Abstract
This paper studies a fluid model driven by an M/M/1 queue with multiple exponential vacations and N-policy. The expression for the Laplace transform of the joint steady-state distribution of the fluid model is of a simple matrix power function form or matrix factorial form. Based on this fact, we introduce a new method of fluid model—modified matrix geometric solution method. The Laplace transform and Laplace-Stieltjes transform of the steady-state distribution of the buffer content are concisely expressed through the minimal positive solution to a crucial quadratic equation. Finally, we give concise expression for the performance measure—mean buffer content, which is useful in parameter design of fluid model and various practical applications.
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Mao, BW., Wang, FW. & Tian, NS. Fluid model driven by an M/M/1 queue with multiple vacations and N-policy. J. Appl. Math. Comput. 38, 119–131 (2012). https://doi.org/10.1007/s12190-010-0467-7
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DOI: https://doi.org/10.1007/s12190-010-0467-7