Problems Lecture Notes in Transportation Systems Engineering Prof. Tom V. Mathew∗
Contents 1 Transportation systems analysis
3
2 Fundamental Parameters of Traffic Flow
3
3 Fundamental Relations of Traffic Flow
3
4 Traffic Stream Models
5
5 Moving Observer Method
7
6 Measurement at a Point
9
7 Measurement over a Short Section
10
8 Measurement Along a Length of Road
10
9 Automated Traffic Measurement
11
10 Intrusive Technologies
11
11 Non-Intrusive Technologies
11
12 Travel Time Data Collection
11
13 Vehicle Arrival Models: Headway
11
14 Vehicle Arrival Models: Count
14
15 Car Following Models
15
16 Lane Changing Models
17
17 Microscopic Traffic Simulation
18
18 Traffic Flow Modeling Analogies
18
19 Cell Transmission Models
18
∗
IIT Bombay (
[email protected]) March 8, 2017
1
20 Traffic Progression Models
18
21 Discrete Simulation Models
19
22 Capacity and Level of Service LOS
19
23 Urban Streets
19
24 Multilane Highways
19
25 Freeway Operations
19
26 Ramp Metering
20
27 Corridor Analysis
20
28 Principles of Traffic Control
20
29 Traffic Signs
20
30 Road Markings
20
31 Uncontrolled Intersection
21
32 Channelization
22
33 Traffic Rotary
22
34 Grade Separated Intersection
24
35 Design Principles of Traffic Signal
24
36 Signalized Intersection Delay Models
24
37 Special Requirement in Traffic Signal
27
38 Capacity and Los Analysis of a Signalized I/S
29
39 Coordinated Traffic Signal
32
40 Vehicle Actuated Signals
33
41 Area Traffic Control
33
42 Parking Studies
33
43 Accident Studies
34
44 Fuel Consumption and Emission Studies
34
45 Congestion Studies
35
46 Queuing Analysis
35
47 Toll Operation
35 2
48 Pedestrian Studies
35
49 Intelligent Transportation System - I
36
50 Intelligent Transportation System - II
36
51 Advanced ITS
36
52 General
36
1
Transportation systems analysis 1. [101-01] Select a current transportation issue for modeling and do the following. (i) Identify the transportation system components, (ii) Activity system that is interest to the transportaion issue, (iii) What could be a suitable service function, (iv) What could be a suitable demand function, (v) Visualize how the activity system may change, (vi) Propose some transport improvement options, (vii) Illustrate flow predictions.
2
Fundamental Parameters of Traffic Flow 1. [51111] An observer standing beside a road starts counting vehicle passing him from 4pm to 4:20pm and he counts about 580 vehicles. What is the average time headway. 2. [51112] An aerial photograph of a stretch of a road of about 200 meter shows the presence of 40 vehicles. What is the average spacing. 3. [51113] If an observer standing beside a road noted that the vehicles are passing him every 3 seconds. If so what is the flowrate.
3
Fundamental Relations of Traffic Flow 1. [51201] Derive the relationship between fundamental parameters of traffic with a detailed illustration of fundamental diagrams of traffic flow. 2. [51202] Derive the relationship between the time mean speed and space mean speed. Verify the above relation using some hypothetical speed data expressed in a frequency table. 3. [51203] Verify the relationship between the time mean speed and space mean speed using some hypothetical speed data generated by you (about 20-30 spot speeds) and represented in a frequency table. 3
4. [51211] Calculate the time mean speed and the space mean speed of the following observation. Speed Range
Volume
(m/sec)
(veh/hr)
10-12
12
12-14
18
14-16
24
16-18
20
18-20
14
5. [51212] Determine the time mean speed and space mean speed from the following data. Verify the relationship between them. Speed m/s
Frequency
1-5
2
6-10
5
11-15
7
16-20
9
6. [51213] The following travel times in seconds were measured for vehicles as they traversed a 3 km segmeny of a highway. " V ehicle 1 2
3
4
5
6
T ravel time 150 144 160 125 135 115
#
Compute the time mean speed and space mean speed for this data. Why space mean speed is always lower than time mean speed, explain with a derivation. 7. [51221] Calculate the time mean speed and the space mean speed of the following spot speed data: Speed Range
Volume
(m/sec)
(veh/hr)
10-12
12
12-14
18
14-16
24
16-18
20
18-20
14
4
8. [51222] For the data given below,compute the time mean speed and space mean speed. Also verify the relationship between them. Finally compute the density of the stream.
