Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ffff i c E n g i n e e r i n g a n d S a f e t y
Time Mean Speed, v t … is the arithmetic mean of the measured speeds of all vehicles passing a fixed roadside point during a given interval of time (the individual speeds are known as ‘spot speeds’)
TRAFFIC FLOW PARAMETERS
1) SPEED (v) Speed is ...... defined as rate of motion, or distance per unit time
n
v
n = number of vehicles observed
i
Space Mean Speed, v s
v s
… is the average travel speed
v s
vt
nL
i 1
n L = average length travelled by the vehicles
n
t
vt
v i = spot speeds (km/hr)
n = number of travel times observed
n i
vt
ti = travel time of the i-th vehicle to traverse the section (hr)
i 1
2
2
L = length of the highway segment (km)
t
vs
2 s = 2 t
s
vs
or
vs
vt
t
vt
variance of the space mean speed
= variance of the time mean speed =
(vi v t )
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ffff i c E n g i n e e r i n g a n d S a f e t y
Three vehicles pass a kilometer post at 60, 75 and 54 km/hr, respectively. What is the time mean speed of the three vehicles? Also, find the approximate space mean speed.
2
t
v
s
60 75 54
3
63
km/hr
3 63
63
61.8
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ffff i c E n g i n e e r i n g a n d S a f e t y
2) VOLUME (V) Volume is ...... the number of vehicles observed or predicted to pass a point during a given time interval. 3) RATE OF FLOW (q)
(60 63)2 (75 63)2 (54 63)2 78
2
n
1
vt
L t
Relationship between Space Mean Speed and Time Mean Speed
nL
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ffff i c E n g i n e e r i n g a n d S a f e t y
Rate of flow is ...... the number of vehicles passing a point during a given time interval less than 1 hour, but expressed as an equivalent hourly rate.
78 Thus, a volume of 200 vehicles observed in a 10-minute period implies a rate of flow of 1200 veh/hr.
km/hr
200
= 1200
(10/60)
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ffff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ffff i c E n g i n e e r i n g a n d S a f e t y
N
4) DENSITY (k) Density is ...... the number of vehicles occupying a given length of lane or roadway, averaged over time.
5) SPACING (s) k = 14 veh / 0.5 km = 28 veh/km
6) HEADWAY (h)
Usually expressed in vehicles/km.
Headway is ...... the corresponding time (seconds) between successive vehicles as they pass a point of a roadway.
Density can be measured directly through aerial photography. Density can also be calculated using the equation:
k = q/v where q = rate of flow v = speed
BDD/BFC32302/1B
Spacing is ...... the distance (meters) between successive vehicles in a traffic stream, measured from front bumper to front bumper.
500 m
What is the density of southbound traffic on this highway?
Spacing and Headway are related to q, v and k: k = 1000/s
k (in veh/km), s (in meters)
h = s/v
h (in sec), v (in m/s)
q = 3600/h
q (in veh/hr), h (in sec)
1
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
7) LANE OCCUPANCY (LO)
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Density can be estimated using the expression ......
Lane Occupancy is ...... the ratio of the time that vehicles are present at a detection station in a traffic lane compared to the time of sampling.
L+C Lane occupancy may also be expressed by R, which is …
LO = Total time vehicle detector is occupied = to Total observation time
k = LO x 1000
T
R = Sum of lengths of vehicles = Li Length of roadway section
to = L + C
where L = average length of vehicle
v s
Then, density can be estimated using the expression ......
C = distance between loop detector
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
During a 60-sec period, a detector is occupied by vehicles for the following times: 0.34, 0.38, 0.40, 0.32 and 0.52 sec.
k = R/L
a)
where L = average length of vehicles
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
b) k=
a) Determine the lane occupancy. b) Estimate the values of q, k and v. (Assume that the loop-detector length is 3 m and the average length of vehicles is 8 ft).
D
v s =
0.0327 1000 2.44 3
n ( L C)
to
= 6.01 veh/km
= 5(2.44 3) = 13.88 m/s = 49.97 km/h
1.96
q = 6.01 49.97 = 300.3 veh/hr
to = 0.34 + 0.38 + 0.40 + 0.32 + 0.52 = 1.96 sec T = 60 sec LO = 1.96 100% = 3.27% 60
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
8) CLEARANCE (c) Clearance is ...... the distance (meters) between successive vehicles in a traffic stream, measured from front bumper to back bumper.
