1. Mr. Vedprakash Maralapalle, Asst. Professor
Traffic Flow
Mr. Vedprakash Maralapalle, Asst. Professor
Department: B.E. Civil Engineering
Subject: Transportation Engineering
Semester: VI
Teaching Aids Service by KRRC Information Section

2. Traffic stream parameters
Speed
Spot speed
Running speed
Journey speed
Time mean and space mean speed
Flow volume
The peak hour observed during mornings and evenings of weekdays, which is usually 8 to 10 per cent of total daily flow or 2 to 3 times the average hourly volume.

3. Types of volume measurement
Average Annual Daily Traffic(AADT)
Average Annual Weekday Traffic(AAWT)
Average Daily Traffic(ADT)
Average Weekday Traffic(AWT)

4. Density Derived characteristics
Number of vehicles occupying a given length of highway or lane and is generally expressed as vehicles per km.
Derived characteristics
Time headway
The microscopic character related to volume is the time headway or simply headway. Time headway is defined as the time difference between any two successive vehicles when they cross a given point
Space headway
The distance between corresponding points of two successive vehicles at any given time.
Time-Space Diagram

5. Fundamental relations
Time mean speed
Space mean speed

6. Relation between T.M.S & S.M.S
Where σ2 is the standard deviation of the spot speed. The standard deviation can be computed in the following equation:

7. Fundamental relations of traffic flow
Let there be a road with length v km, and assume all the vehicles are moving with v km/hr.
Let the number of vehicles counted by an observer at A for one hour be n1. By definition, the number of vehicles counted in one hour is flow(q). Therefore,
n1 = q
Similarly, by definition, density is the number of vehicles in unit distance. Therefore number of vehicles n2 in a road stretch of distance v1 will be density × distance. Therefore,
n2 = k × v

8. Since all the vehicles have speed v, the number of vehicles counted in 1 hour and the number
of vehicles in the stretch of distance v will also be same.(i.e n1 = n2). Therefore,
q = kv
Flow = density * speed
Flow – Density Curve:

9. Speed- Density Speed - Flow

10. Traffic Stream Model

11. Greenshield’s macroscopic stream model
Macroscopic stream models represent how the behavior of one parameter of traffic flow changes with respect to another.
Greenshieldassumed a linear speed-density relationship to derive the model.
v = vf - 𝐯 𝐟 𝐤 𝐣 ∗𝐤
q = vf* k - 𝐯 𝐟 𝐤 𝐣 ∗𝐤2

12. Greenberg’s logarithmic model
v = v0ln k j k
Main drawbacks of this model is that as density tends to zero, speed tends to infinity. This shows the inability of the model to predict the speeds at lower densities.

13. Underwood’s Exponential model
vfThe mo
vf is the free flow speed and k0 is the optimum density, i.e. the density corresponding to the maximum flow.

14. Multi-regime model Shock waves Based on human behavior
Different model for congested and uncongested corridor.
Shock waves
Consider a stream of traffic flowing with steady state conditions, i.e., all the vehicles in the stream are moving with a constant speed, density and flow (state A).
Suddenly due to some obstructions in the stream (like an accident or traffic block) the steady state characteristics changes and they acquire another state of flow, say state B.
The speed, density and flow of state A is denoted as vA , kA , and qA , and state B as vB , kB , and qB respectively.

16. Traffic volume study Objectives of Study Vehicle Composition
Traffic Stream Properties
Average Daily Traffic
Directional Distribution
Flow Fluctuation

17. Spot speed study
When we measure the traffic parameter over a short distance, we generally measure the spot speed.
A spot speed is made by measuring the individual speeds of a sample of the vehicle passing a given spot on a street or highway.
Spot speed studies are used to determine the speed distribution of a traffic stream at a specific location

18. Methods of Measurement
Methods of conducting spot speed Studies are divided into two main categories: Manual and Automatic.
Spot speeds may be estimated by manually measuring the time it takes a vehicle to travel between two defined points on the roadway a known distance apart (short distance), usually less than 90m.