4
speed range
frequency
1-4
2.5
5-8
6.5
9-12
10.5
13-16
14.5
17-20
18.5
Traffic Stream Models 1. [51301] Illustrate neatly on a single graph the speed-density relation by Greenberg, Greenshield, Underwood, Pipe(n=0.5,2), two regime, and three regime models, along with typical field observations 2. [51302] Explain with neat sketch the need and examples of multi-regime stream models. 3. [51303] Sketch the three fundamental diagrams of traffic flow. Derive the relation between maximum flow (qmax ), jam density (kj ), and free flow speed (uf ). Assume k liner speed flow relation: u = uf 1 − kj .
4. [51304] Plot typical speed-density field data points. Draw the shapes of various traffic stream models (5-7) including multi-regime models. Write the equations of these models as well. 5. [51311] In a traffic study, the observed densities were 150, 120, 50, 70 and 20 veh/km and the corresponding speeds were 10, 25, 45, 40 and 32km/h. Find the jam density according to Greenberg’s logarithmic traffic stream model. (Hint: Linearize the expression) 6. [51312] For the following data on speed and concentration, determine the parameters of Greenshields’ model. Find the concentration corresponding to a speed of 40 kmph. Find also the maximum flow.
5
Concentration(veh/km)
Speed(kmph)
180
4
140
20
30
50
75
35
7. [51313] A study of flow at a particular location resulted in a calibrated speed-density relationship as follows. v = 52.5 (1 − 0.35 k). For this relationship, determine free flow speed, jam density, maximum flow, and the relationship between fundamental parameters of traffic. (Illustrate with a sketch) 8. [51314] If the mean speeds in kmph observed from a road stretch at various time is given as: 10, 25, 45, 40, and 50, and the corresponding densities in veh/km are: 150, 120, 50, 70, and 20. What would be the maximum flow on this road stretch. 9. [51322] Determine the parameters of Greenshields model for the following data. Find the maximum flow and density for a speed of 45 kmph. Speed (kmph)
Density (veh/km)
5
150
20
120
30
100
40
70
10. [51323] A study of flow at a particular location resulted in a calibrated speed-density relationship as follows.
v = 47.5(1 − 0.32k) For this relationship, determine free flow speed, jam density, maximum flow, speed-flow relationship, and flow-density relationship. (Illustrate with a sketch) 11. [51332] In a traffic study experiment, density values are obtained as 160, 120, 40, and 72 veh/km corresponding to speed values of 3, 18, 55, 32 respectively. Determine the parameters of Greenshields’ model. Find the density corresponding to a speed of 40 kmph. Find also the maximum flow. 12. [51342] The following speed and density is observed from a road section. If we assume the speed decreases linearly with respect to density, then: (a) what will be the density at a speed of 10 kmph, and (b) what will be the maximum flow across the section 6
Speed (kmph)
Density (veh/km)
5
120
20
90
30
40
40
10
13. [51352] The speed and density observed from a road is given below. What is the density and flow corresponding to a speed of 25 kmph. State the assumptions/model used in the computation.
5
Speed (kmph)
Density (veh/km)
10
200
20
170
30
120
40
100
Moving Observer Method 1. [51401] Derive the equation for flow (q) from the moving observer method. 2. [51402] (a) Derive the expression for flow across a section of road by moving car method. (b) Prove that this formulae actually estimates the stream flow. 3. [51403] Derive expression for the fundamental parameters of traffic flow by moving observer method
(10)
4. [51411] In a traffic stream, 30% of the vehicles travel at a constant speed of 60km/h, 30% at a constant speed of 80km/h, and the remaining vehicles at a constant speed of 100km/h. An observer travelling at a constant speed of 70km/h with the stream over a length of 5km is overtaken by 17 vehicles more than what he has overtaken. The observer met 303 vehicles while traveling against the stream at the same speed and over the same length of highway. What is the mean speed and flow of the traffic stream? 5. [51412] Two friends were traveling from Mumbai to Pune and have decided to count the vehicles on a short stretch of 5 km. The first one sat on the left side and counted vehicles passed by him. The second sat on the right side and counted vehicles overtaken him. They counted 20 and 60 respectively while traveling at 30 kmph. They did the same exercise on the next day about same time and counted 25 and 40 respectively and were traveling at 35 kmph. Assuming same traffic conditions on both days, compute the density, mean speed, and flow on that stretch. 7
Solution:
From the moving observer method, m = m0 − mp = qt − kvo t.
