Braess矛盾現象於需求變動路網之研究

A Study ofBraess' Paradox in A Variant Demand Network

當交通路網處於擁擠狀態時，管理者通常以運輸系統管理方法疏解，但以長期運輸系統規劃而言，解決道路擁擠現象仍以增加道路容量，也就是擴建或增闢路段為主。然而Braess[1968]發現，在一路網中加入一新的路段，當新路網達到使用者均衡時，每個使用者的旅行成本反而會增加，如此不僅浪費時間、建設經費等資源，還會使路網中交通擁擠的情況更嚴重。以往已有許多專家學者對Braess矛盾現象發生的充份必要條件及避免發生矛盾現象的方法進行探討。Pas[1997]提到矛盾現象發生於達到使用者均衡的路網，即以平均成本為旅行成本的路網，若以邊際成本方式收取道路使用費，可消除矛盾現象。儘管如此，對於Braess矛盾現象的討論仍在交通需求固定的情形下進行，實際上從進行路網規劃到施工完成，旅次需求均可能改變，而且用路需求也可能隨著用路成本之增減改變使用者之運具選擇。本研究之目的在於針對旅次需求變動與旅次彈性需求之Braess矛盾現象與其發生變化的情形加以探討，並藉由;寅算例予以說明。

If traffic is congested in a network, the authorities always try to relieve the congestion by transportation system management methods (TSM) first. However, the effects of TSM are restricted by the capacity of the network. The main solution of congestion in long term transportation system planning is to increase road capacity appropriately. Braess (1968) discovered that as a new road link is added on a network and after reaching its user equilibrium, each user's travel time may increase. Thus, increasing a new link may not only make the congestion more serious, but also waste the construction budget and time. Researchers devoted to discuss the sufficient and necessary condition so as to prevent the occurrence of paradox. Pas (1997) mentioned that ifthe road price is charged as marginal cost, the paradox will disappear. In spite of the paradox seems to be solved, the discussion was under certain travel demand condition. In practice, travel demand will change during the planning and construction period and may also change with travel cost. The propose of this paper is going to discuss Braess' paradox under variant demand, and use the classical Braess' network as an example to explain it.