Differentiable Hybrid Traffic Simulation

Macroscopic Model

Figure: To solve ARZ model with Finite Volume Method (FVM), we divide the lane into multiple discrete cells. Each cell has density and relative flow, which is represented as Q here. The n denotes current time step, and i denotes the index of the cell. To simulate traffic flow, we have to compute the cell states at next time step n + 1. We can do that by computing fluxes moving between these cells, which is suggested by ARZ model formulation.

Aw-Rascle-Zhang (ARZ) Model

ARZ model is one of the most widely used macroscopic models to simulate the traffic flow. It describes traffic evolution with a system of Partial Differential Equations (PDEs), which use independent variables of density and relative flow. To solve the PDEs, we use Finite Volume Method (FVM), which discretizes the simulation domain (in our case, a single lane road) into multiple cells. Each of the cells stores density, relative flow, and speed information, at the given time step.

Cell = {density, relative flow, speed}

(Note that speed can be recovered from density and relative flow, and vice versa.)

We update those values by computing flux between cells - we can solve Riemann problem to retrieve the flux. Note that as solution to the Riemann problem is differentiable with respect to the cell states, this whole process is differentiable. We derived analytical gradients for this process, and successfully accelerated the forward simulation and backpropagation. Please refer to our paper for the details about differentiability, and analytical gradients that we derived.

Page updated

Report abuse