(1) (2)
where mo is number of vehicles overtaken the test vehicle, and mp is number of vehicles passed by the test vehicle. In the first trial, m = 60-20= 40, and time taken by test vehicle to complete the stretch t1 =
5 30
= 0.1666. Therefore 40 = 0.1666(q−
30k) In the second trial, m = 40-25= 15, and time taken by test vehicle to complete the stretch t2 =
5 35
= 0.1428.
Therefore 15 = 0.1428(q − 35k) Solving the two equations for q and k, k = 27veh/km and q = 1050veh/hr. vo = 38.89m/s. Alternatively mean speed can be obtained from , vo =
l tw − mqw
=
5 40 0.1667− 1050
= 38.88m/s.
6. [51413] The observations from a moving car method are given below. Assuming linear speed-density relation, what is the maximum flow, speed, and density the following following stretch can take. Show the details of the calculation OvertakenOvertakingMoving Travel Travel by
the
test
the test
against time
time
vehicle
traf-
with
against
fic
the
the
vehicle
stream traf-
traf-
fic
fic
(s)
(s)
5
119
618
422
268
26
12
389
213
188
24
9
401
226
396
2
55
410
274
255
26
9
374
226
396 8
7. [51414] A moving vehicle experiment was conducted on a 2.5 km section of a highway. Two trials were conducted in the direction of dominant traffic flow. In the first trial, number of vehicles that had overtaken the test vehicle is 30, number of vehicles overtaken by the test vehicle is 6, and test vehicle speed is 30 kmph. In the second trial, number of vehicles that had overtaken the test vehicle is 20, number of vehicles overtaken by the test vehicle 26, and test vehicle speed is 35 kmph. Calculate the fundamental parameters of traffic flow and the average headway and spacing. 8. [51415] A person walking from office on a one-way street takes 60 min to get home, of which 12 min was taken talking to the driver of a stalled vehicle. He counted 52 vehicles while he was walking and 25 vehicles while he stopped. What are the travel time and flow of the vehicle stream?
Solution:
Flow of the stream =
No of vehicles counted Duration of count
25 Q = 12 =2.1 veh/min = 125 veh/hr
Travel time of stream = Travel time of test vehicle no of vehicles overtaken test vehicle−no of vehicles overtaken by test vehicle flow of stream nw 52+25 T = Tw − q =60 − 2.1 = 60 - 12 = 23.3 min
9. [51425] A student riding his bicycle from campus on a one-way street takes 50 min to get home, of which 10 min was taken talking to the driver of a stalled vehicle. He counted 42 vehicles while he rode his bicycle and 35 vehicles while he stopped. What are the travel time and flow of the vehicle stream?
6
(6)
Measurement at a Point 1. [52111] The table below shows spot speed data (in meters/sec) and the projected area (PA) of each vehicle type (in square meters) from a study. Find the PCU value of each vehicle type using Chandra’s method.
9
7
No
Car
3W
2W
HCV
PA
5.39
4.48
1.20 24.74
1
11.32
8.67
6.67
7.4
2
6.74
7.25
8.27
6.09
3
11.11
9.68
7.75
5.88
4
6.67
6.98
6.12
6.38
5
8.11
8.77
9.52
5.66
6
7.41
8.77
11.9
5.66
7
8.11
9.52
6.97
5.55
Measurement over a Short Section 1. [52211] Determine the time mean speed, space mean speed, and 85th percentile speed from the following speed (in m/s) data. Speed
Frequency
1- 5
9
6-10
16
11-15
32
16-20
48
21-25
23
26-30
9
2. [52212] For a given road following speed data is collected. 25, 31, 36, 39, 42, 44, 47, 48, 49, 51, 52, 52, 53, 54, 55, 56, 57, 57, 57, 58, 59, 60, 60, 62, 63, 64, 65, 66, 66, 68, 68, 69, 70, 70, 71, 73, 75, 79, 85, 89, 90. What is the speed you will recommend for designing sight distance or radius of circular curve? 3. [52213] The spot speeds of ten vehicles observed at a certain location are 55.1, 40.8, 32.2, 47.8, 64.5, 53.2, 58.2, 67.6, 36.4, and 53.2 kmph. Find the time mean speed, space mean speed and 85th percentile speed
8
Measurement Along a Length of Road 1. [52311] Plot the cumulative frequency distribution curve for the following data and show the 85th percentile speed
10
9
Speed Range
Frequency
20-30
8
30-40
43
40-50
35
50-60
29
60-70
11
70-80
4
Automated Traffic Measurement 1. [52401] Classify with one example the various detections technologies with a brief mention of the merits and demerits of the system.
