Performance Analysis Of Fluid Model Driven By An M/PH/1 Queueing System

Nowadays,the fluid queue has been widely applied in many fields,such as factory production,transportation,financial risk and communication network and so on,which attracts the attention of many scholars and becomes a research hot topic at home and abroad.The effect of fluid queue is used to optimize the design of the system,which can help the system get more economic benefits.Therefore,on the basis of the existing literatures,this paper studies the fluid queue based on phase type service with negative customer or working vacation strategies.Firstly,the fluid model driven by an M/PH/1 queue with negative customers has been proposed in this paper.The steady-state queue length distribution of the driving process is obtained by using quasi-birth-death process and matrix geometric solution methods.Based on the equilibrium equation,the matrix-type ordinary differential equation is derived for the joint distribution characterizing the fluid model dynamics.Further,the performance index of the system in the steady state is obtained.The influence of system parameters for the system indices are analyzed by numerical examples.Secondly,the fluid model driven by an M/PH/1 queueing environment with multiple working vacations has been discussed in this paper.By analyzing the model,the matrix differential equation is obtained and satisfied with the steady state joint distribution function according to the equilibrium conditions.With the help of the Laplace transform and the Laplace-Stieltjes transform,the performance indices of the system are given.Then,apply the model to the Ad Hoc network,the channel utilization and the average effective bandwidth of network system are further derived.Through numerical analysis,we discuss the changes of the indices in the network system under the influence of system parameters.Finally,the fluid model driven by a single working vacation queue with PH service time distribution has been analyzed in this paper.We take the M/PH/1 queueing system with single working vacation as the external driving environment,and the model is analyzed in steady state.By using the analysis method of matrix function based on Laplace transform,the probability for the empty system and the mean of buffer content are given in the steady state.Moreover,the model is extended to Ad Hoc network,and sensitivity analysis is implemented by MATLAB software.Further,we can obtain the trend of network system indices with parameters.