TRAFFIC FLOW BASICS

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TRAFFIC FLOW BASICS
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Objectives

• Identify traffic flow variables
• Determine relationships among terms
• Use time-space diagram for parameter estimation

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Some Terms

• Volume (V)
• Amount of traffic (vehicles)
• Speed (u)
• Distance traveled over time (mph)
• Density (k)
• Volume of traffic over distance (vpm)
• Flow (q)
• Volume of traffic over time (vph)

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Some Terms

• Volume (V)
• Amount of traffic (vehicles)
• Speed (u)
• Distance traveled over time (mph)
• Density (k)
• Volume of traffic over distance (vpm)
• Flow (q)
• Volume of traffic over time (vph)

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Some Terms

• Volume (V)
• Amount of traffic (vehicles)
• Speed (u)
• Distance traveled over time (mph)
• Density (k)
• Volume of traffic over distance (vpm)
• Flow (q)
• Volume of traffic over time (vph)

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Speed (u)

• Distance traveled over time (mph)
• Time Mean Speed (Spot)
• ut 1/n Sui
• Space Mean Speed
• u nl/ Sti

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Density (k)

• Density is the number of vehicles in a given
  length of roadway or a lane.
• k Volume (V) / L
• It is usually expressed in veh./km. or veh./mile.

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Flow (q)

• Volume of traffic over time
• It is usually expresed in vehicles per hour (vph)

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Basic Relationships
High speeds
Low volumes
High volumes
Low speeds
High volumes
High density
No speed
Maximum density
q k u
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Speed/Density
Max u _at_ k 0
Max k _at_ u 0
uufuf/kj k
Speed
Density
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Density/Flow
uufuf/kj k _at_ uq/k
qufk - uf/kj k2
Optimum density
Flow
Density
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Speed/Flow
uufuf/kj k _at_ kq/u
qkju - kj/uf u2
Optimum speed
Speed
qmax uo ko
Flow
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Speed/Flow/Density
uf
uo
qmax
qmax
kj
ko
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Speed/Flow/Density

• Greenshields model
• Linear relationship u/k
• uufuf/kj k
• ONLY FOR GREENSHIELDS MODEL!!!
• ko kj/2 uo uf/2
• qmax uf kj /4

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Speed/Flow/Density
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Example 1
q 55k 0.80k2 uf kj ko uo qmax?
qk u
k u 55k -0.80k2
u 55 -0.80k
uf 55 mph
kj 68.75 vpm
0.80uf /kj
uo uf/2 27.5 mph
qmax kj uf/4 957 vph
ko kj/2 34.38 vpm
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Example 2
u 50 0.10k2 uf kj ko uo qmax?
k0
uf 50 mph
kj q50/0.10 22.36 vpm
u0
q 50k -0.10k3
qmax _at_ dq/dk0
ko
0 50 -0.10(3)k2
k "12.91 vpm
qmax 430.3 vph
qmax 50k -0.10k3
uo 33.3 mph
uo qmax/ko
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Some More Terms (1/2)

• Space Headway (s)
• Distance between vehicles (ft/veh) k5280/s
• Time headway (h)
• Time between vehicles (sec/veh) q3600/h

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Time-Space Diagram (1/3)
Flow At point Xo for t2 t1 q 3/(t2 t1 )
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Time-Space Diagram (2/3)
Density At time to for X2 X1 k 2/(X2 X1 )
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Time-Space Diagram (3/3)
Space headway
Time headway
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Some More Terms (2/2)

• Spacing (S)
• Open distance between vehicles (ft/veh)
• Gap (g)
• Open distance in time between vehicles (sec/veh)