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M/M/1 retrial queue with collisions and working vacation interruption under N-policy

Published online by Cambridge University Press:  10 December 2012

Li Tao ,
Zaiming Liu  and
Zhizhong Wang
Li Tao
Affiliation:
School of Science, Shandong University of Technology, Zibo 255049, China. liltaot@126.com
Zaiming Liu
Affiliation:
School of Mathematics, Central South University, Changsha 410075, China
Zhizhong Wang
Affiliation:
School of Mathematics, Central South University, Changsha 410075, China
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Abstract

Consider an M/M/1 retrial queue with collisions and working vacation interruption under N-policy. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.

Keywords

Retrialcollisionworking vacation interruptionN-policy
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 4 , October 2012 , pp. 355 - 371
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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References

Références

Choi, B., Park, K. and Pearce, C., An M/M/1 retrial queue with control policy and general retrial times. Queueing Syst. 14 (1993) 275–292. Google Scholar
Choi, B., Shin, Y. and Ahn, W., Retrial queues with collision arising from unslotted CSMA/CD protocol. Queueing Syst. 11 (1992) 335–356. Google Scholar
Kumar, B., Vijayalakshmi, G., Krishnamoorthy, A. and Basha, S., A single server feedback retrial queue with collisions. Comput. Oper. Res. 37 (2010) 1247–1255. Google Scholar
Wu, D. and Takagi, H., M/G/1 queue with multiple working vacations. Perform. Eval. 63 (2006) 654–681. Google Scholar
G. Latouche and V. Ramaswami, Introduction to matrix analytic methods in stochastic modelling. ASA-SIAM Series on Applied Probability, USA (1999).
J. Artalejo and A. Corral, Retrial queueing systems. Springer, Berlin (2008).
Kim, J., Retrial queueing system with collision and impatience. Commun. Korean Math. Soc. 25 (2010) 647–653. Google Scholar
Li, J. and Tian, N., Performance analysis of a GI/M/1 queue with single working vacation. Appl. Math. Comput. 217 (2011) 4960–4971. Google Scholar
Li, J. and Tian, N., The M/M/1 queue with working vacations and vacation interruption. J. Syst. Sci. Syst. Eng. 16 (2007) 121–127. Google Scholar
Li, J., Tian, N. and Ma, Z., Performance analysis of GI/M/1 queue with working vacations and vacation interruption. Appl. Math. Modell. 32 (2008) 2715–2730. Google Scholar
Wu, J., Liu, Z. and Peng, Y., A discrete-time Geo/G/1 retrial queue with preemptive resume and collisions. Appl. Math. Modell. 35 (2011) 837–847. Google Scholar
Servi, L. and Finn, S., M/M/1 queue with working vacations (M/M/1/WV). Perform. Eval. 50 (2002) 41–52. Google Scholar
Martin, M. and Corral, A., On the M/G/1 retrial queueing system with liner control policy. Top 3 (1995) 285–305. Google Scholar
Zhang, M. and Hou, Z., Performance analysis of M/G/1 queue with working vacations and vacation interruption. J. Comput. Appl. Math. 234 (2010) 2977-2985. Google Scholar
N. Tian and Z. Zhang, Vacation queueing models-theory and applications. Springer-Verlag, New York (2006).
Lillo, R., A G/M/1 queue witn exponential retrial. Top 4 (1996) 99–120. Google Scholar
Do, T., M/M/1 retrial queue with working vacations. Acta Inform. 47 (2010) 67–75. Google Scholar
Liu, W., Xu, X. and Tian, N., Stochastic decompositions in the M/M/1 queue with working vacations. Oper. Res. Lett. 35 (2007) 595–600. Google Scholar
Baba, Y., Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Lett. 33 (2005) 201–209. Google Scholar
Baba, Y., The M/PH/1 queue with working vacations and vacation interruption. J. Syst. Sci. Syst. Eng. 19 (2010) 496–503. Google Scholar
Zhang, Z. and Xu, X., Analysis for the M/M/1 queue with multiple working vacations and N-policy. Infor. Manag. Sci. 19 (2008) 495–506. Google Scholar