Formalization of Traffic Flow Theory

Abstract

Traffic flow theory allows us to mathematically describe the behavior of traf fic flow and thus deduce interesting properties for transportation engineers. Traditionally, traffic flow problems are analyzed by using paper-and-pencil proof methods, computer-based numerical techniques or computer algebra systems. However all these methods are error-prone and thus the analysis cannot be termed as accurate, which poses a serious threat to the safety critical domain of transportation systems. To guarantee the correctness of the analysis, we propose to use higher-order-logic theorem proving for ana lyzing the traffic flow problems and as a first step in this direction, present a logical framework for the formal analysis of macroscopic models of traffic flow. In particular, we present a formalization of some foundational con cepts of macroscopic models, namely density, flow rate, mean speed, relative occupancy and shockwave using the higher-order-logic theorem prover HOL Light. To illustrate the practical utilization and effectiveness of the proposed idea, we perform the formal analysis of a German freeway, including its input output and shockwave analysis by verifying their corresponding properties using our proposed formalization.