Traffic restraint, road pricing and network equilibrium

Road pricing is now being advocated as an efficient means of managing traffic demand and of meeting other objectives, such as reducing the environmental impact of road traffic and improving public transport. This paper shows how a network toll pattern could be determined so as to reduce network travel demand to a desirable level. The demand between each origin–destination pair is described as a function of the generalized travel cost. When there is no toll charge, higher values of potential demand might cause congestion and queuing at bottleneck links of the road network. Queuing delay at saturated links may grow to choke off enough potential demand to reduce realized demand to the capacity of the network, thus leading to a queuing equilibrium where travel demand and travel cost match each other. In this paper, we first show how an elastic-demand network equilibrium model with queue could be used to determine this demand–supply equilibrium. We then seek a link toll pattern to remove the wasteful queuing delay, and/or restrain the realized demand to a desirable level to satisfy environment capacity constraints. We also show that the link toll pattern that could hold the traffic demand to a desirable level is not unique, a bi-level programming method is developed to select the best toll pattern among the feasible solutions based on pre-specified criteria.