Analysis of Fluid Model Modulated by an M/PH/1 Working Vacation Queue

Abstract

We propose a fluid model driven by the queue length process of a working vacation queue with PH service distribution, which can be applied to the Ad Hoc network with every data group. We obtain the stationary distribution of the queue length in driving process based on a quasi-birth-and-death process. Then, we analyze the fluid model, and derive the differential equations satisfied by the stationary joint distribution of the fluid queue based on the balance equation. Moreover, we obtain some performance indices, such as, the average throughput, server utilization and the mean buffer content. These indices are relevant to pack transmission in the network, and they can be obtained by using the Laplace Transform (LT) and the Laplace-Stieltjes Transform (LST). Finally, some numerical examples have been discussed with respect to the effect of several parameters on the system performance indices.

Keywords

Fluid model / M/PH/1 queue / average throughput / server utilization / buffer content / Ad Hoc network

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