Lec 11, Ch6, pp : Principles of traffic flow (objectives) Know the primary elements of traffic flow Know the difference between TMS and SMS Know the general equation relating flow, density, and space mean speed Be able to draw the fundamental diagram of traffic flow Know thoroughly the characteristics of two most popular macroscopic traffic flow models

What we cover in class today… Time-space diagram Primary elements of traffic flow How to compute TMS and SMS Flow-density relationship Fundamental diagram of traffic flow Macroscopic traffic flow models: Greenshields model and Greenburg model

Time-space diagram (A microscopic way of looking at traffic flow Time Distance Time headway Space headway Flow rate, qThe equivalent hourly rate at which vehicles pass a point during a time period less than 1 hr. q = (n*3600)/T vph Density, kThe number of vehicles traveling over a unit length of highway at an instant in time Speed, uThe distance traveled by a vehicle during a unit of time

Time mean speed vs. space mean speed Time mean speed (TMS): Space mean speed (SMS): (Review Example 6-1)

Flow-density relationships Flow = (density) x (Space mean speed) Space mean speed = (flow) x (Average space headway) where Average space headway = SMS/(Average time headway) where

Fundamental diagram of traffic flow (flow vs. density) Flow (q) Density (k) Optimal flow or capacity,q max Optimal density, k o Jam density, k j Mean free flow speed, u f Optimal speed, u o Speed is the slope. u = q/k Uncongested flow Congested flow

Fundamental diagram of traffic flow (SMS vs. density & SMS vs. flow) kjkj 0 ufuf Density SMS SMS vs. density q max 0 ufuf Flow SMS SMS vs. flow Uncongested flow Congested flow

Greenshields model Nice characteristics of the Greenshields model: This model works for all k = 0 to k = k j

Greenburg model Characteristics of the Greenburg model: or This model does not work near k = 0. Do you know why?