1. © 2014 HDR, Inc., all rights reserved. A Case Study in Colorado Springs Comparative Fidelity of Alternative Traffic Flow Models at the Corridor Level 15 th Transportation Research Board Transportation Planning Applications Conference May 17 – 21, 2015 Atlantic City, New Jersey Speed Data-ing Session: May 21, 2015 Thursday: 8:30 AM – 10:00 AM Presented by: Maureen Paz de Araujo, HDR Carlos Paz de Araujo, University of Colorado Kathie Haire, HDR

2. Traffic Flow Equation Solution Problem Statement Emerging Trends in Traffic Flow Modeling Theoretical Foundations of Traffic Flow Models

3. 01 Problem Statement

4.  Different MOE results are often obtained using different simulation tools. This prompts the questions: Is there a “best” tool or a “right” answer ? Is there a common thread among the tools and can it be improved upon? If so, can we improve upon the “answer ” by tapping that common thread? How can we adapt to address emerging traffic flow modeling needs ? Fillmore St / I-25 DDI Build Alternative - MOE Results Comparison Software/IntersectionChestnut StSB RampsNB Ramps Synchro – on boardLOS C 27.6 sec/veh23.1 sec/veh Synchro - HCS 22.8 sec/veh16.5 sec/veh22.9 sec/veh VISSIM 24.9 sec/veh18.1 sec/veh14.1 sec/veh TSIS-CORSIM 28.6 sec/veh23.9 sec/veh24.0 sec/veh Fillmore Street/I-25 DDI Preferred Alternative – VISSIM MOEs Intersection LOS/Delay Evaluation Fillmore/I-25 DDI – Colorado Springs, CO LOS C LOS B LOS D LOS C

5. 02 Emerging Trends in Traffic Flow Modeling

6. Increasing Convergence : among macro, micro, and mesoscopic models Adaptations to Continuity Equation : to deal with real phenomena Addition of Multi-class Functionality : to expand model reach Hybrid Models : to combine advantages of macroscopic, mesoscopic and microsimulation models Greenshield LWR Lighthill Whitham Richards MACRO MESO MICRO Convergence Hybrid Models Adaptations of Continuity Equation

7. 03 Theoretical Foundations of Traffic Flow Models

8. The Fundamental Diagram  Traffic flow models assume there is a relation between the distance between vehicles and their travel speed  The Greenshields Fundamental Diagram expresses the relation using flow and density, where: Flow = q, average number of vehicles per unit length of road Density = ρ, average number of vehicles per unit of time and: q cap = flow at capacity ρ jam = jam density at which flow is zero Schematic Fundamental Diagram Traffic Flow vs. Density (Greenshields 1935 – Parabolic for Density – Flow )

9. Variations on the Fundamental Diagram  Variations in expression/shape of the Fundamental Relation Parabolic (Greenshields, 1935) Skewed Parabolic (Drake, 1967) Parabolic-linear (Smulders, 1990) Bi-linear (Daganzo, 1994)  Variations in variables used to express the Fundamental Relation Density – Flow Density – Velocity Density – Flow Fundamental Diagram Plots Density – Velocity Fundamental Diagram Plots q cap ρ jam q cap ρ jam q cap ρ jam Greenshields (parbolic) Daganzo (bi-linear) Smulders (parabolic-linear) v max ρ jam v max ρ jam v max ρ jam Greenshields (parbolic) Daganzo (bi-linear) Smulders (parabolic-linear)

10. The Traffic Flow Equation that is common in some form in each model is: Generic Types of Flow: where: ρ = density (vehicles/unit of time) q = flow (vehicles/unit of distance) t = time x = distance ρ = Density t = Time q = Flow x = Distance

11. 04 Traffic Flow Equation Solution

12. First Order Solution:

13. Second Order Solution:

14.  Determine how the traffic flow equation is implemented by various software  Apply closed-form/direct solutions to case study projects  Compare closed-form/direct solution results to simulation results Next Steps:

15. Questions?