交通路網設計問題之矛盾現象預測

Abstract

Braess矛盾現象在運輸規劃和路網設計範疇裡，皆為一重要議題且已被廣泛討論。在從事路網設計時，我們希望藉由新建道路或是提升道路容量來解決擁擠問題，但是Braess矛盾現象卻顯示，若沒有全盤作好路網敏感性分析，例如分析需求或是路段成本函數對整個路網使用者的影響，所新建的道路可能會毫無用武之地；更甚之，使整個路網之起迄成本更高。過去學者研究中，皆以最初Braess所提出簡單路網為基礎，予以探究發生矛盾現象的原因，並給予建議預防。從以往的研究中，可發現Braess矛盾現象發生原因會和路網結構、路段成本函數以及起訖點需求有關。本論文以Dafermos與Nagurney於1984年提出之預測矛盾現象公式為基礎，將其路網假設條件放鬆，其假設條件為路網中，路徑數必須小於等於路段數加上起迄對數，使之模式能應用於大型路網。

In transportation planning and network design, Braess paradox problem has been discussed for many decades. Those researches were originated from the simple network illustrated by Braess. Many works devoted to seek efficient methods to avoid the occurrence of paradox problem or find some rules for network designers to refer. Under link-OD/path matrix is full column rank , i.e., the number of paths is less than the number of links plus origin/destination pairs, Dafermos and Nagurney (Dafermos and Nagurney,1984) derived the formulas to determine whether Braess’ paradox occurs in the network. Using their formula, transportation planners could foresee occurrence of Braess’ paradox before great capital investment in road construction. This study proposes generalized inverse approach to relax the full column rank assumption presented by Dafermos and Nagurney. Then the modified model could be applied to large networks.