1. Capacity, Level of Service, Intersection Design (1)
Lecture 8 (6/3/10)

2. Capacity, Level of Service, Intersection Design
Vehicular Stream Models (Textbook 3.2)
Stream Variables (Textbook 3.3) (1)
Vehicular Stream Equations and Diagrams (Textbook 3.4)
Highways: Uninterrupted Flow (Textbook 4.5) (2)
Highways: Interrupted Flow (Textbook 4.6) (3)
Capacity of Signalized Intersections (Textbook 4.7) (4)

3. Traffic stream
A given flow of traffic through streets, highways of defined characteristics will vary by both location, time, and vehicle mix.

4. Uninterrupted and interrupted Flows
Uninterrupted Flow
Freeways
Multilane Highways
Two-lane Highways
Interrupted Flow
Signalized Intersections
Unsignalized Intersections
Urban and Suburban Arterials
Roundabouts

5. Vehicular Stream Models
Vehicle
Following

6. Vehicular Stream Models
Notation:

7. Vehicular Stream Models

8. Stream Variables Volume (V), flow rate (q) and headway (h) Speed (u)
Density (k), Concentration and Spacing (s)

9. Volume, flow rate and headway
Volume - the total number of vehicles that pass over a given point and section of a lane or roadway during a given time interval
Flow Rate - the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given interval of less than 1 hour, usually 15 minutes
Headway - the time between successive vehicles as they pass a point on a lane or roadway, measured from the same point on each vehicle (e.g., front bumper, rear axle, tec.)

10. Volume, flow rate and headway
Daily volume – Planning purpose
Hourly volume – design and operational analysis purpose
Peak-hour volume - The single hour of the day that has the highest hourly volume. It is the traffic volume within this hour that is of greatest interest to traffic engineers in design or operational analysis.

11. Volume, flow rate and headway
Estimated directional peak hour volume
DDHV = AADT  K  D
DDHV-Directional Design Hour Volume (vph)
AADT - Average Annual Daily Traffic (vpd)
K - The proportion of daily traffic occurring during the peak-hour. (decimal)
D - The proportion of peak-hour traffic traveling in the peak direction (decimal)

12. Volume, flow rate and headway
Subhourly Volumes and Rates of Flow
A facility may have capacity adequate to serve the peak-our demand, but short-term peaks of flow within the peak hour may exceed capacity, thereby creating a breakdown.

13. Volume, flow rate and headway
Peak Hour Factor (PHF)
For analysis purposed, in Highway Capacity manual, 15 minute interview is used.
HV – Hourly Volume
V15 – Maximum 15 minute volume within the hour

14. Volume, flow rate and headway
Peak Hour Factor (PHF)
Example:
HV= 3000 vehicles
V15 = 1000 vehicles
PHF = 3000/(4*1000) = 0.75
NOTE:
 PHF  1.00, normal between 0.70 and 0.98
- Lower PHF indicates a greater degree of variation in flow during the peak-hour.

15. Volume, flow rate and headway
Relationship between headway (h) and flow (q):

16. Speed v - speed (mph or fps) d - distance traversed (mi or ft)
t - time to traverse distance d (hr or sec)

17. Speed Time mean speed and space mean speed:
Time Mean Speed (TMS) is defined as the average speed of all vehicles passing a point on a highway over some specified time period.
TMS =
Point A
(alternative way)

18. Speed Time mean speed and space mean speed:
Space Mean Speed (SMS) is defined as the average speed of all vehicles occupying a given section of a highway over some specified time period. D
SMS =
(alternative way)

19. Speed Relationship between TMS and SMS: (Proved by Wardrop in 1952)
Time Mean Speed (spot speed) is a point measure, while Space Mean Speed is a measure relating to a length of highway or lane.
(Proved by Wardrop in 1952)

20. Speed

21. Speed Average Travel Speed and Average Running Speed :
Travel time (tt) is defined as the total time to traverse a given highway segment.
Running time (tr) is defined as the total time during which the vehicle is in motion while traversing a given highway segment.
Average Travel Speed = D B
Average Running Speed =

22. Speed Operating Speed and Percentile Speed :
Operating Speed is defined as the maximum safe speed at which a vehicle can be conducted in a given traffic stream, without exceeding the design speed of the highway segment.
A Percentile Speed is a speed below which the stated percent of vehicles in the traffic stream travel.
The 85th percentile speed is often used as a measure of the maximum reasonable speed for the traffic stream.
The 15th percentile speed may be used as a measure of the minimum reasonable speed for the traffic stream.

