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Amalor – J Orillo
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GENERAL EQUATION:
q = kūs
WHERE:
q = FLOW
k = DENSITY
ūs = SPACE MEAN
SPEED
Other relationships that exist
among the traffic flow variables
are:
_
k = qt
WHERE:
q = FLOW
k = DENSITY
t = TRAVEL TIME FOR
UNIT
DISTANCE
GENERAL EQUATION:
q = kūs
WHERE:
q = FLOW
k = DENSITY
ūs = SPACE MEAN
SPEED
Other relationships that exist
among the traffic flow variables
are:
_
_
t
dk==ūq
h
s
WHERE:
d
AVERAGE SPEED
q = FLOW
k = DENSITY
HEADWAY
t = TRAVEL TIME FOR
SPACE MEAN
UNIT ūs =DISTANCE
SPEED
h = AVERAGE TIME
HEADWAY
GENERAL EQUATION:
q = kūs
WHERE:
q = FLOW
k = DENSITY
ūs = SPACE MEAN
SPEED
Other relationships that exist
among the traffic flow variables
are:
__ ___
dh==ūds h t
WHERE:
WHERE:
d = AVERAGE SPEED
d = AVERAGE SPEED
HEADWAY
HEADWAY
t = AVERAGE TRAVEL
ū = SPACE MEAN
TIME s
FOR UNIT
SPEED
DISTANCE
h = AVERAGE TIME
h = AVERAGE TIME
HEADWAY
HEADWAY
Fundamental Diagram of
Traffic Flow
1. When the density on the highway is 0, the flow is
also 0 because there are no vehicles on the
highway.
2. As the density increases, the flow also increases.
3. When the density reaches its maximum,
generally referred to as the jam density (kj), the
flow must be 0 because vehicles will tend to line
up end to end.
4. It follows that as density increases from 0, the
flow will also initially increase from 0 to a
maximum value. Further continuous increase in
density will then result in continuous reduction
of the flow, which will eventually be 0 when the
density is equal to the jam density.
SHOCK WAVES
IN TRAFFIC
STREAMS
Types of Shock
Waves
Frontal stationary shock waves
↳ Formed when the capacity suddenly reduces to zero at an
approach or set of lanes having the red indication at a signalized
intersection or when a highway is completely closed because of a
serious incident.
↳ For example, at a signalized intersection, the red signal indicates
that traffic on the approach or set of lanes cannot move across
the intersection, which implies that the capacity is temporarily
reduced to zero resulting in the formation of a frontal stationary
shock wave as shown in Figure
Backward forming shock waves
↳ Formed when the capacity is reduced below the demand flow
rate resulting in the formation of a queue upstream of the
bottleneck. The shock wave moves upstream with its location at
any time indicating the end of the queue at that time.
Rear stationary and forward recovery shock waves
↳ Formed when demand flow rate upstream of a bottleneck is first
higher than the capacity of the bottleneck and then the demand
flow rate reduces to the capacity of the bottleneck.
↳ For example, consider a four-lane (one direction) highway that
leads to a two-lane tunnel in an urban area as shown in Figure.
↳ During the off-peak period when the demand capacity is less
than the tunnel capacity, no shock wave is formed.
Rear stationary and forward recovery shock waves
↳ This shock wave continues to move upstream of the bottleneck
as long as the demand flow is higher than the tunnel capacity as
shown in Figure.
↳ At this point, a rear stationary shock wave is formed until the
demand flow becomes less than the tunnel capacity resulting in
the formation of a forward recovery shock wave as shown in
Figure.