ON SOME TRAFFIC EQUILIBRIUM THEORY PARADOXES
ON SOME TRAFFIC EQUILIBRIUM THEORY PARADOXES
复制标题
DOI：
10.1016/0191-2615(84)90023-7
复制
发表时间：
1984-04
影响因子：
6.8
通讯作者：
S. Dafermos;A. Nagurney
中科院分区：
文献类型：
--
作者：
S. Dafermos;A. Nagurney
我们考虑一个交通网络中具有固定需求的不对称均衡问题，其中每个环节的出行成本可能取决于该网络上的流量以及网络上其他环节的流量，我们研究了出行需求的变化或新路线的增加如何影响出行成本。假设旅行成本函数是强单调的，我们推导出在一定条件下，与特定出发地（O / D）对相关的旅行需求变化如何影响任何O / D对的旅行者成本的公式。然后，我们使用这些公式来表明，与特定o / Dpair（所有其他保持不变）相关的旅行需求的增加总是导致旅行者在该o / Dpair上的成本增加，然而，旅行者在其他o / Dpair上的成本可能会减少。然后，我们推导出在一定条件下，由于增加一条新路径而引起的每o / Dpair上出行者成本变化的公式。这些可以用来确定Braess悖论是否在网络中发生。然后，我们证明，如果测试矩阵是正半定的，当增加一条新路径时，与该路径连接的特定aro / Dpair相关的旅行者成本将减少（因此不会发生Braess悖论）。
We consider the asymmetric equilibrium problem with fixed demands in a transportation network where the travel cost on each link may depend on the flow on this as well as other links of the network and we study how the travellers' cost is affected by changes in the travel demand or addition of new routes. Assuming that the travel cost functions are strongly monotone, we derive formulas which express, under certain conditions, how a change in travel demand associated with a particular origin-destination (O / D) pair will affect the travelers' cost for anyO / Dpair. We then use these formulas to show that an increase in the travel demand associated with a particularO / Dpair (all other remaining fixed) always results in an increase in the travelers' cost on thatO / Dpair, however, the travelers' cost on otherO / Dpairs may decrease. We then derive formulas yielding, under certain conditions, the change in travelers' cost on everyO / Dpair induced by the addition of a new path. These can be used to determine, whether Braess' paradox occurs in the network. We then show that when a new path is added, the travelers' cost associated with the particularO / Dpair joined by this path will decrease (hence Braess' paradox does not occur) if a test matrix is positive semidefinite.