A Markovian Queue With Feedback and Second Optional Working Vacation

Authors

DOI:

https://doi.org/10.26713/cma.v15i2.2715

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 probability ¯r or leave the system with the probability r.We use the matrix-geometric approach to find the essential 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.

Downloads

Download data is not yet available.

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. Ramaswamy, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Mathematics, SIAM, USA, xiv + 334 pages, USA (1999), URL: https://epubs.siam.org/doi/book/10.1137/1.9780898719734.

J. Li and N. Tian, The M/M/1 queue with working vacations and vacation interruptions, Journal of Systems Science and Systems Engineering 16 (2007), 121 – 127, DOI: 10.1007/s11518-006-5030-6.

P. Manoharan and K. S. Sasi, An M/G/1 feedback queueing system with second optional service and with second optional vacation, International Journal of Fuzzy Mathematical Archive 8(2) (2015), 101 – 113.

P. Manoharan, S. P. B. Murugan and A. Sobanapriya, Analysis of a Markovian retrial queue with working vacation under N-control pattern, Communications in Mathematics and Applications 13(3) (2015), 851 – 863, DOI: 10.26713/cma.v13i3.2065.

M. R. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, 352 pages (1981).

K. Santhi and S. P. B. Murugan, An bulk input queueing system with feedback and single working vacations, International Journal of Scientific Research and Management Studies 1(5)(2014), 168 – 176.

L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation 50(1) (2002), 41 – 52, DOI: 10.1016/S0166-5316(02)00057-3.

N. Tian, N. Tian and X. Zhao, Wang Kaiyu, The M/M/1 queue with single working vacation, International Journal of Information and Management Sciences 19(4) (2008), 621 – 634.

N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, 1st edition, Springer-Verlag, New York, xii + 386 pages (2006), DOI: 10.1007/978-0-387-33723-4.

V. L. Wallace, The solution of quasi birth and death processes arising from multiple access computer systems, Ph.D Dissertation, Systems Engineering Laboratory, University of Michigan, Technical Report No. 07742-6-T, (1969), URL: https://deepblue.lib.umich.edu/handle/2027.42/8180.

Q. Ye and L. Liu, The analysis of the M/M/1 queue with two vacation policies (M/M/1/SWV +MV), International Journal of Computer Mathematics 94(1) (2017), 115 – 134, DOI: 10.1080/00207160.2015.1091450.

Downloads

Published

14-11-2024
CITATION

How to Cite

Santhi, K., Murugan, S. P. B., & Senthamizhselvi, T. (2024). A Markovian Queue With Feedback and Second Optional Working Vacation. Communications in Mathematics and Applications, 15(2), 865–873. https://doi.org/10.26713/cma.v15i2.2715

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.