Use of the Probability of Breakdown Concept in Ramp Metering

Clark LetterDr. Lily Elefteriadou

October 30, 2012

University of FloridaTransportation Research Center

• 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?

Where:F(q) = distribution function of breakdown volumeq = 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

PLM Model

Fitting the Data to a Distribution

Derived From Volume

Using Upstream Volume and Ramp Demand Separately

• 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

Recommendations for Generating Probability of Breakdown Model

• 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%)

Application to Ramp Metering

• Initialization Threshold

Ramp Metering Application

Set to the lowest evaluation parameter where breakdown has occurred (10%)

Acceptable Probability of Breakdown

• 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

Previous Research

• 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

STRIDE Project

I-95 Study Site

On-ramp from NW 62nd StOn-ramp from NW 69th St

On-ramp from NW 81st St

On-ramp from NW 103rd St

On-ramp from NW 125th St

On-ramp from NW 95th St

On-ramp from Opa Locka Blvd

On-ramp from US 441

Critical Ramps

Fuzzy Logic Control

Fuzzification

Inputs – Local Occupancy Local SpeedDownstream Occupancy Downstream SpeedQueue Occupancy Advance Queue Occupancy

Fuzzy Logic Control Rule Base

Rule Rule Weight Rule Premise Rule Outcome

1 2.5 If local occupancy is VB Metering rate is VS

2 1.0 If local occupancy is B Metering rate is S

3 1.0 If local occupancy is M Metering rate is M

4 1.0 If local occupancy is S Metering rate is B

5 1.0 If local occupancy is VS Metering rate is VB

6 3.0 If local speed is VS AND local occupancy is VB Metering rate is VS

7 1.0 If local speed is S Metering rate is S

8 1.0 If local speed is B Metering rate is B

9 1.0 If local speed is VB AND local occupancy is VS Metering rate is VB

10 4.0 If downstream occupancy is VB Metering rate is VS

11 2.0 If queue occupancy is VB Metering rate is VB

12 4.0 If advance queue occupancy is VB Metering rate is VB

Defuzzification to Calculate Metering Rate

𝑀𝑒𝑡𝑒𝑟𝑖𝑛𝑔 𝑅𝑎𝑡𝑒=∑𝑖=1

𝑁

𝑤𝑖𝑐 𝑖 𝐼𝑖

∑𝑖=1

𝑁

𝑤 𝑖 𝐼 𝑖wi = the weighting of the ith ruleci = the centroid of the output classIi = the implicated area of the output class

Questions?