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Course Logistics

Explore traffic flow theory, queueing theory, speed-density relationships, and more in transportation logistics, focusing on the soft side of operations.

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Course Logistics

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  1. Course Logistics • HW3 and HW4 returned • Midterms returned Wednesday • HW5 assigned today, due next Monday • Project 1 due Friday

  2. Traffic Concepts CEE 320Anne Goodchild

  3. 2nd 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. Traffic – Time of Day Patterns

  5. From WSDOT 2003 Annual Traffic Report

  6. From WSDOT 2003 Annual Traffic Report

  7. Traffic Flow Theory • Basic Concepts • Flow Rate • Spacing • Headway • Speed • Density • Relationships • Example

  8. Concepts • Definitions • Volume, Speed, Density relationships • Speed • Space mean speed • Time mean speed • Uninterupted flow

  9. 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. Flow • Text also uses flow rate • Flow varies over time • Analysis flow rate is peak 15-minute flow within the hour of interest.

  11. Spacing

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

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

  14. Headway From HCM 2000

  15. 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. 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. Time Mean Speed • Arithmetic mean of speeds observed at some point • Easy to measure

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

  19. 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. Average speed over time and average speed over distance are different 10 miles 40 mph 60 mph 5 minutes 7.5 minutes 12.5 minutes 7.5 minutes 5 minutes

  21. 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. 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. 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). Density (k)

  24. Number of vehicles in length of segment Inverse of average spacing Density (k)

  25. Density

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

  27. Additional definitions • Free-flow speed (uf) • The speed at which vehicles will travel unimpeded • Jam density (kj) • The density of vehicles in stopped traffic • Capacity (qm) • The maximum flow a section of roadway can maintain

  28. Speed-density relationship

  29. Speed vs. Density ufFree Flow Speed Speed (mph) kjJam Density Density (veh/mile)

  30. Flow-density relationship

  31. Flow vs. Density Congested Flow Highest flow, capacity, qm FLow (veh/hr) kmOptimal density kjJam Density Uncongested Flow Density (veh/mile)

  32. Speed-flow relationship

  33. Speed vs. Flow ufFree Flow Speed Uncongested Flow um Speed (mph) Highest flow, capacity, qm Congested Flow Flow (veh/hr) qm is bottleneck discharge rate

  34. 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

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