1. Macroscopic Density Characteristics
Chapter 7
Macroscopic Density Characteristics
거시적 밀도 특성

2. Introduction Use of Traffic Density Definition of Traffic Density
Primary measure of LOS for uninterrupted flow condition
System-wide traffic performance evaluation
On-line traffic responsive freeway control systems
Definition of Traffic Density
Number of vehicles occupying a length of roadway (length is usually 1 mile and single lane)
Range of Density Value
From 0 to values for bumper to bumper condition
Bumper to bumper cond.  jam density ( veh/mile; veh/km))
Relationship with average distance headway

3. Density scale subdivisions
1-42 veh/lane-mile
Demand < capacity
HCM LOS A,B,C,D
42-67 veh/lane-mile
Demand  Capacity
HCM LOS E
Optimum density (because system is most productive in terms of veh-miles of travel)
>67 veh/lane-mile
Demand > Capacity
HCM LOS F

4. Percent Occupancy
Percent of time a point or short section of roadway is occupied
Used as an indicator of density characteristics in freeway control systems (because of the ease of measurement)
Value ranges from 0 to 100%
Relationship with density

5. Summary %occupancy or density is an indication of LOS
Used as control variable in on-line RMS
Density analysis permits :
Shock wave analysis
Travel time estimation
Traffic demand estimation

6. 7.2 Density Measurement Techniques

7. Photographic Technique
Earliest and principal technique before 60’s
 Recently, automatically extract density from video images
Camera mounted on aircraft flying along the route
10-20% overlapping between photographs
10 mile length typically used as study scope
Manually count vehicles to determine density for each subsection

8. Input-Output Count Technique
Density
= (Initial count + input – output) / length
Detectors should be very accurate
Limited to very special situations
Initial count
Detector
Detector
Input
Output
Section length

9. Speed-Flow Calculation Technique
Density calculation by “q=ku” (k=q/u)
Requires measurement of count and speed through detectors
Problems
Time-mean speed used (not space mean speed)
Coverage of the calculated density is vague (density is a measure for spatial roadway length)

10. Occupancy Measurement Technique
Density calculation based on occupancy
Requires average vehicle length and detection zone length

12. 7.3 Density Contour Maps

13. Density Contour Map (Aerial Photo)
Free flow condition
Forward recovery shock wave
Frontal stationary
shock wave
Capacity increase
(lane addition + grade changes)
Recovery
Triangular Shape
(Traffic condition changes along the boundaries)  SHOCK WAVE
Congestion over 4.5 miles and 2.5 hours
 330 minute-miles of congestion
Congestion extending upstream
Backward forming shock wave
Congestion moving dowstream
(Trucks+Upgade)
Congestion
(on-ramp/upgrade)
Near-capacity condition
Near-capacity condition
Free flow condition

14. Contour Map by FTMS

15. Contour Map by Computer Simulation

16. Contour Map by Aerial Photography

17. 7.4 Introduction to Shock Waves

18. Shock Waves Definition
Boundary conditions in time-space domain that demark a discontinuity in flow-density conditions
For simplicity and clarity, only density contour of 60 veh/lane-mile will be considered

19. Example-Signalized Intersection
Demand = constant
Capacity varies over time
Discontinuity
Backward Recovery + Backward Forming

20. Example - Freeway Bottleneck
Demand varies over time
1.5  2.5  2.0  1.5 (lanes of capacity)
Capacity is fixed
= 2.0 lanes
Input=output
Backward forming
Forward Recovery

21. Generalized Illustration of Shock Waves
Forward forming
shock wave
Bottleneck occurred
Forward Recovery
Incident
Frontal stationary
shock wave
Incident removed
Frontal stationary
shock wave
Frontal Stationary
Frontal stationary
Backward Recovery
Trucks slowed down
at upgrade
Bottleneck re-established
Backward forming
shock wave
Backward recovery
(reduced demand between E and C)
Reduces velocity of
shock wave (9-11)
Congestion splits
(due to bottleneck at E)
Frontal stationary
shock wave
Frontal Stationary
Backward forming
shock wave
Forward Recovery
(Further reduction in demand)
Rear Stationary
(Demand decreases until input=output)
First congestion begins
Second congestion begins

22. Classification of Shock Waves
Backward forming
When congestion occurs
Excess demand storage area in t-s domain
Forward recovery
Demand decreasing below bottleneck capacity
Rear stationary
Demand = capacity flow rate at the rear edge of congestion
Backward recovery
Increased bottleneck capacity
Forward forming
“Moving” bottleneck(e.g. slow trucks)
Steeper slope
= fast forming
or recovery

23. Shock Wave Animation Backward Recovery + Backward Forming
Forward Recovery
Forward Forming

25. 7.5 Estimating Total Travel Time

26. Formulation Number of vehicles in the system at time interval t
Average number of vehicles in the system
Total travel time (TTT)
n = number of subsections in the system
Kit= density in subsection i at time t (veh/lane-mile)
Li = length of subsection i (miles)
Ni = number of lanes in subsection i
m = number of observations during the time period
vt= number of vehicles in the system at time t
T = time period of observation (hours)

27. Example
3:45-6:30
TTT=813.2 x 2.75 hrs= veh-hours

28. 7.6 Estimating Traffic Demand

29. Traffic Demand Rate Definition Demand vs. Capacity
Number of vehicles that currently wish to pass a point or short section in a given period of time
Expressed as a rate of flow in veh/hr
Demand vs. Capacity
If Demand < Capacity
Demand = measured flow rate
If Demand > Capacity
Demand ≠ measured flow rate
 Unknown !!

30. Importance of Estimating Demand
Quantifying the need for capacity improvements / demand controls
Measured flow rate at high density section upstream of the bottleneck, at the bottleneck, and downstream of the bottleneck do not represent demand
 Need to determine demand ;
To estimate how much increase in bottleneck capacity is needed
To assess how much traffic demand must be controlled

31. Example Demand flow rate Lane density Excess veh (15-min) Excess
만일, 용량초과현상이 (2-3)TP에서 90만큼 한번 일어났고 다음 TP에서 초과수요가 없다면 (3-4)TP의 VEXE 값은 90으로 유지되어야 하고, 90만큼 계속 초과라면 180이며, 이 예제와 같이 줄어든 값인 경우 수요가 용량을 초과하는 현상은 이미 없어졌으며 거기에다 감소까지 일어났다는 것을 의미
Demand
flow rate
Lane density
Excess veh
(15-min)
Excess
flow rate
Measured
flow rate

32. Flow Rates at Bottleneck
Actions
 6-7% improvement in bottleneck capacity
 Demand control (i.e., ramp control)