Roseedlngt ol th@ Amodean Contml Confinnu Setnio. Washington June 1995 zyx Traffic Flow Stabilization zyx Perry Y. Li, Roberto Horowitz, Luis Alvarez, Jonathan Frankel and Anne M. Robertson Department of Mechanical Engineering University of California at Berkeley Berkeley, CA 94720-1740 zyxw horowitz@canaima.Berkeley.EDU Abstract Link layer controllers for the AVHS architecture proposed in PATH are derived using vehicle conservation flow models. Control laws are developed for three highway topologies: a single lane highway, a highway with multiple discrete lanes and a highway with an arbitrary 2 dimensional flow pattern. The control laws obtained for each of the topologies is dis- tributed and is very suited for implementation at the lower levels of the AVHS control hierarchy. Simulation results are described. 1. Introduction The current Automated Vehicle and Highway System (AVHS) architecture proposed in the California PATH project [lo] consists of five hierarchical layers: (Fig.1): the network layer, the link layer, the coordination (planning) layer, the regulation layer and the physical layer. There is a zyxwvu Roadside system zyxwvutsrqponm I Vehicle system zyxwvutsrqponm 1 routing t a b F ! into. flow, density, incidents &1;;~.;1 maneuver complete r-l (id] r-l dynamics Neighbor Vehicle Neighbor Figure 1: Hierarchical Architecture of AVHS in the PATH project different control objective for each of these layers. The net- work layer routes vehicles within the network of highways 'Research supported by UCB-ITS PATH grant MOU-135 2Currently at Department of Mechanical Engineering, Uni- versity of Pittsburgh so that, on average, vehicles entering the system reach their destinations in the shortest amount of time. The link layer controller establishes traffic conditions, which we define to be density and flow profiles, so as to realize the capability of a stretch of highway. The coordination layer determines when a vehicle should perform a maneuver and ensures that maneuvers occur in an orderly and safe fashion. The regu- lation layer control laws carry out the maneuvers [4, 51. In this paper we focus on a link layer control that regulates aggregate traffic density and velocity to their appropriate values, while acting within this hierarchical structure. The proposed link layer stabilizing control law requires only lo- cal density and commands only local reference velocities. In this sense the controller is decentralized. 2. Background and overview Control strategies at the macroscopic level for the link layer are scarce. We review some of the relevant ones here. In [6], the authors present a detailed traffic flow model based on the behavior of human drivers. It is proposed that, if one of the terms that describe driver behavior is replaced by a control term intended to homogenize the density profile, then the capacity of the highway can be better realized. Chien et al. [2] study the problem of tracking an arbi- trary density profile. Using a one lane macroscopic traffic model similar to that in [6], they derive a controller that commands a desired velocity at each section of the highway such that the density of the entire highway conforms to a specified density profile. Because the control law relies on the inversion of the traffic flow dynamics, the control action can be large when the density in any section of the highway is small. A description of a link layer controller consistent with the AHS architecture in [lo], for a multiple lane highway op- erating under normal conditions, can be found in [9]. The design uses a dynamic model of the coordination and regu- lation layers obtained through extensive simulations under normal operation conditions. A lane change proportion con- trol has been developed and implemented in SmartPath [3] using three control laws intended to balance traffic across the lanes, allow cars to reach their exit and avoid significant increases in travel times, respectively. In zyxwvu [7], the parameters for a spatially discretized traffic flow model of the Southern Boulevard Perpherique of Paris are 144