 751–757.
14. M.ReniSagaya Raj, B.Chandrasekar, S. Anand Gnanaselvam. "A Study on the Queue Length of the State-Dependent of an Unreliable Machine", International Journal of Mathematical Trends and Technology 7 (2014) 42-49.
15. N.M. Edelson, D.K. Hildebrand, Congestion tolls for Poisson queuing process, Econometrica 43 (1) (1982) 81-92
16. P.F. Guo, P. Zipkin, Analysis and comparison of queues with different levels of delay information, Management Science 53 (2007) 962–970.
17. P. Guo, R. Hassine, Strategies behaviour and social optimization in markovian vacation queue, Operation Research 59 (2011) 986-997.
18. P. Naor, The regulation of queue size by levying tolls, Econometrica 37 (1969) 15–24.
19. Pengfi Guo, W. Sun, Y. Whang, Equilibrium and optimal strategies to join a queue with partial information on service time, European Journal of Operation Research 214(2) (2011) 284-297.
20. R. Hassin, Consumer information in markets with random product quality: the case of queues and balking, Econometrica 54 (1986) 1185– 1195.
21. R. Hassin, Information and uncertainty in a queueing system, Probablity in the Engineering and Informational Sciences 21 (2007) 361–380.
22. R. Hassin, M. Haviv, Equilibrium threshold strategies: the case of queues with priorities, Operations Research 45 (1997) 966–973.
23. R. Hassin, M. Haviv, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Kluwer Academic Publishers, Boston, 2003.
24. R. Hassin, M. Henig, Control of arrivals and departures in a state-dependent input–output system, Operations Research Letters 5 (1986) 33–36.
25. S. Stidham Jr., Optimal Design of Queueing Systems, CRC Press, Taylor and Francis Group, Boca Raton, 2009.
26. Senlin Yu ∗, Zaiming Liu, Jinbiao Wu equilibrium strategies of the unobservable M / M /1 queue with balking and delayed repair, Applied Mathematics and Computation 290 (2016) 56–65.
27. W. Sun. S. Li, Q. Li, Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations, Appl. Math. Comput. 248 (2014) 195–214.
28. X. Li, J. Wang, F. Zhang, New results on equilibrium balking strategies in the single-server queue with breakdowns and repairs, Appl. Math. Compute. 241 (2014) 380–388.
29. Z. Liu, S. Yu, The M / M / C queueing system in a random environment, J. Math. Anal. Appl. 436 (1) (2016) 556–567.
30. Zhang, M., & Hou, Z.,Performance analysis of M/G/1 queue working vacation and vacation interruption, Journal of Computational and Applied Mathematics ,234, (2010)2977-2985.
2. Economou, A. Manou, Equilibrium balking strategies for a clearing queueing system in alternating environment, Ann. Oper. Res. 208 (1) (2013) 489–514.
3. Economou, S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs, Operations Research Letters 36 (2008) 696–699
4. Nellai Murugan, S. Vijayakumari Saradha "Queueing Systems – A Numerical Approach", International Journal of Mathematics Trends and Technology, 20(1) (2015).
5. Avi-Itzhak, P. Naor, Some queueing problems with the service station subject to breakdown, Operations Research 10 (1962) 303–320.
6. Doo Ho Lee, (2017) Optimal pricing strategies and customer’s equilibrium behaviour in an unobservable M/M/1 queuing system with negative customer and repair, Hindawi, Mathematical problem in Engineering, Volume (2017), Article ID 8910819,11page
7. G. Falin, The M / M / ∞ queue in a random environment, Queueing Syst. 58 (1) (2008) 65–76.
8. Gajendra k. Saraswat, Single Counter Markovian Queuing Model with Multiple Inputs International Journal of Mathematics Trends and Technology, 60(4) (2018), 205-219.
9. J. Wang, F. Zhang, Equilibrium analysis of the observable queues with balking and delayed repairs, Appl. Math. Compute. 218 (6) (2011) 2716–2729.
10. J. Wang, J. Cao, Q. Li, Reliability analysis of the retrial queue with server breakdowns and repairs, Queueing Systems 38 (2001) 363–380
11. Kalidas, K., & Kasturi, R, A Queue with working breakdown, Computer & Industrial Engineer 63(4) (2012),779-783.
12. Kuo-Hsiung Wang and Ying-Chung Chang, cast analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns, Math Meth Oper Res 56 (2002) 169–180.
13. L. Li, J. Wang, F. Zhang, Equilibrium customer strategies in Markovian queues with partial breakdowns, Comput. Ind. Eng. 66 (4) (2013) 751–757.
14. M.ReniSagaya Raj, B.Chandrasekar, S. Anand Gnanaselvam. "A Study on the Queue Length of the State-Dependent of an Unreliable Machine", International Journal of Mathematical Trends and Technology 7 (2014) 42-49.
15. N.M. Edelson, D.K. Hildebrand, Congestion tolls for Poisson queuing process, Econometrica 43 (1) (1982) 81-92
16. P.F. Guo, P. Zipkin, Analysis and comparison of queues with different levels of delay information, Management Science 53 (2007) 962–970.
17. P. Guo, R. Hassine, Strategies behaviour and social optimization in markovian vacation queue, Operation Research 59 (2011) 986-997.
18. P. Naor, The regulation of queue size by levying tolls, Econometrica 37 (1969) 15–24.
19. Pengfi Guo, W. Sun, Y. Whang, Equilibrium and optimal strategies to join a queue with partial information on service time, European Journal of Operation Research 214(2) (2011) 284-297.
20. R. Hassin, Consumer information in markets with random product quality: the case of queues and balking, Econometrica 54 (1986) 1185– 1195.
21. R. Hassin, Information and uncertainty in a queueing system, Probablity in the Engineering and Informational Sciences 21 (2007) 361–380.
22. R. Hassin, M. Haviv, Equilibrium threshold strategies: the case of queues with priorities, Operations Research 45 (1997) 966–973.
23. R. Hassin, M. Haviv, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Kluwer Academic Publishers, Boston, 2003.
24. R. Hassin, M. Henig, Control of arrivals and departures in a state-dependent input–output system, Operations Research Letters 5 (1986) 33–36.
25. S. Stidham Jr., Optimal Design of Queueing Systems, CRC Press, Taylor and Francis Group, Boca Raton, 2009.
26. Senlin Yu ∗, Zaiming Liu, Jinbiao Wu equilibrium strategies of the unobservable M / M /1 queue with balking and delayed repair, Applied Mathematics and Computation 290 (2016) 56–65.
27. W. Sun. S. Li, Q. Li, Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations, Appl. Math. Comput. 248 (2014) 195–214.
28. X. Li, J. Wang, F. Zhang, New results on equilibrium balking strategies in the single-server queue with breakdowns and repairs, Appl. Math. Compute. 241 (2014) 380–388.
29. Z. Liu, S. Yu, The M / M / C queueing system in a random environment, J. Math. Anal. Appl. 436 (1) (2016) 556–567.
30. Zhang, M., & Hou, Z.,Performance analysis of M/G/1 queue working vacation and vacation interruption, Journal of Computational and Applied Mathematics ,234, (2010)2977-2985.
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Shrivastava, D. R. K., & Dubey, P. G. (2021). The Study of Equilibrium Strategies of the Observable Markovian Queue with Redundant Server for Balking and Delayed Repair. International Journal Of Mathematics And Computer Research, 9(4), 2214-2224. Retrieved from https://ijmcr.in/index.php/ijmcr/article/view/312