Abstract

1. Frontal stationary x q D vAC Impact of Sensor Spacing on Freeway Travel Time Estimation for Traveler Information Wei Feng and Dr. Robert Bertini, Portland State University Forward forming Backward recovery Abstract Travel time estimation is a critical ingredient for transportation management and traveler information-both infrastructure-based and in-vehicle. Focusing on freeway travel time estimation for display on roadside variable message signs, this paper describes a concept developed from principles of traffic flow for establishing optimal sensor density. The methods are based on computing the magnitude of under- and over-prediction of travel time during shock passages. The midpoint method and Coifman methods in four situations are calculated during three types of shock waves considering representative traffic dynamics situations. Vehicle hours traveled (VHT) is used to evaluate travel time estimation errors. Relationships between travel time estimation errors and sensor spacing are established. Optimal sensor spacing expressions are calculated considering the trade-off between cost of VHT estimation error and the sensor construction cost. Comparison of optimal sensor spacing is performed among different travel time estimation methods in each type of shock waves. Sensitivity analysis is also performed, and a summary provided about the relationships between actual VHT, predicted VHT, VHT errors, total cost, optimal sensor spacing and variables speed and flow in different traffic states, segment length and sensor spacing. Results Optimal sensor spacing depends only on speed and flow values and cost coefficients. In Shock wave AC+CD/CE, when the ratio of Cu/Cd is less than 0.4/0.25, the optimal sensor spacing increases sharply with the ratio decreases; when larger than 0.4/0.25, slowly. Comparisons of optimal sensor spacing indicate the longest optimal sensor spacing in AC+CD is Coifman method 3, in AC+CE is Coifman method 2. Add Error, Abs Error and Penalty Error are found to be inversely proportional to the sensor density; Under and Over Error are also found to be inversely proportional but combined with constants. Acknowledgments Galen McGill of ODOT posed the sensor density question and supported this research. Dr. Robert Bertini and David Lovell established fundamentals of this research. vCD A qA C B qC E qE vCE Forward recovery Backward forming vf vc Rear stationary t k A. Types of Transitions B. Assumed Traffic Flow Relation x Empirical Comparison of German and U.S. Traffic Sensor Data and Impact on Driver Assistance Systems Steven Hansen and Dr. Robert L. Bertini, Portland State University B x vf bn B vAC vCE C D vf bn CE AC A CD DA E Fundamentals and Assumptions Midpoint AC Travel Time Estimations C VHT Errors vs. Sensor Spacing tdeact t vms vms A AC vCD A vAC tdeact t AC: n sensors in l segment length Steve Hansen, Dr. Robert Bertini, Portland State University Sensor Spacing Optimization Coifman (1) AC : segment length, (mile) : sensor spacing, (mile) : total cost, ($) : sensor cost, ($ per sensor) : cost coefficient, convert under or over estimated VHT error into $, [$/(hr*mile)] Optimal Sensor spacing Relationships between Measurements and Variables is a function of the speed and flow variables, combined as a constant to reflect the relation among measurements, segment length and sensor spacing. each is different in each cell www.its.pdx.edu www.its.pdx.edu