Traffic Flow Characteristics (2)

Learning Objectives To differentiate between interrupted and uninterrupted flow facilities To define general and linear speed-density relationships To derive, sketch, and apply Greenshield’s Model of traffic flow

Recap Spacing

Recap Clearance

Recap Density # vehicles/Distance

Recap… Speed (v) – ft/sec or mph Flow (q) – veh/sec or vph Density (k) – veh/ft or vpm Spacing (s) – ft/veh Headway (h) – sec/veh Clearance (c) – ft/veh Gap (g) – sec/veh Remember, units are critical!

Fundamental Relationships q = k  v (veh/hr) = (veh/mi)  (mi/hr) h = 1 / q (sec/veh) = 1 / (veh/hr)  (3600) s = 1 / k (ft/veh) = 1 / (veh/mi)  (5280)

Types of Facilities Uninterrupted flow –Freeways –Multilane highways –Two-lane highways

Types of Facilities Interrupted flow –Signalized streets –Un-signalized streets with stop signs –Transit lanes –Pedestrian walkways

General Speed-Density Relationship Free V K Jam Density Density at Capacity S Q Traffic Jam Capacity normal flow forced flow p.130

General Speed-Density Relationship Free V K Jam Density Density at Capacity K Q Traffic Jam Capacity normal flow forced flow p.137

General Speed-Density Relationship Free V K Jam Density Density at Capacity Q V Traffic Jam Capacity p.137

Greenshield’s Model Assume a linear relationship between v and k: High Density = Low Speed Low Density = High Speed vfvf kjkj

Greenshield’s Model K Q Max flow q max K0K0 KjKj vfvf v0v0

Greenshield’s Model Q V Max flow Q max VfVf V0V0 1/k 0 =s 0

Example Assuming a linear v-k relationship, the mean free speed is 60 mph near zero density, and the corresponding jam density is 140 vpm. Assume the average length of vehicles is 20 ft. Find: –v(k) and q(k) –Sketch v-k, v-q, and q-k diagrams –Compute v and k at q=1000 vph –Compute the average headway, spacings, clearances, and gaps when the flow is maximum