Abstract
In this paper, an M/G/1 queue with exponentially working vacations is analyzed. This queueing system is modeled as a two-dimensional embedded Markov chain which has an M/G/1-type transition probability matrix. Using the matrix analytic method, we obtain the distribution for the stationary queue length at departure epochs. Then, based on the classical vacation decomposition in the M/G/1 queue, we derive a conditional stochastic decomposition result. The joint distribution for the stationary queue length and service status at the arbitrary epoch is also obtained by analyzing the semi-Markov process. Furthermore, we provide the stationary waiting time and busy period analysis. Finally, several special cases and numerical examples are presented.
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Li, Jh., Tian, Ns., Zhang, Z.G. et al. Analysis of the M/G/1 queue with exponentially working vacations—a matrix analytic approach. Queueing Syst 61, 139–166 (2009). https://doi.org/10.1007/s11134-008-9103-8
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DOI: https://doi.org/10.1007/s11134-008-9103-8
Keywords
- Working vacations
- Embedded Markov chain
- M/G/1-type matrix
- Stochastic decomposition
- Conditional waiting time