19. Origin-Destination Study
Road side interview method
License plate method
Return postcard method
Tag on car method
Home interview method

20. Basic traffic manoeuvers
Diverging
Merging
Crossing
Weaving
Headway
Time headway
Space headway

21. Traffic capacity study
Basic capacity (ideal condition)
Possible capacity (prevailing condition)
Practical capacity (less traffic density)
Theoretical or basic capacity = 1000v s
S = average c/c spacing
V = speed of vehicle

22. V/c ratio Passenger car unit Factors affecting PCU
Min. space headway = min. space gap + L
L = average length of vehicle
V/c ratio
Passenger car unit
Factors affecting PCU

23. Traffic sign Road markings Regulatory Warning Informative longitudinal
Transverse
Object marking
Word messages

24. Signalized intersection
Design Principles of Traffic Signal
Cycle
Cycle Length
Interval
Change interval
Clearance interval
Green interval
Red interval
Phase
Lost time

25. Phase design
Guided by the geometry of the intersection, the flow pattern especially the turning movements, and the relative magnitudes of flow.
Two phase signal four phase signal

26. Cycle time The time interval between two vehicles, referred as headway
First headway is the time interval between the initiation of the green signal and the instant vehicle crossing the curb line.
Second headway will be comparatively lower because the second driver can overlap his/her reaction time with that of the first driver’s. After few vehicles, the headway will become constant.
This constant headway which characterizes all headways beginning with the fourth or fifth vehicle, is defined as the saturation headway, and is denoted as h.

27. Conflicts at an intersection
The number of conflicts for competing through movements are 4, while competing right turn and through movements are 8.

28. Levels of control Passive Semi control Active control No control
Traffic signs
Traffic signs plus marking
Semi control
Channelization
Traffic rotaries
Active control
Traffic signals
Grade separated intersections

29. Grade separated intersections
Trumpet interchange
Diamond interchange
Cloverleaf interchange

30. Channelization

31. Traffic rotaries Key advantages of a rotary intersection
Traffic flow is regulated to only one direction of movement, thus eliminating severe conflicts between crossing movements.
All the vehicles entering the rotary are gently forced to reduce the speed and continue to move at slower speed.
Rotaries are self governing and do not need practically any control by police or traffic signals.
They are ideally suited for moderate traffic, especially with irregular geometry, or intersections with more than three or four approaches.

32. Limitations for rotaries
All the vehicles are forced to slow down and negotiate the intersection. Cumulative delay will be much higher than channelized intersection.
Even when there is relatively low traffic, the vehicles are forced to reduce their speed.
Rotaries require large area of relatively at land making them costly at urban areas.
Not suitable when there is high pedestrian movements.

33. Guidelines for the selection of rotaries
Rotaries are suitable when the traffic entering from all the four approaches are relatively equal.
A total volume of about 3000 vehicles per hour can be considered as the upper limiting case and a volume of 500 vehicles per hour is the lower limit.
A rotary is very beneficial when the proportion of the right-turn traffic is very high; typically if it is more than 30 percent.
Rotaries are suitable when there are more than four approaches or if there is no separate lanes available for right-turn traffic. Rotaries are ideally suited if the intersection geometry is complex.

34. Design of a rotary

35. Design elements Design speed Entry, exit and island radius
Radius at the entry depends on various factors like design speed, super-elevation, and coefficient of friction.
The entry radius of about 20 and 25 metres is ideal for an urban and rural design respectively.
Exit radius as 1.5 to 2 times the entry radius
Width of rotary
Governed by the traffic entering and leaving the intersection and the width of the approaching road

36. Weaving width = e 1 + e m
e1is the width of the carriageway at the entry
e2is the carriageway width at exit
Based on many factors such as weaving width, proportion of weaving traffic to the non-weaving traffic
Achieved by making the ratio of weaving length to the weaving width very high. A ratio of 4 is the minimum value suggested by IRC

37. Capacity of rotary
The capacity of rotary is determined by the capacity of each weaving section.
TRL formula, Qw= 280∗𝑤∗ 1+ 𝑒 𝑤 ∗(1 − 𝑝 3 ) 1+ 𝑤 𝑙
Where e is the average entry and exit width, i.e. 𝑒 1 + 𝑒 2 2 ,
w is the weaving width
l is the length of weaving
p is the proportion of weaving traffic to the non-weaving traffic

38. a and d are the non-weaving traffic and b and c are the weaving traffic. Therefore,
P = 𝑏+𝑐 𝑎+𝑏+𝑐+𝑑
Capacity formula is valid only if the following conditions are satisfied:
Weaving width at the rotary is in between 6 and 18 metres.
The ratio of average width of the carriage way at entry and exit to the weaving width is in the range of 0.4 to 1.
The ratio of weaving width to weaving length of the roundabout is in between and 0.4.
The proportion of weaving traffic to non-weaving traffic in the rotary is in the range of 0.4 and 1.
The weaving length available at the intersection is in between 18 and 90 m.

