Analysis of a Markovian Retrial Queue With Working Vacation Under N-Control Pattern

Authors

DOI:

https://doi.org/10.26713/cma.v13i3.2065

Keywords:

Markovian retrial queue, Working vacation, N-control pattern, Conditional stochastic decomposition

Abstract

A Markovian retrial queue with working vacation under N-control pattern is investigated in this article. To describe the system, we employ a QBD analogy. The model’s stability condition is deduced. The stationary probability distribution is generated by utilizing the matrix-analytic technique. The conditional stochastic decomposition of the line length in the orbit is calculated. The performance measures and special cases are designed. The model’s firmness is demonstrated numerically.

Downloads

Download data is not yet available.

References

J. Artalejo and A. Gómez-Corral, Retrial Queueing Systems, Springer, Berlin (2008), DOI: 10.1007/978-3-540-78725-9.

B. D. Choi, K. K. Park and C. E. M. Pearce, An M/M/1 retrial queue with control policy and general retrial times, Queueing Systems 14 (1993), 275 – 292, DOI: 10.1007/BF01158869.

T. V. Do, M/M/1 retrial queue with working vacations, Acta Informatica 47 (2010), 67 – 75, DOI: 10.1007/s00236-009-0110-y.

R. Kalyanaraman and S. P. B. Murugan, A single server retrial queue with vacation, Journal of Applied Mathematics & Informatics 26(3-4) (2008), 721 – 732, https://koreascience.kr/article/JAKO200822179193859.page.

G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modelling, xiv + 317, ASA-SIAM Series on Applied Probability, SIAM, USA (1999), DOI: 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.

W.-Y. Liu, X.-L. Xu and N.-S. Tian, Stochastic decompositions in the M/M/1 queue with working vacations, Operation Research Letters 35(5) (2007), 595 – 600, DOI: 10.1016/j.orl.2006.12.007.

P. Manoharan and T. Jeeva, An M/M/1 retrial queue with working vacation Interruption and setup time, International Journal of Management Technology and Engineering IX(VII) (2019), 204 – 211.

S. P. B. Murugan and K. Santhi, An M/G/1 queue with two stage heterogeneous service and multiple working vacation, International Journal of Mathematics Sciences and Applications, 3(1) (2013), 233 – 249.

M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models, 352 pages, Johns Hopkins University Press, Baltimore (1981).

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

L. Tao, Z. Liu and Z. Wang, M/M/1 retrial queue with collisions and working vacation interruption under N-policy, RAIRO – Operations Research 46(4) (2012), 355 – 371, DOI: 10.1051/ro/2012022.

N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer-Verlag, New York (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, Technical Report UMR4381, University of Michigan, (1969), https://hdl.handle.net/2027.42/8180.

D.-A. Wu and H. Takagi, M/G/1 queue with multiple working vacations, Performance Evaluation 63(7) (2006), 654–681, DOI: 10.1016/j.peva.2005.05.005.

M. Yadin and P. Naor, Queueing system with a removable service station, Operational Research Quarterly 14(4) (1963), 393 – 405, DOI: 10.2307/3006802.

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.

M. Zhang and Z. Hou, Performance analysis of M/G/1 queue with working vacations and vacation interruption, Journal of Computational and Applied Mathematics 234(10) (2010), 2977 – 2985, DOI: 10.1016/j.cam.2010.04.010.

Z. Zhang and X. Xu, Analysis for the M/M/1 queue with multiple working vacations and N-policy, International Journal of Information and Management Sciences19 (2008), 495 – 506.

Downloads

Published

29-11-2022
CITATION

How to Cite

Manoharan, P., Bala Murugan, S. P., & Sobanappriya, A. (2022). Analysis of a Markovian Retrial Queue With Working Vacation Under N-Control Pattern. Communications in Mathematics and Applications, 13(3), 851–863. https://doi.org/10.26713/cma.v13i3.2065

Issue

Vol. 13 No. 3 (2022)

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.