Stationary Analysis Of The Fluid Model Driven By M/M/c Queueing System With Working Vacation

In recent years,Fluid model is a hot topic in applied probability research.Compared with traditional queuing model,fluid model can solve some practical problems more efficiently.The research of fluid model can be widely used in practical production and life such as financial analysis,transportation,communication network and computer technology.By analyzing the influence of parameters in the fluid model on various performance indicators,the model can be optimized and designed to better It is applied in real life to improve economic efficiency and reduce costs,so it has great research value and significance.Based on the fluid model driven by the multi-service-desk queuing system,this thesis adds two-stage vacation and optional service strategies to the drive system,studies the fluid model driven by the M/M/c queuing system with single working vacation,and further improves it the theoretical system of fluid model,the main content is roughly divided into the following parts:Firstly,the fluid model driven by the M/M/c queuing system with single working vacation is studied.The steady-state queue length distribution of the driving system is obtained by using the pseudo-birth-death process and the matrix geometric solution.By constructing the net input rate structure,the stability of the fluid model is derived.The matrix differential equation satisfied by the state joint distribution function,and the empty buffer probability and the mean expression of the buffer stock in the steady state is gained by the Laplace-Stieltjes transform(LST)method.Finally,the application of the model in the wireless Mesh network is given.The effect of parameter changes on system performance indicators is shown by Numerical examples.Secondly,on the basis of working vacation M/M/c queuing,the strategy of selecting the second service is introduced.In this system,after the first service is over,the customer chooses to directly perform the second service with probability ,and leave the system directly with probability 1-.The steady-state queue length distribution of the drive system is obtained by analysis.The net input rate structure is constructed,the differential equation,the Laplace transform(LT)and LST satisfied by the steady-state distribution function of the fluid model are obtained,and the empty buffer probability and the mean expression are obtained.Finally,combined with the example of shared washing machine,the influence of parameter variation on system performance index is analyzed.Finally,considering the more complex actual situation,the two-stage vacation strategy is integrated into the M/M/c queuing drive system.The strategy includes two stages: vacation and working vacation,steady-state queue length distribution of drive system is derived by using quasi birth-and-death process and matrix geometry method.The matrix differential equation satisfied by the steady-state joint distribution of the fluid model joint distribution is obtained by analysis,combining LT and LST,the empty storage probability and mean expression of buffer storage in steady state are obtained.Based on the street lamp solar lighting control system,a numerical analysis is proposed to analyze the influence of parameter changes on system performance indicators.