Quantifying travel time variability at a single bottleneck based on stochastic capacity and demand distributions

ABSTRACT

Travel time reliability, an essential factor in traveler route and departure time decisions, serves as an important quality of service measure for dynamic transportation systems. This article investigates a fundamental problem of quantifying travel time variability from its root sources: stochastic capacity and demand variations that follow commonly used log-normal distributions. A volume-to-capacity ratio-based travel time function and a point queue model are used to demonstrate how day-to-day travel time variability can be explained from the underlying demand and capacity variations. One important finding is that closed-form solutions can be derived to formulate travel time variations as a function of random demand/capacity distributions, but there are certain cases in which a closed-form expression does not exist and numerical approximation methods are required. This article also uses probabilistic capacity reduction information to estimate time-dependent travel time variability distributions under conditions of non-recurring traffic congestion. The proposed models provide theoretically rigorous and practically useful tools for understanding the causes of travel time unreliability and evaluating the system-wide benefit of reducing demand and capacity variability.

KEYWORDS:

• bottleneck
• stochastic capacity
• stochastic demand
• travel time variability

Funding

This article is partially supported through a U.S. University Transportation Center project titled [NTC2015-MU-R-05]: Data Fusion Aided Freeway Analysis for HCM. The second author is partially supported by the National Science Foundation—U.S. grant CMMI 1538105, “Collaborative Research: Improving Spatial Observability of Dynamic Traffic Systems through Active Mobile Sensor Networks and Crowdsourced Data.” The work presented in this article remains the sole responsibility of the authors.