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Analysis of GI/M(n)/1/N Queue with Single Working Vacation and Vacation Interruption

Authors: P. Vijaya Laxmi, V. Goswami, V. Suchitra

Abstract:

This paper presents a finite buffer renewal input single working vacation and vacation interruption queue with state dependent services and state dependent vacations, which has a wide range of applications in several areas including manufacturing, wireless communication systems. Service times during busy period, vacation period and vacation times are exponentially distributed and are state dependent. As a result of the finite waiting space, state dependent services and state dependent vacation policies, the analysis of these queueing models needs special attention. We provide a recursive method using the supplementary variable technique to compute the stationary queue length distributions at pre-arrival and arbitrary epochs. An efficient computational algorithm of the model is presented which is fast and accurate and easy to implement. Various performance measures have been discussed. Finally, some special cases and numerical results have been depicted in the form of tables and graphs. 

Keywords: Blocking probability, single working vacation, State Dependent Service, Vacation Interruption, Supplementary Variable

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088314

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References:


[1] B. T. Doshi, Queueing Systems with Vacations - A Survey, Queueing Systems, Vol. 1 , pp. 29–66, 1986.
[2] N. Tian, N and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer-Verlag, New York, 2006.
[3] L. D. Servi and S. G. Finn, The M/M/1 Queues with Working Vacations (M/M/1/WV ), Perf. Eval., Vol. 50, pp. 41–52, 2002.
[4] W. Y. Liu, X. L. Xu, N. Tian, Stochastic decompositions in the M/M/1 queue with working vacations, Oper. Res. Lett., Vol. 35, pp. 596-600, 2007.
[5] N.Tian, X. Xhao and K. H. Wang, The M/M/1 Queue with Single Working Vacation, Int. J. Inform. Manage. Sci., Vol. 19, pp. 621–634, 2008.
[6] Y. Baba, Analysis of a GI/M/1 Queue with Multiple Working Vacations, Oper. Res. Lett., Vol. 33, 201–209, 2005.
[7] D. Wu and H. Takagi, M/G/1 queue with multiple working vacations, Perform. Eval., Vol. 63, pp. 654–681, 2006.
[8] M. Zhang and Z. Hou, Performance analysis of M/G/1 queue with working vacations and vacation interruption, Journal of Computational and Applied Mathematics, Vol. 234, pp. 2977–2985, 2010.
[9] A. D. Banik, Analysis of Single Working Vacation in GI/M/1/N and GI/M/1 Queueing Systems, Int. J. Oper. Res., Vol.7, 314–333, 2010.
[10] A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N Queue with Multiple Working Vacations - Analytic Analysis and Computation, Appl. Math. Modell., Vol. 31, 1701–1710, 2007.
[11] J. Li and N. Tian, Performance Analysis of a GI/M/1 Queue with Single Working Vacation, Appl. Math. Comput. , Vol. 217, pp. 4960– 4971, 2011.
[12] K. C. Chae, D. E. Lim and W. S. Yang, The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation, Perform. Eval., Vol. 66, pp. 356–367, 2009.
[13] Z. Zhang and X. Xu, Analysis for the M/M/1 Queue with Multiple Working Vacations and N-Policy, Int. J. Inform. Manage. Sci., Vol. 19, pp. 495–506, 2008.
[14] J. Li and N. Tian, The M/M/1 Queue with Working Vacations and Vacation Interuptions, J. Syst. Sci. Syst. Eng., Vol. 16, pp. 121–127, 2007.
[15] J. Li, N. Tian and Z. Ma, Performence Analysis of GI/M/1 Queue with Working Vacation and Vacation Interruption, Appl. Math. Modell., Vol. 32, pp. 2715–2730, 2008.
[16] G. Zhao, X. Du and N. Tian, GI/M/1 Queue with Setup Period and Working Vacation and Vacation Interruption, Int. J. Inform. Manage. Sci., Vol. 20, pp. 351–363, 2009.
[17] S. Guo and Z. Liu, AnM/G/1 Queue with Single Working Vacation and Vacation Interruption under Bernoulli Schedule, Appl. Math. Modell., in press, 2012.
[18] Q. Wang and J. M. Peha, State Dependent Pricing and its Economic Implications, Telecommu. Syst., Vol. 18, pp. 315–329, 2001.
[19] M. Kijima and N. Makimoto, A Unified Approach to GI/M(n)/1/K and M(n)/G/1/K Queues via Finite Quasi-Birth-Death Processes, Commun. Stat. Stoch. Models, Vol. 8, pp. 269–288, 1992.
[20] P. Yang, Unified Algorithm for Computing the Stationary Queue Length Distribution in M(k)/G(n)/1/N and GI/M(k)/1/N Queues, Queueing Systems, Vol. 17, pp. 383–401, 1994.
[21] X. Chao and R. Rahman, Anlysis and Computational Algorithem for Queues with State Dependent Vacations I: G/M(n)/1/K, J. Syst. Sci. Complex., Vol. 19, pp. 36–53, 2006.
[22] X. Chao and R. Rahman, Anlysis and Computational Algorithem for Queues with State Dependent Vacations II: M(n)/G/1/K, J. Syst. Sci. Complex., Vol. 19, pp. 191–210, 2006.