10 Intrusive Technologies 1. [52511] It was observed that the inductive loop was on for 0.39, 0.46, 0.43, 0.47, 0.50, 0.51, 0.48, 0.46, 0.32, 0.44, 0.50, 0.45, 0.44 seconds during one minute interval. If the effective length of a vehicle is 7 meters, compute the density
11 Non-Intrusive Technologies 1. [52601] Write brief notes on the working principle, merits, and demerits of: (i) Video image detection, (ii) Infrared sensors, (iii) Microwave - Doppler and Radar, (iv) Pulsed and active ultrasonic, and (v) Passive acoustic array Sensors.
12 Travel Time Data Collection 1. [52701] In the absense of any automated equipments, how would you conduct a survey to get travel time data in a stretch of road.
13 Vehicle Arrival Models: Headway 1. [53101] (a) Derive the relationship between time mean speed and space mean speed. (b) Write the probability density function for normal distribution and Parson type III distribution and its special cases with various notations used.
11
2. [53111] An observation of headways for 800 samples is given below. Mean headway and standard deviation observed are 2.76 and 1.79. Fit Pearson type III distribution if the shift parameter is 0.5. t
t + δt
Observed Proportion
0.0
1.0
191
1.0
2.0
131
2.0
3.0
170
3.0
4.0
98
4.0
5.0
82
5.0
6.0
81
6.0
7.0
44
> 7.0
2
3. [53112] An observer counts 300 vehicles in an hour at a location. Assuming that the vehicle arrival follows Poisson distribution: (i) estimate the probability of a pedestrian getting a gap of at least 5 seconds; and (ii) estimate how many vehicles will be generated in two minutes (Assume 20 second interval and use the following random numbers: 0.60, 0.42, 0.54, 0.48, 0.69, 0.42) 4. [53113] Using the following random numbers generate vehicle arrival for a period of 20 sec. Assume headways to follow exponential distribution with mean time headway 6 sec. [0.59, 0.45, 0.26, 0.70, 0.14, 0.28] 5. [53114] At a particular section on a highway the following headways are observed: 0.04, 1.37, 1.98, 5.09, 3.00, 2.32, 2.54, 1.37, 0.94, 1.79, 1.10, 6.24, 4.82, 2.77, 4.82, 6.44. Fit an exponential distribution and compare the observed and estimated mean. [Assume headway ranges as 0-2, 2-4, 4-6, and 6-8] 6. [53115] A headway survey gave a mean of 3.76 and standard deviation of 1.17. Fit a Pearson type III distribution and find probability that the headway is between 2 and 4 seconds. Assume a shift parameter of 0.5 and an interval of 0.5 for calculations. 7. [53116] If the flow rate at a given section of road is 1600 and if we assume the inter arrival time of vehicles follow an exponential distribution, then: (a) the probability of headways greater than 1.8 second (b) the probability of headway between 1.2 and 2.4 seconds (c) the probability of headways less than the mean headway
12
8. [53117] An obseravtion from 3424 samples is given table below. Mean headway observed was 3.5 seconds and the standard deviation 2.6 seconds. Fit a negative exponetial distribution. Table 1: Obsered headway distribution h h + dh pobs i 0.0
0.5
0.012
0.5
1.0
0.064
1.0
1.5
0.114
1.5
2.0
0.159
2.0
2.5
0.157
2.5
3.0
0.130
3.0
3.5
0.088
3.5
4.0
0.065
4.0
4.5
0.043
4.5
5.0
0.033
5.0
5.5
0.022
5.5
6.0
0.019
6.0
6.5
0.014
6.5
7.0
0.010
7.0
7.5
0.012
7.5
8.0
0.008
8.0
8.5
0.005
8.5
9.0
0.007
9.0
9.5
0.005
9.5
>
0.033
Total
1.00
9. [53118] An obseravtion from 3424 samples is given table below. Mean headway observed was 3.5 seconds and the standard deviation 2.6 seconds. Fit a normal distrbution, if we assume minimum expected headway is 0.5. 10. [53121] An obseravtion from 3424 samples is given table below. Mean headway observed was 3.5 seconds and the standard deviation 2.6 seconds. Fit a Person Type III Distribution. 11. [53124] Given the headways observed from a survey is given below. Fit an exponential 13
