Traffic Theory

This paper extends Vickrey's (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening...

According to the duality theory of traffic flow any well-posed kinematic wave (KW) and/or variational theory (VT) problem can be solved with the same methods either on the time-space plane or the time vs vehicle number plane. To achieve this symmetry, the model parameters and the boundary data need to be expressed in a form appropriate for each plane. It turns out, however, that when boundary data that are bounded in one plane are transformed for the other, singular points with infinite density (jumps in vehicle number) sometimes arise. These singularities require a new form of weak...

A growing literature exploits macroscopic theories of traffic to model congestion pricing policies in downtown zones. This study introduces trip length heterogeneity into this analysis and proposes a usage-based, time-varying congestion toll that alleviates congestion while prioritizing shorter trips. Unlike conventional trip-based tolls the scheme is intended to align the fees paid by drivers with the actual congestion damage they do, and to increase the toll’s benefits as a result. The scheme is intended to maximize the number of people that finish their trips close to their desired...

An agent-based, multichannel simulation of a downtown area reveals the impacts of both time-shifting traffic demand with congestion pricing, and supplying extra capacity by banning left turns. The downtown street network was idealized, and loosely resembles central Los Angeles. On the demand-side, prices were set based on time-of-day and distance traveled. On the supply side, left-turn maneuvers were prohibited at all intersections on the network. Although both traffic management measures reduced travel costs when used alone, the left-turn ban was much less effective than pricing. When...