Clearance (m) / Gap (s)
9) GAP (g) Gap is ...... the corresponding time (seconds) between successive vehicles as they pass a point of a roadway.
g = h – (L/v) c = g x v
BDD/BFC32302/1B
where
g = mean gap (sec) L = mean length of vehicles (m) c = mean clearance (m) h = mean headway (sec) v = mean speed (m/s)
Spacing (m) / Headway (s)
2
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
CATEGORIES OF TRAFFIC FLOW
CATEGORIES OF TRAFFIC FLOW
UNINTERRUPTED FLOW
INTERRUPTED FLOW
Occurs on facilities that have no fixed elements (such as traffic signals or stop signs) external to the tra ffic stream, that cause interruptions to traffic flow. Traffic flow conditions are thus the result of interactions among vehicles in the traffic system and between vehicles and the geometric characteristics of the roadway/guideway system. The driver of the vehicle does not expect to be required to stop by factors external to the traffic stream Uninterrupted Flow facilities: Expressways, Exclusive bus lanes, Rail Transit Lines
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Occurs on facilities that have fixed elements c ausing periodic interruptions to traffic flow. Traffic is stopped or significally slowed down periodically irrespective of how much traffic exists. The driver expects to be required to stop as and when required by fixed elements that are part of the facility Interrupted Flow facilities: Signalized streets, Unsignalized streets with stop signs, Arterials, Pedestrian walkways, Bicycle paths. *Note: Uninterrupted/Interrupted Flow are terms that describe the facility, and not the quality of flow!
Lecturer: Dr. Basil David Daniel
What type of facilities are these?
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
UNINTERRUPTED TRAFFIC FLOW MODEL
Uninterrupted flow facility or Interrupted flow facility?
Speed (km/hr) C D
Normal flow B
Forced flow
UNINTERRUPTED FLOW FACILITY
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
A
INTERRUPTED FLOW FACILITY
Lecturer: Dr. Basil David Daniel
Imagine several vehicles, driven by rational drivers along a section of freeway.
Congestion
Flow (veh/hr)
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
SPEED, FLOW and DENSITY relationship Speed, v
As vehicles speed and spacing increases, the speeds approach the free speed, and drivers adopt their own speed when uninfluenced by other vehicles in the traffic stream (point C).
Speed, v
A v = A – Bk A/2
The dashed curve represents the normal flow behaviour if all drivers were to have the same free speed (point D).
It has been observed that drivers are uninfluenced by other vehicles in the traffic lane at flows about half the capacity flow (point B).
Capacity
A/B
Density, k
Flow, q
Flow, q A2 /4B
Maximum traffic density occurs (point A) when traffic has virtually come to a complete stop. In the forced flow region, e ach vehicle adopts its minimum spacing and clearance distance. A/2B
BDD/BFC32302/1B
A/B
Density, k
3
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
Speed-Density relationship
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
Flow-Density relationship
Lecturer: Dr. Basil David Daniel
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
Speed-Flow relationship Maximum flow (qmax) occurs at optimal speed (v m) and optimal density (km). qmax = v m x km = v f x k j 2 2 = v f x k j 4
B F C 3 2 3 0 2 T r a ff i c E n g i n e e r i n g a n d S a f e t y
Lecturer: Dr. Basil David Daniel
A traffic stream is moving at a steady state when entering a mountain grade. Upon entering the grade, the speed, density and flow are 72 km/h, 25 veh/km and 1800 veh/hr respectively. On the grade, a truck drops to a speed of 15 km/h causing traffic to bunch up to a density of 85 veh/km. When the truck pulls over, traffic accelerates to the maximum flow until steady state flow conditions resume. Calculate (a) the flow of traffic behind the truck on the mountain grade (b) the jam density and free flow speed for this road (c) the density and speed when traffic resumes a steady state flow (d) the maximum flow
BDD/BFC32302/1B
4
