CEE 320 Fall 2008 Course Logistics Course grading scheme correct Team assignments posted HW 1 posted Note-taker needed Website and Transportation wiki Traffic Concepts

CEE 320 Fall 2008 Have you ever driven out of a traffic jam only to find that nothing was apparently causing it? Why does stop and go traffic happen? Why does traffic slow down as it gets heavier? How do we predict congestion? Traffic questions

CEE 320 Fall 2008 Traffic Concepts CEE 320 Anne Goodchild

CEE 320 Fall 2008 Traffic – Time of Day Patterns

CEE 320 Fall 2008 How can we describe trafficHow can we describe traffic?

CEE 320 Fall 2008 How can we describe traffic? Consider one lane of traffic Traffic is constantly changing

CEE 320 Fall 2008 From WSDOT 2003 Annual Traffic Report

CEE 320 Fall 2008 From WSDOT 2003 Annual Traffic Report

CEE 320 Fall 2008 How would you model traffic flow? As a liquid? As a glacier? Discrete event simulation? …

CEE 320 Fall 2008 Concepts Flow Speed Density

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

CEE 320 Fall 2008 Flow Text also uses flow rate Flow is constantly varying! Analysis flow rate is peak 15-minute flow within the hour of interest.

CEE 320 Fall 2008 Spacing

CEE 320 Fall 2008 How much space do you leave between vehicles? 2 chevrons! Depends on speed Varies for each person

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

CEE 320 Fall 2008 Spacing Density –the number of vehicles over a length of freeway Occupancy –Measured by loop detectors –The percent of time the loop is covered by a vehicle

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

CEE 320 Fall 2008 Headway From HCM 2000

CEE 320 Fall 2008 How do we measure average speed? The average speed of vehicles that pass by a specific point in space over a specific time period (TMS). Time necessary for a vehicle to travel a length of roadway (SMS).

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

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

CEE 320 Fall 2008 Space Mean Speed It is the harmonic mean Used in traffic models, but harder to measure

CEE 320 Fall 2008 Example 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? What is your average speed over that distance?

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

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))/( ) = 48 mph

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 = hours Therefore, average speed over that distance 1 mile/ hours = mph

CEE 320 Fall 2008 Density (k - konzentration) 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).

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

CEE 320 Fall 2008 Density

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

CEE 320 Fall 2008 Complete the charts speed density flow density

CEE 320 Fall 2008 Complete the charts speed flow

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

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

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

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

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 is easy to measure Occupancy is measure of density Only need to measure 2 of 3

CEE 320 Fall 2008 Loop Detector Freeway Monitoring

CEE 320 Fall 2008 Loop Detector Signatures

CEE 320 Fall 2008 Inductance Loop Detectors Loop inductance decreases when a car is on top of it. T = t on T = t off Inductance Time t off t on 0

CEE 320 Fall 2008 Inductance Loop Detectors Single loops can measure: –Occupancy (O): % of time loop is occupied per interval –Volume (N): vehicles per interval Single loop measurements? Time Inductance High low TnTn T n+1 t n1 t n2 t n3

CEE 320 Fall 2008 How do you estimate speed from a single loop detector? You know how long it took the object to pass over the detector You know the percent of time (in a short interval) the loop was covered by a vehicle What else do you need to know?

CEE 320 Fall 2008 Can We Get Speed from a Single Loop? s=speed (ft/sec) EVL=effective vehicle length (ft) toto =occupancy time (s) EVL ~ vehicle length + detector length (24 feet)

CEE 320 Fall 2008 Estimating Speed from a Single Loop? Using typical traffic data s=speed (miles/hr) N=number of vehicles in the observation interval T=observation interval (s) O=percentage of time the loop is occupied by vehicles during the observation interval (occupancy) g=speed estimation parameter 100 converts percent to decimal

CEE 320 Fall 2008 What speed is this? TMS