Abstract
We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M(n)/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O(K 3).
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The research is partially supported by National Science Foundation under DMI-0200306.
The first author is also supported in part by a grant from National Natural Science Foundation of China under No. 70228001.
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Chao, X., Rahman, A. Analysis and Computational Algorithm for Queues with State-Dependent Vacations II: M(n)/G/1/K . Jrl Syst Sci & Complex 19, 191–210 (2006). https://doi.org/10.1007/s11424-006-0191-4
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DOI: https://doi.org/10.1007/s11424-006-0191-4