Use of the Probability of Breakdown Concept in Ramp Metering

1. Use of the Probability of Breakdown Concept in Ramp Metering Clark Letter Dr. Lily Elefteriadou October 30, 2012 University of Florida Transportation Research Center

2. What is Probability of Breakdown? • Estimates the probability that a particular freeway flow (or combination of ramp and freeway flows) would lead to breakdown. • Estimates the proportion of flows that have resulted in breakdown. That proportion can then be used as the probability that a given flow would lead to breakdown. • To accomplish this numerically, flows at breakdown {B} and flows prior to breakdown {F} are obtained and used in calculations.

3. Calculating Probability of Breakdown Where: F(q) = distribution function of breakdown volume q = traffic volume (veh/h/ln) qi = traffic volume in interval i, which is the one prior to the drop in speeds, i.e., the breakdown flow (veh/h/ln) ki = number of intervals with a traffic volume of q ≥ qi {B} = set of breakdown intervals (1-minute observations)

4. PLM Model

5. Fitting the Data to a Distribution

6. Derived From Volume

7. Using Upstream Volume and Ramp Demand Separately

8. Recommendations for Generating Probability of Breakdown Model • One year of screened data • One minute intervals • Record approximately 10 observations before breakdown • Use of Speed-Based Algorithm to identify breakdown data • Based on identifying the abrupt speed reduction coinciding with the breakdown occurrence, the low speeds during the congestion period, and the subsequent increase in speeds at the end of the congested period

9. Application to Ramp Metering • Identify Critical Ramps • Apply Probability of Breakdown concept to Critical Ramps • Implement an Initialization Threshold • Use an Acceptable Probability of Breakdown to Calculate Capacity Dynamically • From NCHRP 3-87 (15 %– 20%)

10. Ramp Metering Application • Initialization Threshold Set to the lowest evaluation parameter where breakdown has occurred (10%)

11. Acceptable Probability of Breakdown

12. Previous Research • Recommendations for Implementation • Implement Probability of Breakdown at critical ramps • Maintain existing ramp metering algorithm at non-critical ramps • Speed used for breakdown identification • Observed Benefits • Postponing the time to breakdown • Reducing average travel time • Reducing the duration of congestion

13. STRIDE Project • Collaboration through STRIDE between FIU and UF • Dr. Mohammed Hadi, Associate Professor, Florida International University • Dr. Yan Xiao, Research Associate, Florida International University • Dr. Tao Wang, Research Associate, Florida International University • Investigation of ATDM Strategies to Reduce the Probability of Breakdown • I-95 Miami study site • Incorporate the utilization of the flow breakdown probability concept in the fuzzy logic ramp metering algorithm • Evaluate the effectiveness of the modifications using the CORSIM microsimulator

14. I-95 Study Site On-ramp from US 441 On-ramp from Opa Locka Blvd On-ramp from NW 125th St Critical Ramps On-ramp from NW 103rd St On-ramp from NW 95th St On-ramp from NW 81st St On-ramp from NW 69th St On-ramp from NW 62nd St

15. Fuzzy Logic Control Inputs – Local Occupancy Local Speed Downstream Occupancy Downstream Speed Queue Occupancy Advance Queue Occupancy Fuzzification

16. Fuzzy Logic Control Rule Base

17. Defuzzification to Calculate Metering Rate wi= the weighting of the ith rule ci = the centroid of the output class Ii = the implicated area of the output class

18. Questions?