The M/M/1 queue with single working vacation and set-up times

International Journal of Operational Research

Volumn 6, Issue 3, 2009, Pages 420-434

  Xu, Xiuli ^a   Zhang, Zhongjun ^a   Tian, Naishuo ^a  

^a YANSHAN UNIVERSITY   (China)

Author keywords

Matrix geometric solution; QBD process; Set up times; Single working vacation; Stochastic decomposition

Indexed keywords

EID: 67650699224     PISSN: 17457645     EISSN: 17457653     Source Type: Journal    
DOI: 10.1504/IJOR.2009.026941     Document Type: Article

References (16)

1. Baba, Y. (2005) 'Analysis of a GI/M/1 queue with multiple working vacations', Operations Research Letters, Vol. 33, No. 2, pp.201-209.
2. Banik, A., Gupta, U. and Pathak, S. (2007) 'On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation', Applied Mathematical Modelling, Vol. 31, No. 9, pp.1701-1710.
3. Doshi, B. (1986) 'Queueing systems with vacations-a survey', Queueing Systems, Vol. 1, No. 1, pp.29-66.
4. Kim, J., Choi, D. and Chae, K. (2003) 'Analysis of queue-length distribution of the M/G/1 queue with working vacations', International Conference on Statistics and Related Fields, Hawaii.
5. Latouche, G. and Ramaswami, V. (1999) 'Introduction to matrix analysis methods in statistics modeling', ASA-SIAM Series on Applied Probability, pp.56-89.
6. Li, J. and Tian, N. (2007) 'The discrete time GI/Geom/1 queue with working vacation and service interruption', Applied Mathematics and Computation, Vol. 185, No. 1, pp.1-10.
7. Liu, W., Xu, X. and Tian, N. (2007) 'Some results on the M/M/1 queue with working vacations', Operations Research Letters, Vol. 35, No. 5, pp.595-600.
8. Neuts, M. (1981) Matrix-Geometric Solutions in Stochastic Models, Johns Hopkins University Press, Baltimore.
9. Servi, L. and Finn, S. (2002) 'M/M/1 queue with working vacations (M/M/1/ WV)', Performance Evaluation, Vol. 50, No. 1, pp.41-52.
10. Takagi, H. (1991) Queueing Analysis, Vol. 1, Elsevier Science Publishers, Amsterdam.
11. Teghem, J. (1986) 'Control of the service process in a queueing system', Eupropean Journal of Operational Research, Vol. 23, No. 2, pp.141-168.
12. Tian, N. and Zhang, G. (2006a) Vacation Queueing Models-Theory and Applications, Springer-Verlag, New York.
13. Tian, N. and Zhang, G. (2006b) 'A two threshold vacation policy in multiserver queueing systems', Eupropean Journal of Operational Research, Vol. 168, No. 1, pp.153-163.
14. Wu, D. and Takagi, H. (2006) 'M/G/1 queue with multiple working vacations', Performance Evaluation, Vol. 63, No. 7, pp.654-681.
15. Xu, X. and Zhang, G. (2006) 'Analysis of multi-server queue with a single vacation (e,d)-policy', Performance Evaluation, Vol. 63, No. 8, pp.625-638.
16. Zhang, G., Tian, N. and Love, E. (2006) 'Adjusting the workload of an under utilized server by scheduling supplementary work', International Journal of Operations Research, Vol. 3, No. 1, pp.47-55.