Improving Travel Time Reliability with Variable Speed Limits

Abstract

This paper investigates how variable speed limits can optimize travel time reliability for commuters. We focus on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. Traffic demand during peak hours is modeled as a stochastic variable, with the optimization objective being a linear combination of the expected value and standard deviation of total travel time. To solve this problem, we develop a three-stage optimization algorithm based on the kinematic wave model of traffic flow (Lighthill & Whitham (1955), Richards (1956)). We demonstrate its practical applicability using a numerical example calibrated with empirical data. In contrast to existing approaches, our method provides an exact solution within the framework of the kinematic wave model without requiring prior discretization of space and time. This enables the determination of actually optimal positions and timing for the implementation of speed limits.