1. CEE 320 Fall 2008 Course Logistics HW3 and HW4 returned Midterms returned Wednesday HW5 assigned today, due next Monday Project 1 due Friday

2. CEE 320 Fall 2008 Traffic Concepts CEE 320 Anne Goodchild

3. CEE 320 Fall 2008 2 nd Phase of Class Move from infrastructure or hard side of transportation to operations or soft side of transportation Consider models of the vehicles moving on the infrastructure and how to analyze or manage them –Traffic flow theory –Queueing theory

4. CEE 320 Fall 2008 Traffic – Time of Day Patterns

5. CEE 320 Fall 2008 From WSDOT 2003 Annual Traffic Report

6. CEE 320 Fall 2008 From WSDOT 2003 Annual Traffic Report

7. CEE 320 Fall 2008 Traffic Flow Theory 1.Basic Concepts a.Flow Rate b.Spacing c.Headway d.Speed e.Density 2.Relationships 3.Example

8. CEE 320 Fall 2008 Concepts Definitions Volume, Speed, Density relationships Speed –Space mean speed –Time mean speed Uninterupted flow

9. CEE 320 Fall 2008 Flow (q) The number of vehicles (n) passing some designated roadway point in a given time interval (t) Units typically vehicles/hour Volume typically refers to flow in an hour

10. CEE 320 Fall 2008 Flow Text also uses flow rate Flow varies over time Analysis flow rate is peak 15-minute flow within the hour of interest.

11. CEE 320 Fall 2008 Spacing

12. CEE 320 Fall 2008 Spacing The distance (ft) between successive vehicles in a traffic stream, as measured from front bumper to front bumper

13. CEE 320 Fall 2008 Headway (h) The time (in seconds) between successive vehicles, as their front bumpers pass a given point.

14. CEE 320 Fall 2008 Headway From HCM 2000

15. CEE 320 Fall 2008 Measuring Speed Time mean speed –Taken at a specific point –Average of instantaneous speeds Space mean speed –Harmonic speed –Look at a segment of roadway –Average speed of all vehicles in that segment

16. CEE 320 Fall 2008 Speed Time mean speed (spot speed) –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

17. CEE 320 Fall 2008 Time Mean Speed Arithmetic mean of speeds observed at some point Easy to measure

18. CEE 320 Fall 2008 Space Mean Speed It is the harmonic mean More intuitive as measure of traffic, but harder to measure

19. CEE 320 Fall 2008 Example time You are in a vehicle traveling a total of 10 miles. –the first 5 miles you travel at 40 mph –the next 5 miles you travel at exactly 60 mph What is your average speed over the time you spent traveling that 10 miles?

20. CEE 320 Fall 2008 Average speed over time and average speed over distance are different 10 miles 40 mph60 mph 7.5 minutes 5 minutes 12.5 minutes 7.5 minutes5 minutes

21. CEE 320 Fall 2008 Example time You are in a vehicle traveling a total of 10 miles. –the first 5 miles you travel at 40 mph –the next 5 miles you travel at exactly 60 mph What is your average speed over the time you spent traveling that 10 miles? 5 miles at 40 mph = 7.5 minutes 5 miles at 60 mph = 5 minutes weighted average = (40(7.5) + 60(5))/(7.5 + 5) = 48 mph

22. CEE 320 Fall 2008 Example - distance 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 = 0.0182 hours Therefore, average speed over that distance 1 mile/0.0182 hours = 55.05 mph

23. CEE 320 Fall 2008 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).

24. CEE 320 Fall 2008 Density (k) Number of vehicles in length of segment Inverse of average spacing

25. CEE 320 Fall 2008 Density

26. CEE 320 Fall 2008 Traffic Flow Theory A model for the relationship between flow, density, and speed Represents idealized behavior and fundamental relationships Useful for traffic analysis

27. CEE 320 Fall 2008 Additional definitions Free-flow speed (u f ) –The speed at which vehicles will travel unimpeded Jam density (k j ) –The density of vehicles in stopped traffic Capacity (q m ) –The maximum flow a section of roadway can maintain

28. CEE 320 Fall 2008 Speed-density relationship

29. CEE 320 Fall 2008 Speed vs. Density Density (veh/mile) Speed (mph) k j Jam Density u f Free Flow Speed

30. CEE 320 Fall 2008 Flow-density relationship

31. CEE 320 Fall 2008 Flow vs. Density Density (veh/mile) FLow (veh/hr) k j Jam Density Highest flow, capacity, q m k m Optimal density Uncongested Flow Congested Flow

32. CEE 320 Fall 2008 Speed-flow relationship

33. CEE 320 Fall 2008 Speed vs. Flow Flow (veh/hr) Speed (mph) u f Free Flow Speed Highest flow, capacity, q m Uncongested Flow Congested Flow umum q m is bottleneck discharge rate

34. CEE 320 Fall 2008 Measurement Density can easily be measured by remote sensing, but has historically been difficult to measure –Use occupancy obtained from loop-detectors TMS more easy to measure than SMS –Use correction or approximation –Easy to measure with remote sensing (GPS) Flow and headway are easy to measure Occupancy is measure of density Only need to measure 2 of 3