23. Density, concentration & spacing
Density or concentration (k) is defined as the number of vehicles occupying a given length of highway or lane (vpm) or (vpmpl).
Spacing (s) is defined as the distance between successive vehicles in a traffic stream, measured from the same point on each vehicle (e.g., front bumper, rear axle, tec.)
Spacing
1 mile
*average spacing

24. Density, concentration & spacing
u - space mean speed (mph)
q - flow rate (vph)

25. Time-distance diagram of flow
Space t1
Spacing1 t2
Spacing2
Headway1
Headway2 x1 x2

26. Time-distance diagram: uniform flow

27. Vehicular Stream Equations and Diagrams
Fundamental equation of a vehicular stream
Case of uniform flow
Note:

28. Vehicular Stream Equations and Diagrams (highway flow)

32. Examples of realistic q-u-k relationship

33. Vehicular Stream Equations and Diagrams (highway flow)

34. Vehicular Stream Equations and Diagrams (highway flow)

35. Capacity, Level of Service, Intersection Design (2)
Lecture 9 (6/3/10)

36. Highways: Uninterrupted Flow
Background
Level of Service
Freeway Base Conditions
Freeway Capacity and Level of Service
Freeway Congestions Quantification
Capacity Restrictions

37. Background
Only for “Basic freeway segment”: outside the area of influence of:
Freeway weaving areas
Freeway ramp junctions
Level of service based on average passenger car speed vs flow rate curve (u-q) with thresholds defined by concentration (k) – range from LOS A (free flow) to LOS F (unstable flow)

38. Level of Service (LOS)
A – free flow; 480 ft min spacing (k<11 pc/mi/ln)
B – reasonably free flow; 290 ft min spacing (k<18 pc/mi/ln)
C – nearly free flow speed; maneuvers limited; reduced comfort; 200 ft min spacing (k<26 pc/mi/ln)
D – reduced speeds; limited freedom to maneuver; potential for queuing; 150 ft min spacing (k<35 pc/mi/ln)
E – at capacity; unstable flow; 120 ft min spacing (k<45 pc/mi/ln)
F – extensive queuing behind breakdown points

39. Speed-Flow Curve and LOS

40. Freeway base conditions
12-ft minimum lane width
6-ft minimum right side lateral clearance between the edge of the travel lane and the nearest object that influences driving behavior
2-ft minimum lateral clearance from left-side median
All passenger-car traffic composition
Five or more lanes per direction (urban freeways only)
Access spacing of 2 mi or greater
Level terrain (grades no greater than 2%)
Driver population consisting mostly of regular users of the facility (commuters)

41. Volume and flow rate
Volume - the total number of vehicles that pass over a given point and section of a lane or roadway during a given time interval
Flow Rate - the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given interval of less than 1 hour, usually 15 minutes

42. Peak Hour Factor

43. Peak Hour Factor
V = 250 veh/h

44. Peak Hour Factor
Criterion for LOS based on equivalent hourly flow rate for peak 15 minute period
Convert full hour demand volume by using peak hour factor (PHF):
v = V/PHF
v is equivalent hourly flow rate for peak 15 minutes
V = full-hour volume (vph)
Peak Hour Factor (PHF):
PHF = V
(4 * peak 15 minute volume)

45. Example of a PHF question
Period
Volume (vph)
7:00 - 7:15
100
7:15 - 7:30
120
7:30 - 7:45
130
7:45 - 8:00
125
8:00 - 8:15
135
8:15 - 8:30
140
8:30 - 8: 45
8:45 - 9:00
115
When is the peak hour?
What is the peak hour volume?
What is the PHF?

46. Solution of the PHF question
Period
Volume
(vph)
Accumulated Volume
7:00 - 7:15
100
7:15 - 7:30
120
7:30 - 7:45
130
7:45 - 8:00
125
475
8:00 - 8:15
140
515
8:15 - 8:30
135
530
Largest
8:30 - 8: 45
525
8:45 - 9:00
115
The peak hour is from 7:30 AM to 8:30 AM
The peak hour volume is 530 vph
The PHF = 530 / (4*140) = 0.946

47. Freeway capacity and level of service (LOS)

48. Speed-Flow curve for basic freeway segment (HCM)

49. Freeway capacity and level of service (LOS)

50. Freeway capacity and level of service (LOS)
Important Concept:
Compute Vp and S in order to Compute D.
Use “density thresholds” to determine LOS

51. Freeway capacity and level of service (LOS)

52. Freeway capacity and level of service (LOS)

53. Freeway capacity and level of service (LOS)

54. Freeway capacity and level of service (LOS)

55. Freeway capacity and level of service (LOS)

56. Example 4.5: LOS Estimation
An extended urban freeway segment with largely level terrain has three 11 ft wide lanes per direction, a 3-ft lateral clearance, and about one interchange per mile. It has an observed volume of 3080 veh/h with corresponding PHF=0.88 and 154 trucks and buses, and no recreational vehicles. An all-commuter motorist composition may be assumed. Estimate the LOS for this set of conditions.

57. Solution of Example 4.5

58. Freeway congestion quantification
In addition to LOS, there are other measures:
Travel rate
Delay
Relative delay
Total delay
Corridor mobility index
Accessibility

59. Capacity restrictions
Freeway capacity can be reduced due to:
Accidents
Spilled loads
Disabled and slow-moving vehicles, and
Other extraordinary events