Table 2: Obsered headway distribution h h+dh pobs i 0.0
0.5
0.012
0.5
1.0
0.064
1.0
1.5
0.114
1.5
2.0
0.159
2.0
2.5
0.157
2.5
3.0
0.130
3.0
3.5
0.088
3.5
4.0
0.065
4.0
4.5
0.043
4.5
5.0
0.033
5.0
5.5
0.022
5.5
6.0
0.019
6.0
6.5
0.014
6.5
7.0
0.010
7.0
7.5
0.012
7.5
8.0
0.008
8.0
8.5
0.005
8.5
9.0
0.007
9.0
9.5
0.005
9.5
>
0.033
Total
1.00
distribution and compare the actual and computed mean and standard deviation. 5.15, 1.22, 2.65, 2.35, 0.47, 2.8, 7.67, 4.74, 2.42, 4.87, 5.94, 8.58, 9.74, 0.56, 0.66, 6.72, 7.41, 6.94, 2.42, 5.61
14 Vehicle Arrival Models: Count 1. [53211] The number of vehicles arriving on a single lane highway from one direction in successive 10 seconds intervals is shown below. Fit a poisson distribution to this data and comment on the results. Plot the observed and modeled values in a graph sheet.
14
Table 3: Obtained headway distribution h h+dh pi obs 0.0
0.5
0.012
0.5
1.0
0.064
1.0
1.5
0.114
1.5
2.0
0.159
2.0
2.5
0.157
2.5
3.0
0.130
3.0
3.5
0.088
3.5
4.0
0.065
4.0
4.5
0.043
4.5
5.0
0.033
5.0
5.5
0.022
5.5
6.0
0.019
6.0
6.5
0.014
6.5
7.0
0.010
7.0
7.5
0.012
7.5
8.0
0.008
8.0
8.5
0.005
8.5
9.0
0.007
9.0
9.5
0.005
9.5
>
0.033
Total
Vehicle arriving
1.00
0
1
2
3
4
5 6
12 24 10
6 0
in 20s interval Frequency
17 31
15 Car Following Models 1. [53301] Discuss the concepts and model formulations of Generalised GM model, Gipps’ model, and Wiedemann 74 car-following models. 2. [53302] Discuss the concepts and model formulations of Generalised GM model. 3. [53311] A line of vehicles are in car following mode and all vehicles are travelling at 18 m/s with distance headway of 20 m. After 1.2 seconds, the lead vehicle suddenly 15
decelerates at a rate of 1.2 m/s2 until it stops completely. simulate the behaviour of first following vehicle using the GM fifth car following model for the first 2.5 seconds. Tabulate the results. Assume headway exponent 1.2, speed exponent 1.6, sensitivity coefficient 0.8, reaction time 0.6 seconds, and scan interval 0.3 seconds. 4. [53312] Simulate the following vehicle behaviour for the following data using Widemann 74 model. (a) For the case of stand still distance 3.5m, additive part of safety distance 1.5, and multiplicative part of safety distance 0.8. (b) For the case of stand still distance 3.5m, additive part of safety distance 1.5, and multiplicative part of safety distance 0.8. Comment on the following vehicle behaviour for the above two cases. 5. [53321] A car is travelling with a speed of 16 m/sec at time t=0. Another car follows the first at a distance of 28 m with same velocity. If the first car accelerated by 1 m/sec2 from t=1 to 2 and decelerate by 1 m/sec2 from t=2 to 3, find the speed, acceleration and spacing of the follower at time t=3.0 sec. Assume the reaction time is 1 sec, vehicle dynamics are updated every 0.5 seconds, and the car following model is given by Eq. 3. (Use of a tabular form is encouraged). un (t − 1) − un+1 (t − 1) an+1 (t) = 15 × xn (t − 1) − xn+1 (t − 1)
(3)
6. [53331] In a simulation experiment on a single lane road, one vehicle is travelling at 18 m/s. After 1.5 seconds, the vehicle suddenly accelerates at a rate of 1.5 m/s2 for the next 1.8 seconds. Simulate the behaviour of subsequent vehicle with an initial speed of 16 m/s using GM fifth car following model for the first 3 seconds if the initial distance headway is 20 m. Tabulate the results. Assume headway exponent 1.2, speed exponent 1.5, sensitivity coefficient 0.8, reaction time 0.6 seconds, and update interval of 0.3 seconds. 