Research On Planning Of Parking Space For New Energy Vehicles Based On Queuing Theory And Robust Optimization

Since 2019,China has started to carry out garbage classification in an all-round way,and people’s awareness of environmental protection has continued to increase.At the same time,with the rapid development of Electric vehicle technology,people are more and more in favor of energy-saving and environmentally-friendly Electric vehicles.The following problem of vehicle charging also puts forward new requirements for parking lot.The parking lot is not only a place to provide parking,but also an energy station that stores energy for cars.In this paper,we studied how to meet the needs of users and maximize the revenue of the parking lot.Using the loss system queuing theory model that conforms to the parking lot situation to simulate the arrival,service and departure process of vehicles.We established a programming with the number of parking spaces as a decision variable to maximize profits.Considering the uncertainty of vehicle parking time,we used robust optimization to solve the problem.Using the law of iterated logarithms to estimate the upper and lower bounds of the total service time,and by adding the uncertainty budget to balance the conservativeness and optimality of model.Finally,we studied more complex Time-varying queuing theory.We considered the impact of time-varying arrival rate by using modified-offered-load(MOL)approximation,which makes the model more practical reference value.In the model based on queuing theory,due to the complexity of the loss rate expression in the objective function,it is difficult to solve the original programming.Through the numerical experiment,we found that the objective function is convex and approximate to the piecewise linear function.After derivation and proof,we got an approximate linear piecewise function of the objective function,which makes the solution process simpler.Through the simulation and numerical experiments,the optimal solution of simulation and numerical experiment is basically the same.The accuracy of the linear approximate solution is improved after a proper optimization of the objective function’s slope.And then the optimal solution is basically the same as simulation.In the model based on robust optimization,the objective function is scaled to achieve the solution.Through numerical experiments,when the variance of the service time is small,the optimal solution of model and simulation is basically the same.Due to the conservatism of the robust model,the optimal solution will decrease when the variance becomes larger,so as to reduce the adverse impact of service time uncertainty on profit.Finally,in the time-varying model based on the modified-offered-load(MOL)approximation,the number of service vehicles in a period of time is calculated in the form of integral.Because the expression of loss rate about time t in the integrand function is complex,we considered using simple function approximation.After numerical experiments,we found when the arrival rate is a linear piecewise function of time,then the loss rate’s expression of time t is also approximate to a piecewise linear function.Therefore,the linear approximation function is used to approximate the loss rate’s expression of time t for simplifying the integral solution.Through derivation,the final income function is approximately a constant minus a series of sum of loss rates unrelated to tand related to n,so it can be solved.After numerical experiments,we found the optimal solution of model has higher reference value.Combined with the above models,this article can provide some guidance on how to plan the two types of parking spaces in the parking lot,so as to maximize the interests of users and themselves.