39. Problem
The width of a carriage way approaching an intersection is given as 15 m. The entry and exit width at the rotary is 10 m. The traffic approaching the intersection from the four sides. Find the capacity of the rotary using the given data.

40. Solution Weaving width = 𝑒1+𝑒2 2 +3.5=13.5𝑚
Weaving length, l = 4*w = 54m
Find out proportion of weaving traffic in all approaches
Find out the highest proportion of weaving traffic
Calculate capacity based on that proportion

41. Saturation flow S = 3600 h Startup lost time l1 = 𝑖=1 𝑛 𝑒 𝑖 The green time required to clear N vehicles, Tg = l1 + h*N Effective green time: gi= Gi+ Yi− tl Lane capacity: ci = Si * (g/C) Problem: Let the cycle time of an intersection is 60 seconds, the green time for a phase is 27 seconds and the corresponding yellow time is 4 seconds. If the saturation headway is 2.4 seconds per vehicle, the start-up lost time is 2 seconds per phase, and the clearance lost time is 1 second per phase, find the capacity of the movement per lane?

42. Solution Total lost time, tl= 2+1 = 3 seconds
Effective green time = – 3 = 28sec
Sat. flow rate = ℎ = = 1500 veh/hr
Capacity = 1500* 𝑔 𝑐 = 1500* = 700 veh/hr/lane
Concept of Critical lane

43. Determination of cycle length:
L = Ntl (total lost time in n phase)
If C is the cycle length in seconds,
number of cycles per hour = c
Total lost time in 1hour = ∗𝑛 t l C
Effective green time Tg= ∗𝑛 t l C
= 3600*(1 - N t l C )
Vc = 𝑇 𝑔 ℎ = 3600∗(1 − n t l c ) ℎ = Si *(1 - N𝑛 C )
C = 𝐍 𝐭 𝐥 𝟏 − 𝐯 𝐜 𝐒 = 𝒏 𝐭 𝐥 𝟏 − 𝐯 𝐜 𝐒 𝐢 ∗𝐏𝐇𝐅∗ 𝑿 𝒄
As per HCM, C = 𝒏𝑳 𝑿 𝒄 𝐗 𝐜 − v i s i

44. Problem
The traffic flow in an intersection is shown in the figure. Given start-up lost time is 3 seconds, saturation head way is 2.3 seconds, compute the cycle length for that intersection. Assume a two-phase signal

45. Performance evaluation of signal
Green splitting =
tg = C – ntl
If lost time is different in diff. phases,
tg = C - i=1 n t li
Actual green time Gi= gi - yi+ t li
Problem:
The phase diagram with flow values of an intersection with two phases is shown in figure. The lost time and yellow time for the first phase is 2.5 and 3 seconds respectively. For the second phase the lost time and yellow time are 3.5 and 4 seconds respectively. If the cycle time is 120 seconds, and the green time allocated for the two phases.

46. Pedestrian crossing requirements
By suitable phase design or by providing an exclusive pedestrian phase.
Green time for pedestrian crossing Gpcan be found out by,
Gp= 𝑡 𝑠 + 𝑑𝑥 𝑢𝑝
Gpis the minimum safe time required for the pedestrians to cross
tsis the start-up lost time
dx is the crossing distance in metres
upis the walking speed of pedestrians which is about 15th percentile speed.
The start-up lost time ts can be assumed as 4.7 seconds and the walking speed can be assumed to be 1.2 m/s.

47. Performance measures Evaluate the effectiveness of the design
Many parameters involved to evaluate the effectiveness of the design and most common of these include delay, queuing, and stops.

49. Types of delay Stopped delay Approach delay Control delay Problem
The traffic flow for a four-legged intersection is shown in figure. Given that the lost time per phase is 2.4 sec, saturation headway is 2.2 sec, amber time is 3 sec per phase, and the cycle length, green time and performance measure(delay per cycle). Assume critical v/c ratio as 0.9.

50. Solution:
Find out sum of critical lane volume
Saturation flow rate s
Then, 𝑣 𝑐𝑖 𝑠 𝑖
Cycle length = 𝒏𝑳 𝑿 𝒄 𝐗 𝐜 − v c 𝑠 = 80.68s

51. Effective green time gi = C – ntl = 80 – 4*2.4 = 70.4s
Green splitting for phase 1,2,3,4 = gi * Xci
Actual green time 1,2,3,4 = ( gi* Xci ) – amber + lost time
Pedestrian time = lost time + 𝑑𝑠 𝑢 𝑝 = ∗
actual cycle time, phase i = actual green +amber+red
Find delay in each movement