旅行分布的重力模式与交通模型的关系
收稿日期: 2007-01-18
修回日期: 2007-04-29
网络出版日期: 2007-08-25
基金资助
国家自然科学基金项目(40635026)
Linking the Doubly Constr ained Gr avity Model and the Tr anspor tation Model for Tr ip Distr ibutions: A New Approach
Received date: 2007-01-18
Revised date: 2007-04-29
Online published: 2007-08-25
Supported by
National Natural Science Foundation of China, No.40635026
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。
梁进社, 贺灿飞, 张华 . 旅行分布的重力模式与交通模型的关系[J]. 地理学报, 2007 , 62(8) : 840 -848 . DOI: 10.11821/xb200708006
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.
[1] Hitchcock F L. The distribution of a product from several source to numerous localities. Journal of Mathematics and Physics, 1941, 20: 224-230.
[2] Dorfman R, Samuelson P A, Solow R M. Linear Programming and Economic Analysis. New York: McGraw-Hill, 1958.
[3] Sen A, Smith T. Gravity Models of Spatial Interaction Behavior. Heidelberg: Springer, 1995.
[4] Batten F, Boyce E. Spatial interaction, transportation, and interregional commodity flow models. In: Nijkamp P. Handbook of Regional and Urban Economics, Volume 1, Regional Economics. North-Holland: Amsterdam, 1986. 357-406.
[5] Wilson G. A statistical theory of spatial distribution model. Transportation Research, 1967, 1: 253-269.
[6] Wilson G. Entropy in Urban and Regional Modeling. London: Pion, 1970.
[7] Wilson G, Bennett R J. Mathematical Models in Human Geography and Planning. John Wiley & Sons, 1985.
[8] Evans P. A relationship between the gravity model for trip distribution and the transportation problem in linear programming. Transportation Research, 1973, 7: 39-61.
[9] Golob T F, Beckmannn M J. A utility model for travel forecasting. Transportation Science, 1971, 5: 79-90.
[10] Beckmannn M J. The economic activity equilibrium approach. In: Bertuglia C S, Leonardi G, Occelli S. Urban System: Contemporary Approaches. Croom Helm, 1987. 79-135.
[11] Beckmannn M J, Wallance J P. Evaluation of user benefits arising from changes in transportation systems. Transportation Science, 1969, 3: 344-351.
[12] Zhu Dewei, Liang Jinshe. Quantitative analysis of mass goods and material's supply-sale location and its extension. Acta Geographica Sinica, 1986, 41(4): 350-359.
[ 朱德威, 梁进社. 大宗物资供销区位的定量分析及其引申. 地理学 报, 1986, 41(4): 350-359.]
[13] Ford Jr. L R, Fulkerson D R. A simple algorithm for finding maximal network flow and an application to the hitchcock problem. Canad. J. Math., 1957, 9: 210-218.
[14] Guan Meigu, Zheng Handing. Linear Programming. Jinan: Shandong Science and Technology Press, 1983.
[管梅谷, 郑 汉鼎. 线性规划. 济南: 山东科学技术出版社, 1983.]
[15] Dantzig D B, Ford Jr L R, Fulkerson D R. A primal-dual algorithm for linear programs, linear inequalities and related systems. In: Annals of Mathematics Study 38. Princeton University Press, 1956.
[16] Domencich T, McFadden D. Urban Travel Demand: A Behavioral Analysis. North-Holland: Amsterdam, 1975.
[17] McFadden D. The mathematical theory of demand models. In: Stopher P R, Meyburg A. Behavioral Travel Demand Models. Lexington Books, Lexington Mass, 1976, 305-314.
[18] McFadden, D. The measurement of urban travel demand. Journal of Public Economics, 1974, 3: 303-328.
[19] Jin Fengjun. A study on network of domestic air passenger flow in China. Geographical Research, 2001, 20(1): 31-39.
[金凤君. 我国航空客流网络发展及其地域系统研究. 地理研究, 2001, 20(1): 31-39.]
[20] Zhou Yixing, Hu Zhiyong. Looking into the network structure of Chinese urban system from the perspective of air transportation. Geographical Research, 2002, 21(3): 276-286.
[周一星, 胡智勇. 从航空运输看中国城镇体系的空间网 络结构. 地理研究, 2002, 21(3): 276-286.]
[21] Yang Qi. A model for interregional trip distribution in China. Acta Geographica Sinica, 1990, 45(3): 264-274.
[ 杨齐. 区域客流分布模型的研究. 地理学报, 1990, 45(3): 264-274.]
/
| 〈 |
|
〉 |