Xiuli Xu
ABSTRACT
In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.
- B. T. Doshi, "Queueing systems with vacations-a survey," Queueing Systems, vol. 1, pp. 29--66, 1986. Google Scholar
Digital Library
- H. Takagi, Queueing Analysis, A foundation of Performance Evaluation, Vol. 1: Vacation and Priority Systems. Amsterdam: Elsevier Science Publishers, 1991.Google Scholar
- N. Tian, Z. G. Zhang, Vacation Queueing Models-Theory and Applications. New York: Springer-Verlag, 2006. Google ScholarDigital Library
- L. Servi, S. Finn, "M/M/1 queue with working vacations (M/M/1/WV)," Performance Evaluation, vol. 50, pp. 41--52, 2002. Google ScholarDigital Library
- J. Kim, D. Choi and K. Chae, "Analysis of queue-length distribution of the M/G/1 queue with working vacations," International Conference on Statistics and Related Fields, Hawaii, 2003.Google Scholar
- D. Wu and H. Takagi, "M/G/1 queue with multiple working vacations," Performance Evaluation, vol. 63, pp. 654--681, 2006. Google ScholarDigital Library
- Y. Baba, "Analysis of a GI/M/1 queue with multiple working vacations," Oper. Res. Letters, vol. 33, pp. 201--209, 2005. Google ScholarDigital Library
- W. Liu, X. Xu and N. Tian, "Some results on the M/M/1 queue with working vacations," Oper. Res. Letters, vol. 35, pp. 595--600, 2007. Google ScholarDigital Library
- J. Li, N. Tian and W. Liu, "Discrete-time GI/Geo/1 queue with working vacations," Queueing Systems, vol. 56, pp. 53--63, 2007. Google ScholarDigital Library
- M. Neuts. Structured stochastic matrixs of M/G/1 type and their applications. New York: Marcel Dekker, 1989.Google Scholar
- N. Tian, X. Xu and Z. Ma, discrete time queue theory. Beijing: Science press, 2008.Google Scholar
Index Terms
- Performance analysis for the Geom/G/1 queue with single working vacation
Recommendations
Performance Analysis of the GI/M/1 Queue with Single Working Vacation and Vacations
AbstractIn this paper, we consider a new class of the GI/M/1 queue with single working vacation and vacations. When the system become empty at the end of each regular service period, the server first enters a working vacation during which the server ...
Modified vacation policy for M/G/1 retrial queue with balking and feedback
This paper studies a general retrial queue with balking and Bernoulli feedback, where the server operates a modified vacation policy. If the server is busy or on vacation, an arriving customer either enters an orbit with probability b, or balks (does ...
Analysis of the discrete-time Geo/G/1 working vacation queue and its application to network scheduling
In this paper we present an exact steady-state analysis of a discrete-time Geo/G/1 queueing system with working vacations, where the server can keep on working, but at a slower speed during the vacation period. The transition probability matrix ...
Comments