Traffic Flow Characteristics (2). Learning Objectives To differentiate between interrupted and uninterrupted flow facilities To define general and linear.

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