Free Market on the Freeway

Abstract

his paper studies a trading mechanism allowing autonomous cars to change lanes on a freeway in congested traffic. When no room is available on the adjacent lane, the mechanism enable a car to change lanes if it pays a small fee to the car occupying the space it is moving into, compensating it for slowing down. We model the impact of this mechanism as a market for speed, which is free in the sense that it can be implemented by peer-to-peer technology without the intervention of the freeway operator. The term market is warranted by the simultaneous presence of multiple lane buyers and lane sellers. We use the term freeway to emphasize that we are not modeling toll-lanes. We develop conditions that the price system should satisfy. The presence of uncertainty in traffic density as well as price makes us model them as the solution of a system of stochastic partial differential equations. We simulate our model and perform sensitivity analysis on the parameters and initial conditions.