Simultaneous Occurrence of the Braess and Emission Paradoxes

Abstract

Braess' paradox is well-known and examined. However, an emission paradox, an analogue to Braess' paradox for vehicular emissions, is not. Without considering the emission paradox, the road network improvement that mitigates congestion may increase harmful vehicular emissions. In this paper, we analytically examine the occurrence of the emission paradox and the simultaneous occurrence of the Braess and emission paradoxes in the classical Braess' network. We ascertain that the occurrence of the emission paradox depends on the demand for travel, the parameters of link performance functions as well as link emission factors. We also find that the Braess and emission paradoxes do not always occur at the same time, and that the emission paradox is more likely to occur than the Braess paradox in some networks. More importantly, we discover that under some conditions of the parameters of link performance functions, the emission paradox does occur but Braess' paradox does not. This implies that road network design for mitigating congestion alone may not be able to avoid the increase in vehicular emissions. A more comprehensive view for road network design is necessary to avoid the occurrence of both the Braess and emission paradoxes.