| With the rapid development of modern technology,the traditional discrete queuing model has great limitations in modeling analysis,so the fluid model comes into being.The fluid model deals with an input-output system in which the inflow and outflow of fluids are controlled by an external driving system.The research on fluid model gradually rises,and has been widely used in information network,digital intelligent factory and so on.According to different application background,the fluid model driven by two-stage vacation queuing system is established and its performance is analyzed.Firstly,the fluid model driven by M/M/1 queue with two-stage vacation and -policy is considered.It is based on the operation mechanism of the factory order assembly system.The mathematical expression of the stationary buffer content is deduced by using matrix geometric solution and Laplace transformation(LT).Then the expected buffer content is derived by Laplace transformation(LST).In order to improve the production efficiency of factory and reduce inventory accumulation,the model is combined with the operation mechanism of factory order assembly system.And a reasonable cost function is established according to the obtained performance index.The influence of parameter variation on performance index and cost is given in numerical analysis.Secondly,the fluid model driven by M/M/1/ queueing system with set-up time,optional service and two-stage vacation is studied by considering the finite capacity of the system.The infinite small generators of the two-dimensional Markov process are decomposed into a blocky Jacobian matrix form.Then,the stationary probability distribution of the driving system is obtained by using matrix-geometric method.The differential and difference equations of the fluid level in steady-state conditions are obtained by using the probability analysis method.Then,the expected buffer content and the probability of the empty buffer of the model are obtained by using LT and LST methods.Based on the take-out operation model of the store,the cost function is established according to the performance index to help the store reasonably control the required cost.And the influence of parameter variation on system performance index and cost is given by the numerical experiments.Finally,the fluid model driven by M/M/1 queueing system with set-up time,complete failure and two-stage vacation is constructed and analyzed.The driving system is described.Then the net input rate structure of the fluid model is introduced,and the expected buffer content and the probability of the empty buffer under steady-state conditions are obtained by using LST methods.The cost function of the system is constructed according to the performance index.The results of the model are applied to the energy conversion mechanism of wind power street lamps.Then the cost function of the system is constructed according to the performance index.The effects of system parameters on performance index and cost function are verified by numerical experiments. |