7. [53341] A line of vehicles are in car following mode and all vehicles are travelling at 15 m/s with distance headway of 20 m. After 1.2 seconds, the lead vehicle suddenly decelerates at a rate of 1.2 m/s2 until it stops completely. simulate the behaviour of first following vehicle using the GM fifth car following model for the first 2.5 seconds. Tabulate the results. Assume headway exponent 1.2, speed exponent 1.6, sensitivity coefficient 0.6, reaction time 0.6 seconds, and scan interval 0.3 seconds. 8. [53351] In a simulation experiment on a single lane road, one vehicle is travelling at 16 m/s. After 0.6 seconds, the vehicle suddenly accelerates at a rate of 1.2 m/s2 for the next 0.9 seconds. Simulate the behaviour of subsequent vehicle with an initial speed of 16 m/s using GM fifth car following model for the first 2.1 seconds if the initial distance headway is 25 m. Tabulate the results. Assume headway exponent 1.2, 16
speed exponent 1.4, sensitivity coefficient 0.6, reaction time 0.6 seconds, and update interval of 0.3 seconds. 9. [53361] A line of vehicles are in car following mode and all vehicles are travelling at 15 m/s with distance headway of 25 m. After 1 second, the lead vehicle suddenly decelerates at a rate of 1.2m/s2 until it stops completely. Simulate the behaviour of first following vehicle using the GM fifth car following model for the first 3 seconds. Tabulate the results. Assume headway exponent 1.0, speed exponent 1.5, sensitivity coefficient 0.5, reaction time 0.5 seconds, and scan interval 0.25 seconds.
16 Lane Changing Models 1. [53401] Explain the conceptual frame work of basic lane change model and distinguish between MLC and DLC models 2. [53411] A roadway has 3 lanes. A vehicle is travelling in the middle lane (i.e., 2nd ) and has the options of either travelling in the same lane or changing either to the 1st or 3rd lanes. These decisions are governed by the utlities of the lanes (Ul ) and gaps (Ug ) . If the vehicle has decided to leave the current lane, the decisions of choosing among the other two lanes are governed by the utilities of gaps (Ug ) in those lanes. On which lane would the vehicle like to travel probably? Ul = 3.467 − 0.0757 × Relativespeed − 0.0064 × F rontgap Ug = 5.567 − 0.03 × Leadgap − 0.0129 × Laggap Lane
Relative Front
Lead
Lag
No.
speed
gap
gap
gap
(m/s)
(m)
(m)
(m)
1
5
8
5
3
2
3
-
-
-
3
8
-
9
6
3. [53412] The mid-block section of a three lane highway with the current traffic state is shown in Figure 1. Determine if the driver of the subject vehicle will change the lane. Given that, the maximum sage deceleration is 2 m/s2 , the critical time gap (both lead and lag) is 0.7 sec, the coefficient of the gap acceptance model is 0.78, the sensitivity coefficient of the car following model is 25, the speed exponent is one, and the distance exponent is two.
17
Figure 1: Lane change scenario
17 Microscopic Traffic Simulation 1. [53501] Write brief notes on calibration, validation, and verification and how these are used in traffic simulators.
18 Traffic Flow Modeling Analogies 1. [54101] Write a brief note on the shockwave phenomenon and illustrate with neat sketches. 2. [54102] Explain the shock-wave phenomenon and derive the expression for speed of a shock wave with the help of neat diagrams. 3. [54103] Derive the flow conservation equation for a mid-block section. 4. [54104] Derive the LWR formulation of traffic flow if we assume Greenshilds linear model relating speed and density. 5. [54105] Illustrate the method of characteristics for solving an LWR formulation. 6. [54106] Derive the numerical formulation to solve an LWR formulation using finite difference method. Illustrate the scheme also.
