Abstract
In this study, the authors are concerned with the traffic flow system on a multi-lane road, where vehicles with heterogeneous values-of-time (VOTs) can trade their rights-of-way (ROWs) so as to minimize individualsâ?? travel costs. The resulting traffic flow violates the First-In-First-Out (FIFO) principle, since vehicles with higher VOTs would travel faster by paying those with lower VOTs. A novel multi-commodity kinematic wave model is developed for such a system based on the following five assumptions: (A1) Travel speeds of vehicles not participating in the trade scheme and average speed of all vehicles in the system are not impacted; (A2) The total budget is balanced; (A3) The system reaches user equilibrium, and no driver can reduce his/her cost by unilaterally change his/her choice in speed and payment; (A4) The total cost is minimized, and the system reaches the system optimal state; (A5) The benefits of the scheme are shared among all users. From these assumptions the authors first derive a unifiable fundamental diagram, in which the relative speed ratios of different commodities are constant and proportional to the square root of the VOTs. The authors show that the scheme is always Pareto-improving when the system optimality is achieved. The authors analytically solve the Riemann problem for a traffic system with three commodities, in which two groups of users with different VOTs participate in the scheme, and a third group does not participate. The authors demonstrate that different commodities would react differently to shock and rarefaction waves. Finally, the authors conclude the study with future extensions.