Unifiable Multi-Commodity Kinematic Wave Model for Traffic Systems with Tradable Right of Way
With the emergence of connected vehicle technologies, many interesting applications become possible. We look at one such application that allows trac system users with heterogeneous values of time (VOT) to trade their right of way (ROW) among other users so as to minimize individuals' total travel costs, which includes time cost and nancial transaction. Our proposed system allows users on a multi-lane road to trade their ROWs, and 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 assumptions of choice, uniability, prices, budget-balance, utility maximization, referred to as A1 through A5.
From these assumptions, we study a simple case of such a system in which two groups of users with different VOTs participate in the scheme, and a third group does not participate. We derive a uniable fundamental diagram in which the relative speed ratios of different
commodities are constant and proportional to the square root of the VOTs. We show that the scheme is Pareto-improving at the system optimal solution. The Riemann Problem is solved both analytically and numerically for this system, and we demonstrate that different
commodities (user groups) would react differently to shockwaves and rarefaction waves. The study is concluded with future extensions.