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. 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. What is Probability of Breakdown?

3. 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) Calculating Probability of Breakdown

4. PLM Model

5. Fitting the Data to a Distribution

6. Derived From Volume

7. Using Upstream Volume and Ramp Demand Separately

8. One year of screened data One year of screened data One minute intervals One minute intervals Record approximately 10 observations before breakdown Record approximately 10 observations before breakdown Use of Speed-Based Algorithm to identify breakdown data 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 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 Recommendations for Generating Probability of Breakdown Model

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

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

11. Acceptable Probability of Breakdown

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

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

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

15. Fuzzy Logic Control Fuzzification Inputs – Local OccupancyLocal Speed Downstream OccupancyDownstream Speed Queue OccupancyAdvance Queue Occupancy

16. Fuzzy Logic Control Rule Base RuleRule WeightRule PremiseRule Outcome 12.5If local occupancy is VBMetering rate is VS 21.0If local occupancy is BMetering rate is S 31.0If local occupancy is MMetering rate is M 41.0If local occupancy is SMetering rate is B 51.0If local occupancy is VSMetering rate is VB 63.0If local speed is VS AND local occupancy is VBMetering rate is VS 71.0If local speed is SMetering rate is S 81.0If local speed is BMetering rate is B 91.0If local speed is VB AND local occupancy is VSMetering rate is VB 104.0If downstream occupancy is VBMetering rate is VS 112.0If queue occupancy is VBMetering rate is VB 124.0If advance queue occupancy is VBMetering rate is VB

17. Defuzzification to Calculate Metering Rate w i = the weighting of the ith rule c i = the centroid of the output class I i = the implicated area of the output class

18. Questions?