Paradox links can improve system efficiency: An illustration in traffic assignment problem

This paper demonstrates a counter-intuitive phenomenon that “paradox links” (i.e. marginally improving or adding these links will increase a system's cost) can sometimes decrease a system's cost. It can be expressed that simultaneously improving the paradox link to a certain threshold (rather than only marginal improvement) or adding more paradox links may counter-intuitively avoid the paradox. Here, we refer this phenomenon as the “non-monotonicity” of the paradox with regard to the degree of link improvement and the number of additional paradox links. Firstly, a formal definition of "non-monotonicity" property of paradox in a rigorous mathematical manner is proposed. Then this non-monotonicity property is demonstrated to widely exist in the user equilibrium (UE), the stochastic assignment, and the stochastic user equilibrium (SUE) models by two simple networks, where the underlying reasons for this phenomenon in different scenarios are analyzed and compared. Finally, the non-monotonicity of the traffic paradox is corroborated in a road sub-network of Harbin. The conclusions of this study provide new insights into features of traffic paradoxes and new ideas to eliminate them.