Swarm-Inspired Modeling of a Highway System With Stability Analysis

Naturally occurring flocks and swarms have long commanded human attention, with much engineering inspiration drawn from the beauty, order, and capability of these highly decentralized systems. More recent simulation and modeling of swarms has given rise to interesting mathematical problems as well as useful control strategies for machine applications. Although highway systems are sometimes mentioned in the literature as a possible swarm theory application, a microscopic, decentralized model of vehicle interactions based on swarming philosophy does not exist to our knowledge. In this paper, a decentralized model made up of ordinary differential equations and smooth functions is developed. It is designed to describe the interactions of vehicles on a two-lane highway. The purpose of this new model is not primarily traffic simulation, but rather cooperative control design. The philosophy behind the modeling is borrowed from work on swarm theory, especially those simulations employing the motion control ideas known as Reynolds' Rules. Vehicles in the swarm have different desired speeds, which can be maintained by changing lanes to avoid slower-moving lead vehicles, while also avoiding both frontal and side collisions. Stability analysis of the proposed model has been presented, as well as simulation results and possible uses.