Analysis of the M/M/1 queue with single working vacation and vacation interruption

Shakir Majid; P.Manoharan

doi:https://doi.org/10.14445/22315373/IJMTT-V47P505

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 47 | Number 1 | Year 2017 | Article Id. IJMTT-V47P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V47P505

Analysis of the M/M/1 queue with single working vacation and vacation interruption

Shakir Majid, P.Manoharan

Abstract

In this work, a vacation interruption in M/M/1 queue with single working vacation is considered. Using the matrix analytic method, we obtain the distributions for the mean queue length and the mean sojourn time and their stochastic decomposition structures. Finally, we demonstrate the effects of system parameters on the performance measures and present some special cases.

Keywords

M/M/1 queue, Vacation, Working vacation, Stochastic decomposition, Matrix-geometric solution.

References

1. Doshi,B.T., 1986. Queueing systems with vacations-A survey, Queueing Syst. 1, 29-66.
2. Takagi,H., 1991. Queueing Analysis: A Foundation of Performance Evaluation. Vol. 1: Vacation and Priority Systems, Part1, North-Holland Elsevier, New York.
3. Tian,N.,Zhang,Z.G., 2006. Vacation Queueing Models-theory and Application. Springer, New York.
4. Servi,L.D.,Finn, S.G., 2002. M/M/1 queues with working vacation (M/M/1/WV). Perform. Eval. 50, 41-52.
5. Liu, W.,Xu,X.,Tian,N.,2007. Stochastic decompositions in the M/M/1 queue with working vacations. Oper. Res. Lett. 35, 595-600.
6. Tian,N.,Zhao,X., 2008. The M/M/1 queue with single working vacation. Int. J. Inf. Manage. Sci. 19(4), 621-634.
7. Kim, J.D.,Choi, D.W.,Chae,K.C., 2003. Analysis of queue-length distribution of the M/G/1 queue with working vacation. Hawaii International Conference on Statistics and Related Fields.
8. Wu, D.,Takagi,H., 2006. M/G/1 queue with multiple working vacations. Perform. Eval. 63, 654-681.
9. Li,J.,Tian, N.,Zhang,Z.G.,Luh,H.P, 2011. Analysis of the M/G/1 queue with exponentially working vacationsa matrix analytic approach. Queueing Syst. 61, 139-166.
10. Baba,Y., 2005. Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Lett. 33, 201-209.
Li,J.,Tian, N., 2011. Performance analysis of an GI/M/1 queue with single working vacation. Appl. Math. Comput. 217, 4960-4971.
11. Li, J., Tian, N., 2007. The M/M/1 queue with working vacations and vacation interruptions. Journal of System Sciences and Systems Engineering 16(1), 121-127.
12. Li, J., Tian, N., 2007. The discrete-time GI/Geo/1 queue with working vacations and vacation interruption. Applied Mathematics and Computation 185(1), 1-10.
13. Li, J., Tian, N., Ma, Z., 2008. Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Applied Mathematical Modelling 32(12), 2715-30.
14. Zhang, M., Hou, Z., 2010. Performance analysis of M/G/1 queue with working vacations and vacation interruption. Journal of Computational and Applied Mathematics 234(10), 2977-85.
15. Gao, S.,Wang, J., Li,WW., 2014. AnM/G/1 retrial queue with general retrial times, working vacations and vacation interruption. Asia-Pacific Journal of Operational Research 31(2), article no. 1440006.
16. Zhang, M., Hou, Z., 2011. Performance analysis of MAP/G/1 queue with working vacations and vacation interruption. Applied Mathematical Modelling 35(4), 1551-60.
17. Laxmi, PV., Jyothsna, K., 2015. Impatient customer queue with Bernoulli schedule vacation interruption. Computers and Operations Research 56, 1-7.
18. Neuts,M., 1981. Matrix-Geometric Solution in Stochastic Model, Hopkins University Press, Baltimore.
19. Keilson,J.,Sevi,L.D., 1988. A distribution form of Littles law, Oper. Res. Lett. 7(5), 223-227.

Citation :

Shakir Majid, P.Manoharan, "Analysis of the M/M/1 queue with single working vacation and vacation interruption," International Journal of Mathematics Trends and Technology (IJMTT), vol. 47, no. 1, pp. 31-39, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V47P505