1. Traffic Concepts
CEE 320 Steve Muench

2. Outline Basic Concepts Relationships Example Flow Rate Spacing Headway
Speed
Density
Relationships
Example

3. Concepts Definitions Volume, Speed, Density relationships Speed
Space mean speed
Time mean speed

4. Flow Rate (q)
The number of vehicles (n) passing some designated roadway point in a given time interval (t)
Units are typically vehicles/hour
Flow rate is different than volume

5. Spacing
The distance (ft) between successive vehicles in a traffic stream, as measured from front bumper to front bumper
AMC Pacer and AMC Gremlin

6. Headway (h)
The time (in seconds) between successive vehicles, as their front bumpers pass a given point.

7. Headway
From HCM 2000

8. Speed Time mean speed (spot speed) Space mean speed (u)
Arithmetic mean of all instantaneous vehicle speeds at a given “spot” on a roadway section
Space mean speed (u)
The mean travel speed of vehicles traversing a roadway segment of a known distance (d)
More useful for traffic applications

9. Space Mean Speed It is the harmonic mean (1/H = 1/a + 1/b + …)
Space mean speed is always less than time mean speed
A harmonic mean is just another way to describe a set of data
In this case it is more descriptive for vehicle speeds
Example party trick to show you are a knowledgeable engineer
You are in a vehicle traveling a total of 10 miles. For the first 5 miles you travel at exactly 40 mph and for the next 5 miles you travel at exactly 60 mph. What is your average speed over the time you spent traveling that 10 miles? Intuitively, you were going at 40 mph for longer than you were going at 60 mph so your average velocity for the entire trip is going to be less than the arithmetic mean of 50 mph
It’s 48 mph by harmonic mean
distance = speed * time
5 miles at 40 mph = 7.5 minutes
5 miles at 60 mph = 5 minutes
weighted average = (40(7.5) + 60(5))/( ) = 48 mph
Example
5 vehicles over a given 1 mile section take 1.0, 1.2, 1.5, 0.75 and 1.0 minutes respectively
Average travel time = 5.45/5 = 1.09 minutes = hours
Therefore, average speed = 1 mile/ hours = mph

10. Time Mean vs. Space Mean Speed
From HCM 2000

11. Density (k)
The number of vehicles (n) occupying a given length (l) of a lane or roadway at a particular instant
Unit of density is vehicles per mile (vpm).
Occupancy is often used as a surrogate

12. Other Concepts Free-flow speed (uf) Jam density (kj) Capacity (qm)
Occupancy often used as a surrogate to density because it’s easier to measure
Density is difficult to measure because you have to essentially image a long stretch of road
Occupancy and density are correlated by not perfectly

13. Speed vs. Density uf Free Flow Speed kj Jam Density Speed (mph)
Density (veh/mile)

14. Flow vs. Density Optimal flow, capacity, qm Congested Flow
FLow (veh/hr)
km Optimal density
kj Jam Density
Uncongested Flow
Density (veh/mile)

15. Speed vs. Flow uf Free Flow Speed Uncongested Flow um
Speed (mph)
Lots of measurements in the top part, a few in the queue part and a few in the congested part
Segment 1 = top part = uncongested
Segment 2 = straight part = queue discharge
Segment 3 = bottom part = within a queue
Optimal flow, capacity, qm
Congested Flow
Flow (veh/hr)

16. 3-D Model
Occupancy is a surrogate for density since density is often difficult to measure

17. Example
I-5 over the ship canal bridge has 4 lanes in each direction. The northbound capacity is 8200 veh/hr/lane and the free-flow speed is 65 mph. What is the maximum flow rate, maximum density, jam density? If a one-hour vehicle count in the northbound direction for the outside lane gives 7034 vehicles in a non-congested condition, what is the estimated space mean speed of these 7034 vehicles?
Maximum flow rate, qm = 8200 veh/hr as given
At maximum flow: dq/dk = uf(1-2km/kj) = 0
Since uf is not zero, 1-2km/kj = 0
Therefore km = kj/2
Similarly, um = uf/2
Therefore, um = 65/2 = 32.5 mph.
Therefore, maximum density, km = qm/um = 8200/32.5 = vehicles/mile
kj = 2*km = 2*(252.31) = veh/mile/lane
Using the speed-flow relationship:
q = kj(u – u2/uf)
Solve for q = 7034 = (u – u2/65)
13.94 = u – u2/65
= 65u – u2
u2 – 65u = 0
u = 44.7 or 20.2 mph
Choose 41.6 since this is the higher of the two and the observed flow is less than qm so we know we are not in the congested area of the curve

18. Traffic – Time of Day Patterns
Truck travel is driven by business needs. Passenger car travel is driven by personal needs. These are different. Thus, trucks often move at different times than cars.

19. From WSDOT 2003 Annual Traffic Report

20. From WSDOT 2003 Annual Traffic Report

21. Just north of the SR 520 interchange
This graph shows a good example of how HOV and GP volumes change over time on I-405 in the south end.
An interesting aspect of I-405 is that usage stays high throughout the day. At this location (near Kennydale), the two GP lanes stay fairly full throughout the day.

22. Effects of an incident around 2pm
This picture shows the impact of a rendering truck accident on I-5 in Seattle. You can see the traditional morning congestion, and the afternoon congestion caused by the accident. You can really see the loss of facility capacity (and thus throughput), and the duration of the slow speeds,long after the accident has been cleared. This type of picture is an excellent tool for describing to decision makers and the general public why incident response is needed, as well as serving as an excellent tool for examining the effectiveness of those measure you do implement.

23. In this case, we plotted two different lanes in order to show how HOV lanes work on weekends in Seattle. The number of legal “carpools” is high on weekends, but people don’t end to use those lanes unless the facility gets congested. This graphic illustrates how the GP lane and HOV lane volumes converge, once congestion occurs.

24. This graphic compares HOV and GP lane performance
This graphic compares HOV and GP lane performance. Only the GP lane is color coded and the congestion histogram applies only to the GP lane. At this location, we can see the effect persistent congestion has on GP volumes. It also shows very well, how GP congestion can help encourage HOV use.
This site also shows how HOV lane volumes can be reasonably high (if not equal to GP lane volumes) even during the middle of the day.

25. SR 520 Traffic Profile General Purpose Lanes 1997 Weekday Average West
Time PM AM 2 4 6 8 10 12
405 5
Montlake Blvd.
520
Arboretum
92nd
Ave.
B’vue. Way
148
th Ave.
NE 60th St.
84th Ave.
Lk. Wash.
Uncongested, near
speed limit
Restricted movement
but near speed limit
More heavily congested,
mph
Extremely congested,
unstable flow
West
bound
SR 520
Traffic Profile
General Purpose Lanes
1997 Weekday Average Ea st

26. Primary References
Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition. Chapter 5
Transportation Research Board. (2000). Highway Capacity Manual National Research Council, Washington, D.C.