The Study of Equilibrium Strategies of the Unobservable Markovian Queue with Redundant Server for Balking and Delayed Repair

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-2
Year of Publication : 2021
Authors : Preeti Gautami Dubey, Dr. R. K. Shrivastava
  10.14445/22315373/IJMTT-V67I2P519

MLA

MLA Style:  Preeti Gautami Dubey, Dr. R. K. Shrivastava. "The Study of Equilibrium Strategies of the Unobservable Markovian Queue with Redundant Server for Balking and Delayed Repair" International Journal of Mathematics Trends and Technology 67.2 (2021):130-139. 

APA Style: Preeti Gautami Dubey, Dr. R. K. Shrivastava(2021). The Study of Equilibrium Strategies of the Unobservable Markovian Queue with Redundant Server for Balking and Delayed Repair. International Journal of Mathematics Trends and Technology, 130-139.

Abstract
Senlin and Zaiming (2016) [21] studied the equilibrium strategies for the fully unobservable and almost unobservable single-server queues with breakdowns and delayed repairs. The present paper aims to study the customers behavior of the system in markovian single server queue with presence of redundant server. Redundant server is an extra server which is used in our model so that the system provides a reliable working facility to the customer. In unobservable case an arriving customer does not know length of queue. The model under consideration can be observed as an M / M /1 queue in a casual environment. Equilibrium balking strategies in single server markovian queue with redundant server are calculated for the almost unobservable and fully unobservable queues. Finally, we demonstrate the effect of several system parameters on the equilibrium behavior.

Reference

[1] A. Burnetas, A. Economou, Equilibrium customer strategies in a single server Markovian queue with setup times, Queueing Syst. 56 (3-4) (2007) 213–228.
[2] A. Economou, S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs, Oper. Res. Lett. 36 (6) (2008) 696–699.
[3] A. Economou, A. Manou, Equilibrium balking strategies for a clearing queueing system in alternating environment, Ann. Oper. Res. 208 (1) (2013) 489–514.
[4] A. Nellai Murugan, S. Vijayakumari Saradha "Queueing Systems – A Numerical Approach", International Journal of Mathematics Trends and Technology ,20(1) (2015).
[5] 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
[6] G. Falin, The M / M / ∞ queue in a random environment, Queueing Syst. 58 (1) (2008) 65–76.
[7] Gajendra k. Saraswat , Single Counter Markovian Queuing Model with Multiple Inputs International Journal of Mathematics Trends and Technology, 60(4) (2018), 205-219.
[8] J. Wang, F. Zhang, Equilibrium analysis of the observable queues with balking and delayed repairs, Appl. Math. Compute. 218 (6) (2011) 2716–2729.
[9] K. Jagannathan, I. Menache, E. Modiano, G. Zussman, Non-cooperative spectrum access-the delicated vs. free spectrum choice, IEEE J. Sel. Area. Com- mun. 30 (11) (2012) 2251–2261
[10] Kalidas, K., & Kasturi, R, A Queue with working breakdown, Computer & Industrial Engineer63(4) (2012),779-783.
[11] 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.
[12] L. Li, J. Wang, F. Zhang, Equilibrium customer strategies in Markovian queues with partial breakdowns, Comput. Ind. Eng. 66 (4) (2013) 751–757.
[13] M. Baykal-Gursoy, W. Xiao, Stochastic decomposition in M/ M / ∞ queues with Markov modulated service rates, Queueing Syst. 48 (1-2) (2004) 75–88.
[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 queue with different level 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 (1) (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, M. Haviv, To queue or not to queue: Equilibrium behaviour in queuing system, Kulwer Academic Publishers, (2003).
[21] 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.
[22] 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.
[23] 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.
[24] Z. Liu, S. Yu, The M / M / C queueing system in a random environment, J. Math. Anal. Appl. 436 (1) (2016) 556–567.
[25] 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.

Keywords : Equilibrium, Markovian queue, Queueing Theory, Redundant, Unobservable queue.