19 Cell Transmission Models 1. [54201] Discuss in detail about basic cell transmission model
20 Traffic Progression Models 1. [54311] In a case study, the average travel time for a particular stretch was found out to be 22.8 seconds, standard deviation is 5.951 and model time step duration is 10 sec. Find out the Robertsons model parameters and also the flow at downstream at different time steps where the upstream flows are as follows q10 = 20, q20 = 10, q30 = 15, q40 = 18, q50 = 14, q60 = 12
18
21 Discrete Simulation Models 1. [54401] Illustrate the lane changing modeling and the associated rules on a two lane road using cellular automata. 2. [54411] Assume a single lane road stretch divided into 9 cells and vehicles are present in the first ,fourth , seventh and eight cells with 3, 2 , 2, 1 as their velocities respectively. Apply the rules of CA and update the position of the vehicles in the next second.
22 Capacity and Level of Service LOS 1. [55101] Define capacity and write brief notes on various factors affecting capacity. 2. [55102] Illustrate the concept of capacity and level of service for a typical mid-block road section and show the factors affecting capacity.
23 Urban Streets 1. [55201] How do you measure operational performance of a given urban arterial? Explain the HCM method of assessment
24 Multilane Highways 1. [55311] A 6 km undivided four lane highway on level terrain has free flow speed of 75 kmph. The lane width is 3.5m with peak hour volume of 1600 veh/hr and 12% trucks and buses, 2% Recreational vehicles. Find the capacity and level of service. Assume peak hour factor 0.9. 2. [55312] A segment of undivided four-lane highway on level terrain has field-measured FFS 74.0-km/h, lane width 3.4-m, peak-hour volume 1,900-veh/h, 13 percent trucks and buses, 2 percent RVs, and 0.90 PHF. What is the peak-hour speed, and density for the level terrain portion of the highway? (fp = 1, ER = 1.2 and ET = 1.5)
25 Freeway Operations 1. [55411] Consider an existing four lane free-way in rural area, having very restricted geometry with rolling terrain. Peak hour volume is 2000 veh/h with 5% trucks. The 19
traffic is commuter type with peak hour factor 0.92 and interchange density as 0.6 interchanges per kilometer. Free-way consists of two lanes in each direction of 3.3 m width with lateral clearance of 0.6 m. Find the LOS of free-way during peak hour.
26 Ramp Metering 1. [55501] Define ramp meter and explain various objectives of ramp metering 2. [55502] Discuss in detail (i) the concept of capacity and LOS in HCM 2000 and (ii) how it is used in the analysis of ramp metering.
27 Corridor Analysis 1. [55601] Discuss briefly how the performance of a corridor is evaluated in HCM 2000.
28 Principles of Traffic Control 1. [56101] Describe the levels of intersection control. 2. [56102] Discuss various traffic control measures at a typical 4 legged intersection in an urban area. Illustrate them with the help of neat sketches. Explore all the options other than rotary, signal and grade separation.
29 Traffic Signs 1. [56201] What is the difference between a stop sign and give way sign? Under what circumstances are they required? Illustrate with neat sketches. 2. [56202] Give two examples for each of the following categories of traffic signs: [A] Right of way series, [B] Movement series, [C] Informatory signs, and [D] Warning signs
30 Road Markings 1. [56301] A road has four lanes. A bridge goes over the road, which has a pile at the middle of road. Illustrate with neat sketch the road markings that are to be provided. 2. [56302] Illustrate with neat sketch various road markings at a signalized intersection 20
3. [56303] Discuss any five road markings with the help of neat sketches. 4. [56304] (a) Describe the main categories of traffic signs with two examples for each category alongwith neat sketches. (b) Describe any two longitudinal markings with the help of neat diagrams. 5. [56305] With the help of neat diagrams show the traffic signs and road markings for (a) Ramp from an urban arterial joining the freeway, (b) Rotary, (c) Uncontrolled intersection joining a minor and major road, (d) Signalised intersection. 6. [56306] (a) Illustrate with a neat sketch what traffic signs and road markings you propose at the IITB main gate? (b) Illustrate with a neat sketch no passing zone markings at a horizontal curve when the stopping sight distance is less than the radius of the curve (Assume the road is two lane bidirectional).
31 Uncontrolled Intersection 1. [56401] How do you channelize a three legged intersection for a high volume traffic in an urban area? 2. [56411] At an uncontrolled intersection the cumulative number of gaps accepted and rejected have been tabulated as shown below. Determine critical gap using Raff’s method (illustrate the result graphically).
