Numerical And Graphical Study Of The Average Queue Length For A Hierarchical Feedback Queuing System With Four Servers And The Limited Number Of Revisits To Any One Server
Keywords:
Feedback Queuing System, Four Types of Servers, Hierarchical Order, Limited Revisits to Servers.
Abstract
In this paper, a feedback queueing model that takes into account four servers, connected in hierarchical order. Customers enter the system only through the first server and may proceed to the second, third, or fourth server after that from lower order to higher order server. The customer may return to the previously visited server up to limited number of times if the service does not meet their needs. With each revisit, the chances of returning to the servers are considered to be distinct. The variations in system's average mean queue lengths have been determined using numericals and graphics.
References
1. Atar R and Mendelson G, “On the non-markovian multi-class queue under risk-sensitive cost”, Queuing Systems, 84 (3-4), 2016, 265-78.
2. Atencia, I and Moreno, P; “Discrete-time Geo[X]/GH/1 Retrial Queue with Bernoulli Feedback”, Computers & Mathematics with Applications, 47, (8–9) , April–May 2004, 1273-94.
3. Avrachenkov K, Morozov E and Steyaert B, “Sufficient stability conditions for multi class constant retrial rate systems”, Queuing Systems, 82(1-2), 2016, 149-71.
4. Ginting D.A., Aristotles and Endah O.D., “Implementation of multi-level feedback queue algorithm in restaurant order food application development for android and ios platforms”, International Journals of Computer Applications, 180 (13), 2013, 24-30.
5. Gupta, V.K., Joshi T.N. and Tiwari, S.K., “A balked M/D/1 feedback queuing models”, IOSR- JM, 12(1), 2016, 83-87.
6. Kalyanaraman R and Suvitha V.; “A single server vacation queue with type of services and with restricted admissibility”, Far East Journal of Mathematical Sciences, 103 (1) 2018, 125-157.
7. Ke J.C. and Chang F.M., “Modified vacation policy for M/G/1 retrial queue with balking and feedback”, Computers and Industrial Engineering, 57 (1), 2009, 433-43.
8. Kumar B.K., Arivudainambi D and Krishanmoorthy A, “Some results on a generalized M/G/1 feedback queue with negative customers”, Annals of Operation Research, 143(1), 2006, 277-96.
9. Kumar, B.K, Madheshwari S.P. and Kumar, A.V., “The M/G/1 retrial queue with feedback and starting failures”, Applied Mathematical Modeling, 26 (11), 2002, 1057-75.
10. Kumar, B.K, Madheshwari, S.P. and Lakshmi S.R.A., “An M/G/1 Bernoulli feedback retrial queuing system with negative customers”, Operation Research, 13(2), 2013, 187-210.
11. Kumar B.K and Raja J, “On multi-server feedback retrial queues with balking and control retrial rate”, Annals of Operation Research, 141(1), 2006, 211-32.
12. Kumar S. and Taneja G.; “Analysis of a hierarchical structured queuing system with three service channels, and chances of repetition of service with feedback”, International Jounal of Pure and Applied Mathematics, 115 (2) 2017, 383-363.
13. Latouche, Guy, Nguyen and Giang T.; “Feedback Control: Two-Sided Markov-Modulated Brownian Motion with Instantaneous Change of Phase at Boundaries”, Performance Evaluation, 106, December 2016, 30–49.
14. Sundri S.M. and Srinivasan S, “Multi-phase M/G/1 queue with Bernoulli feedback and multiple server vacation”, 52(1), 2012, 18-23.
15. Tang J and Zhao Y.Q., “Stationary tail asymptotic of a tandem queue with feedback”, Annals of Operation Research, 160 (1), 2008,173-89.
16. Kamal et al. (2023). Mathematical modeling of some feedback queueing systems. Ph. D. Thesis, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana.
17. Nidhi et al. (2024). Modeling and analysis of some feedback queueing networks. Ph. D.Thesis, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana.
2. Atencia, I and Moreno, P; “Discrete-time Geo[X]/GH/1 Retrial Queue with Bernoulli Feedback”, Computers & Mathematics with Applications, 47, (8–9) , April–May 2004, 1273-94.
3. Avrachenkov K, Morozov E and Steyaert B, “Sufficient stability conditions for multi class constant retrial rate systems”, Queuing Systems, 82(1-2), 2016, 149-71.
4. Ginting D.A., Aristotles and Endah O.D., “Implementation of multi-level feedback queue algorithm in restaurant order food application development for android and ios platforms”, International Journals of Computer Applications, 180 (13), 2013, 24-30.
5. Gupta, V.K., Joshi T.N. and Tiwari, S.K., “A balked M/D/1 feedback queuing models”, IOSR- JM, 12(1), 2016, 83-87.
6. Kalyanaraman R and Suvitha V.; “A single server vacation queue with type of services and with restricted admissibility”, Far East Journal of Mathematical Sciences, 103 (1) 2018, 125-157.
7. Ke J.C. and Chang F.M., “Modified vacation policy for M/G/1 retrial queue with balking and feedback”, Computers and Industrial Engineering, 57 (1), 2009, 433-43.
8. Kumar B.K., Arivudainambi D and Krishanmoorthy A, “Some results on a generalized M/G/1 feedback queue with negative customers”, Annals of Operation Research, 143(1), 2006, 277-96.
9. Kumar, B.K, Madheshwari S.P. and Kumar, A.V., “The M/G/1 retrial queue with feedback and starting failures”, Applied Mathematical Modeling, 26 (11), 2002, 1057-75.
10. Kumar, B.K, Madheshwari, S.P. and Lakshmi S.R.A., “An M/G/1 Bernoulli feedback retrial queuing system with negative customers”, Operation Research, 13(2), 2013, 187-210.
11. Kumar B.K and Raja J, “On multi-server feedback retrial queues with balking and control retrial rate”, Annals of Operation Research, 141(1), 2006, 211-32.
12. Kumar S. and Taneja G.; “Analysis of a hierarchical structured queuing system with three service channels, and chances of repetition of service with feedback”, International Jounal of Pure and Applied Mathematics, 115 (2) 2017, 383-363.
13. Latouche, Guy, Nguyen and Giang T.; “Feedback Control: Two-Sided Markov-Modulated Brownian Motion with Instantaneous Change of Phase at Boundaries”, Performance Evaluation, 106, December 2016, 30–49.
14. Sundri S.M. and Srinivasan S, “Multi-phase M/G/1 queue with Bernoulli feedback and multiple server vacation”, 52(1), 2012, 18-23.
15. Tang J and Zhao Y.Q., “Stationary tail asymptotic of a tandem queue with feedback”, Annals of Operation Research, 160 (1), 2008,173-89.
16. Kamal et al. (2023). Mathematical modeling of some feedback queueing systems. Ph. D. Thesis, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana.
17. Nidhi et al. (2024). Modeling and analysis of some feedback queueing networks. Ph. D.Thesis, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana.
Published
2024-08-14
How to Cite
Surender Kumar, Pooja Bhatia, & Neelam. (2024). Numerical And Graphical Study Of The Average Queue Length For A Hierarchical Feedback Queuing System With Four Servers And The Limited Number Of Revisits To Any One Server. Revista Electronica De Veterinaria, 25(2), 1382-1393. https://doi.org/10.69980/redvet.v25i2.1812
Section
Articles
