停车许可证的动态最优供给策略

考虑可预约和不可预约公共停车设施共存情况，制定停车许可证动态最优供给策略.构建随机最优控制模型以实现系统总时间损失期望值最小化，利用动态规划原理推导出最优性条件，即哈密尔顿-雅克比-贝尔曼方程，采用一种预设最优值函数方法得到动态最优供给策略的解析解.结果表明：动态最优供给策略为一个反馈控制，即车辆排队时间的函数；依据排队时间是否存在，动态最优供给策略分为两种情况.以北京市国贸地区为例进行蒙特卡洛实验可知：相较停车许可证完全供给策略，动态最优供给策略可节约时间0.45~1.94 min/veh；随着停车许可证用户行为不确定性增加，动态最优供给策略节约时间的平均值上升，变异系数下降.

Dynamic Optimal Supply Strategy of Parking Permits

This study aims to clarify a dynamic optimal supply of parking permits considering the situation in which reservable and unreservable public parking facilities exist in an area simultaneously. We first mathematically established a stochastic optimal control model to minimize the expectation of the total time lost. We then analyzed the optimality condition, i.e., Hamilton-Jacobi-Bellman equation, by applying the dynamic programming principle. Finally, with the estimated parameters in the predetermined optimal value function, we obtained the analytic solution of the dynamic optimal supply strategy. The results show that the dynamic optimal supply strategy is a feedback control strategy, which means the proposed strategy is a function of queuing time. The dynamic optimal supply strategy can be divided into two patterns basing on the existence of queuing time. Taking the Guomao area in Beijing City as an example, the Monte-Carlo experiment results show that the dynamic optimal supply strategy can save 0.45~1.94 min/veh compared with the full supply strategy of parking permits. With the increase of the uncertainty in the parking permits holders' behavior, the average time-saving value increases, but the coefficient of variation decreases.