5traffic Flow 2

Traffic Flow Characteristics (2)

Traffic Flow Characteristics (2)

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

KJam

DensityDensity at Capacity

S

QTraffic

JamCapacity

normal flow

forced flow

p.130

General Speed-Density Relationship

Free

V

KJam

DensityDensity at Capacity

K

Q

Traffic Jam

Capacity

normal flow

forced flow

p.137

General Speed-Density Relationship

Free

V

KJam

DensityDensity at Capacity

Q

VTraffic Jam

Capacity

p.137

Greenshield’s Model

• Assume a linear relationship between v and k:

High Density = Low Speed

Low Density = High Speedvf

kj

kk

vvv

j

ff

Greenshield’s Model

K

QMax flow

qmax

K0Kj

vf v0 2kk

vkvq

j

ff

Greenshield’s Model

Q

V

Max flowQmax

Vf

V0

1/k0=s0

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