论文信息 - Performance analysis for the Geom/G/1 queue with single working vacation

Performance analysis for the Geom/G/1 queue with single working vacation

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.

[1] B. T. Doshi,et al. Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[2] Leslie D. Servi,et al. M/M/1 queues with working vacations (M/M/1/WV) , 2002, Perform. Evaluation.

[3] Naishuo Tian,et al. Stochastic decompositions in the M/M/1 queue with working vacations , 2007, Oper. Res. Lett..

[4] Naishuo Tian,et al. Discrete-time GI/Geo/1 queue with multiple working vacations , 2007, Queueing Syst. Theory Appl..

[5] B. Conolly. Structured Stochastic Matrices of M/G/1 Type and Their Applications , 1991 .

[6] Naishuo Tian,et al. Vacation Queueing Models Theory and Applications , 2006 .

[7] Hideaki Takagi,et al. M/G/1 queue with multiple working vacations , 2006, Perform. Evaluation.

[8] Hideaki Takagi,et al. Queueing analysis: a foundation of performance evaluation , 1993 .

[9] Yutaka Baba,et al. Analysis of a GI/M/1 queue with multiple working vacations , 2005, Oper. Res. Lett..

[10] Naishuo Tian,et al. Vacation Queueing Models: Theory and Applications (International Series in Operations Research & Management Science) , 2006 .