A MARKOVIAN QUEUE WITH FEEDBACK AND SECOND OPTIONAL WORKING VACATION

Authors

  • Dr. K. Santhi Assistant Professor,Dept of Mathematics, Annamalai University
  • Dr. S. Pazhani Bala Murugan Associate Professor, Department Of Mathematics, Annamalai University, Annamalainagar-608002,Tamilnadu,India.
  • Mrs. T. Senthamizhselvi Research Scholar, Department of Mathematics, Annamalai University, Annamalainagar-608002,Tamilnadu,India.

Keywords:

Second optional Working Vacation, Feedback, Matrix-Geometric Method.

Abstract

A Markovian queue with feedback and second optional working vacation is analysed in this study. Rather of fully suspending service during a vacation, the server operates with varying service times. After the completion of the regular working vacation, the server may opt for second optional working vacation. After getting the service the customer who is unsatisfied with incomplete, partial or unsatisfactory service may opt the feedback with prob. r¯ or leave the system with the prob. r. We use the Matrix-Geometric approach to find theessential and acceptable conditions for the system to be secure. After deriving the stationary probability distribution, various performance indicators are calculated. Some numerical examples are illustrated to show the model’s stability.

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References

G. Choudhury, An M/G/1 queue with an optional second vacation, Information and Management Sciences,17(3) (2006), 19–30.

G. Latouche and V. Ramaswami, Introduction to matrix analytic methods in

stochastic modelling, ASA-SIAM Series on Applied Probability, USA (1999),

doi:10.1155/S1048953399000362.

P. Manoharan and K. Sankara Sasi. An M/G/1 feedback queueing system with second

optional service and with second optional vacation, International Journal of Fuzzy Mathematical Archive, (2015) 8(2) 101-113.

P. Manoharan, S. Pazhani Bala Murugan and A. Sobanapriya Analysis of a markovian

retrial queue with working vacation under N-Control pattern, Communications in Mathematics and Applications (2015) 13(3) 851-863. doi:10.26713/cma.v13i3.2065

Naishuo Tian, The M/M/1 queue with single working vacation, International Journal of Information and Management Sciences19 (14)(2008), 621-634.doi:10.1007/s11518-006-5030-6

M.F. Neuts, Matrix - Geometric solutions in Stochastic models, Johns Hopkins University

Press, Baltimore (1981), doi:https://doi.org/10.1002/net.3230130219.

Qingqing Ye and Liwei Liu, The analysis of the M/M/1 queue with two vacation policies, international journal of computer mathematics 1-20(2015),

doi:10.1080/00207160.2015.1091450.

K. Santhi and S. Pazhani Bala Murugan, An M/G/1 feedback queue with single working

vacations, International Conference on Mathematical Methods and Computations, (2014),

-474.

K. Santhi and S. Pazhani Bala Murugan, An bulk input queueing system with feedback

and single working vacations, International journal of Scientific Research and Mangement

Studies, 1(5)(2014), 168-176.

L. Servi and S. Finn, M/M/1 queue with working vacations (M/M/1/WV), Perform. Eval,

(2002), 41–52, doi:https://doi.org/10.1016/S0166-5316(02)00057-3.

N. Tian and Z. Zhang, Vacation queueing models-theory and applications, Springer-Verlag,

New York (2006), doi:10.1007/978-0-387-33723-4.

P. Wallace, The solution of birth and death processes arising from multiple access computer

systems, Ph. D. diss. Systems Engineering Laboratory, University of Michigan. Tech. rept 07742- 6 T (1969), URL:https://deepblue.lib.umich.edu/handle/2027.42/8180.

Published

14-11-2024

How to Cite

K. Santhi, S, P. B. M., & T, S. (2024). A MARKOVIAN QUEUE WITH FEEDBACK AND SECOND OPTIONAL WORKING VACATION. Communications in Mathematics and Applications, 15(2). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2715

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

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