旅行分布的重力模式与交通模型的关系

从交通问题的对偶规划出发, 引入由Beckmann 和Wallance, Golob 和Beckman 等提出的不确定性效用方法, 建立交通问题和双约束重力模型的关系。证明当旅行者效用概率分布密度函数的标准差趋于零时, 双约束重力模型中的距离摩擦系数趋于正无穷, 由双约束重力模型确定的旅行分布使得总的交通成本达到最小。在这种关系中, 双约束重力模型中平衡因子的作用是市场调整旅行终点服务价格进而调整旅行者消费者剩余的结果。通过建立的分 析方法对北京、上海、广州、西安、武汉、成都和昆明等七个城市间航空交通的应用, 发现多数航线的模拟较好。结果表明各终点的差异性、消费者偏好的不同、交通工具的替代性和旅行目的之差异性等可以导致一些较大的误差, 这些差异性可以采用对起终点对的单位交通费用的调整来体现, 从而达到较好的模拟和分析效果。

Linking the Doubly Constr ained Gr avity Model and the Tr anspor tation Model for Tr ip Distr ibutions: A New Approach

The premise condition of doubly constrained gravity model is the same as that of transportation model in linear programming, but the results derived from the models are diverse because of the different behavior assumptions of travelers. It has been proved by Evans that the parameter β in doubly constrained gravity model represents the relative importance of total transportation costs and the possibility of the trip distribution. Based on dual programming of transportation problem and uncertain utility method put forward by Beckmannn & Wallance and Golob & Beckmannn, this study establishes the relationship between doubly constrained gravity model and transportation model. This paper discovers that the parameter " in doubly constrained gravity model goes to positive-infinity and the total transportation costs of trip distribution derived from doubly constrained gravity model meet minimum level as the standard deviation of probability density distribution function for traveler's utility goes to zero. This paper points further out that the balance factors in doubly constrained gravity model reflect market adjustment of the price for travel ends services and the consumer surplus of travelers. Using this method, trip distribution on airlines between seven cities in China in 2003 is simulated. The result also indicates that the difference of travel ends and consumer preferences, substitution of transportation tools, and variety of travel purposes may lead to simulation error and the error can be reduced by transportation cost parameter adjustment.