1. Asst. Prof. Dr. Mongkut Piantanakulchai
CES 341:Transportation Engineering and Planning Chapter 8 Traffic Analysis Techniques
Asst. Prof. Dr. Mongkut Piantanakulchai

2. 8.1 Space-Time Relationships
Figure 8.1 Space-time diagram
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

3. 8.1 Space-Time Relationships
Note: Assume vehicle’s length is negligible
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

4. 8. 1. 1 Direct Graphical Solution Fig. 8
8.1.1 Direct Graphical Solution Fig. 8.2 Location and size of double-track sections
Transit system
Single track 15 km long
Train 10 min interval dispatched from each end (W-E)
5 min layovers
Neglect stop time at stations
Uniform speed 45 km/h both directions
Determine number and location of double-track sections, and the minimum length required for such sections in order for trains running as much as 2 min behind schedule to pass one another without delay
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

5. 8.1.1 Direct Graphical Solution Fig. 8.3 Train dispatch problem
Rail line 90 km long
7.5 km long double-track section located between km from W end
A train leaves W end at 1:00 p.m. and travel E at constant speed of 45 km/h
The second train leaves from the E end at 1:30 p.m. and may travel at any speed up to 90 km/h
1) Determine earliest time the W-bound train can arrive at the W end of the line
2) Determine the latest dispatch time (after 1:00 p.m.) that will allow the W-bound train to reach its destination without unnecessary delay
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

6. 8.1.2 Development of Analytical Solutions
Complicated space-time problems
Space-time diagrams are used to derive analytical solutions
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

7. Example: Runway Capacity Analysis
Fig. 8.5 Time separation at runway threshold, vi ≥ vj
Fig. 8.4 Time separation at runway threshold, vi ≤ vj
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

8. Example: Runway Capacity Analysis
Capacity is expressed by
Weighted average of interarrival time
(10.1)
(10.2)
where pij = probability of arrival pair i-j
If arrivals are independent
(10.3)
Note: Assume arrivals only, no departures
More details in CES 446 Port and Airport Engineering
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

9. 8.1.3 Development of Simulation Models
More complicated problems
Space-time diagrams are used to develop simulation models
Behavior of system in a step-by-step manner
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

10. Example: Block Signal Control System for Rail Line
Objective: To protect train collisions and other hazards such as broken rails
System consists of
Electronically insulated section of tracks = blocks
Train detection system: to determine if a train is in a particular block (the block is occupied)
Signal system (warn or control)
System of blocks and aspects (combination of signal lights)
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

11. Example: Block Signal Control System for Rail Line
Fig. 8.6 Block signal control systems
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

12. Example: Block Signal Control System
0.75 km long blocks
Three-block, four aspect system
RR –stop and proceed at 7.5 km/h prepared to stop
RY – proceed at 30 km/h, prepare to stop at next signal
GY – proceed at 60 km/h
GG – proceed at full speed
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

13. Example: Block Signal Control System
A train traveling at 45 km/h, passes a point A, which is located at a block boundary, at 11:00 a.m.
Five min and 30 s later, a second train passes this point traveling at 90 km/h in the same direction
Both trains are km long
Describe the motion of the second train, determine the time that the rear of second train passes point B, located km beyond point A
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

14. Time-space diagram of the first train
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

15. Signal indication after the first train
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

16. Trajectory of the second train according to block signals
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

17. Trajectory of the second train (front) according to block signals
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

18. Trajectory of the second train (front&rear) according to block signals
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

19. 8.14 Non-trajectory Space-Time Diagrams
Display information about traffic states (speed, flow rate, density) as well as vehicle trajectories
Contour diagram can be used to display region with similar traffic state values
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

20. 8.14 Non-trajectory Space-Time Diagrams
Figure 8.11 Speed contours
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

21. 8.2 Queuing Analysis Figure 8.12 Queuing System
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

22. 8.2.1 Queuing Theory Fundamentals
Figure 8.13 Arrival function for airport runway
Figure 8.14 Arrival and departure functions for airport runway
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

23. 8.2.1 Queuing Theory Fundamentals
Figure 8.14 Queuing diagram, smooth curve approximation
Figure 8.14 Queuing diagram features
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

24. 8.2.2 Queue Discipline First-in, first-out (FIFO)
Last-in, first-out (LIFO)
Random service
Priority service
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

25. Relationship of Delay (w(t)) and Queue Length (Q(t)) of Individual at Time t
W(t) = Waiting time (Delay) of an individual at time t
Q(t) = Queue length at time t
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

26. 8.2.3 Stochastic Queuing Models
Deterministic queuing models – arrival and service rate are deterministic (known as some function)
Stochastic queuing models
constant long term arrival and service rates
short-term random fluctuations around the average rates
arrival rate may exceed service rate for short time intervals and queues will form
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

27. Stochastic Queuing Models
M/D/1
M/M/1
One Channel
Arrivals
Exponentially
Distributed
Service
Deterministic
(No random variation)
Inter-arrival times follow
Negative Exponential Distribution
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

28. M/D/1 CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

29. M/M/1 CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

30. General relationships
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

31. 8.2.4 Transportation Applications of Queuing Theory
Server opens after arrivals begin
Arrival rate temporary exceeds
constant service rate
Service rate varies
Server temporarily shut down
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

32. 8.2.5 Queue Density, Storage, and Spillback
Density (vehicles per unit distance)
Occupancy – fraction of time vehicles are over the detector
Objectives of studying queue density
Locating queues and bottlenecks in traffic
Determine the length of the queue and space needed for queue storage, control the queue spillback to upstream section
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

33. Example Problem 8.1
Morning peak traffic upstream of a toll booth is given in the table
The toll plaza consists of three booths, each of which can handle an average of one vehicle every 6 s.
Using queuing diagram, determine the maximum queue, the longest delay to an individual vehicle, and the total delay
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

34. Example Problem 8.1 7:00-7:10 200 7:10-7:20 400 600 7:20-7:30 500 1100
Time period
10 min volume
Cumulative volume
7:00-7:10
200
7:10-7:20
400
600
7:20-7:30
500
1100
7:30-7:40
250
1350
7:40-7:50
1550
7:50-8:00
150
1700
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

35. 8-21 Cumulative volume, A(t) 300 veh/min, D(t)
D(t)>A(t) {Show A(t), No queues}
8-21
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

36. 8.3 Network Analysis Network Link characteristics
Nodes : Usually points of facilities intersect
Origins or destinations of trips (source or sink nodes)
Decision points
Links : Usually road or railway segments
Link characteristics
Link costs: Distance, travel time, generalized costs (weighted sum of several costs)
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

37. Network Elements 8-23 CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

38. Minimum path algorithm, step 1
Example network
Minimum path algorithm, step 1
8-25
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

39. Minimum path algorithm, step 2
8-26
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

40. Minimum path algorithm, step 3
8-27
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

41. Minimum path algorithm, step 4
8-28
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

42. Minimum path algorithm, step 5
8-29
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

43. Minimum path algorithm, step 6
8-30
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

44. Table 8.1 Link-cost array Node 1 2 3 4 5 6 -1 8 10
CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

45. 8-31 CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

46. 8-32 CES 341 Transportation Engineering and Planning
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CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

47. 8-33 CES 341 Transportation Engineering and Planning
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques

48. 8-34 CES 341 Transportation Engineering and Planning
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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CES 341 Transportation Engineering and Planning
Chapter8: Traffic Analysis Techniques