21
Gap (sec)
Accepted gaps
Rejected gaps
0.0
0
208
0.5
0
208
1.0
0
193
1.5
1
135
2.0
10
84
2.5
26
55
3.0
45
30
3.5
67
15
4.0
86
9
4.5
106
8
5.0
122
4
5.5
140
1
9.5
227
0
32 Channelization 1. [56501] Channelize the intersection given in the Figure 2 with the help of a neat sketch. Show the paths of movements by short arrows. All the roads are bidirectional.
Figure 2: Intersection layout
33 Traffic Rotary 1. [56611] The entry and exit width of a rotary intersection are 9m and 11m respectively. The width of approaches at the intersection is 15m. The traffic from the four approaches traversing the intersection is given below. If the traffic composition is 50% car, 40% two-wheelers and 10% trucks and the passenger car units of two-wheelers and trucks are 0.5 and 3 respectively, find the capacity of the rotary using TRL formulae.
22
Approach
Left turn
Straight
Right turn
North
500
800
300
South
400
350
450
East
250
400
500
West
300
450
500
2. [56612] The entry and exit width of a rotary intersection are 9m and 11m respectively. The width of approaches at the intersection is 15m. The traffic from the four approaches traversing the intersection is given below. Find the capacity of the rotary. Approach
Left turn
Straight
Right turn
North
500
800
300
South
400
350
450
East
250
400
500
West
300
450
500
3. [56622] The entry and exit width of a rotary intersection are 8m and 10m respectively. The width of approaches at the intersection is 14 m. The traffic from the four approaches traversing the intersection is given below. Find the capacity of the rotary using TRL formulae. Approach
Left turn
Straight
Right turn
North
550
750
340
South
450
390
450
East
280
400
520
West
350
480
500
4. [56632] The entry and exit width of a rotary intersection are 8 m and 10 m respectively. Assume the length of the weaving section is four times the weaving width. The traffic from the four approaches traversing the intersection is given below. Find the capacity of the rotary using TRL formulae. Approach
Left turn
Straight
Right turn
North
550
750
340
South
450
390
440
East
280
400
520
West
350
480
500
23
5. [56642] The entry and exit width of a rotary intersection are 10m each. The width of approaches at the intersection is 15m. The traffic from the four approaches traversing the intersection is given below. Find the capacity of the rotary using TRL formulae Approach
Left turn
Straight
Right turn
North
415
643
350
South
549
358
424
East
408
450
402
West
450
423
493
34 Grade Separated Intersection 1. [56701] Draw a neat sketch of a fully clover leaf intersection and mark all the traffic movements. 2. [56702] Illustrate with neat sketches: (i) A diamond interchange showing the movement of all the flows. (ii) Road markings on a two lane bi-directional horizontal curve when the sight distance is less than the length of the curve. (iii) The concept of flow prediction in a transportation system when the supply is improved.
35 Design Principles of Traffic Signal 1. [57111] A person standing at a stop line of signalized intersection found that the vehicles arrive at 3.7, 6.9, 9.7, 12, 14.1, 16, 17.9, and 19.8 seconds after the start of the green. The signal turns red at 20th second. Find the lost time, saturation flow and lane capacity. (Assume cycle is 60 second, amber is 3 s) 2. [57112] A person standing at a stop line of signalized intersection found that the vehicles arrive at 3.7, 6.9, 9.7, 12, 14.1, 16, 17.9, and 19.8 seconds after the start of the green. Find the lost time and saturation headway.
36 Signalized Intersection Delay Models 1. [57201] Derive an expression for webster’s uniform delay and state the assumptions involved. 2. [57202] (i) Illustrate the concept of stopped delay, control delay and approach delay at a signalized junction. (ii) Illustrate the concept of unsaturated uniform delay, random delay and using over-saturate delay using appropriate sketches. 24
3. [57203] (a) Derive an expression for cycle length calculation for a signalized intersection. (b) Write briefly on Webster’s stopped delay calculations 4. [57211] The traffic flow and phase plan for a four-legged intersection is as shown in Figure 9. The E-W flow is 1420, W-E flow is 1150, N-S flow is 640, and S-N flow is 580 vehicles per hour. Assume for all the phases the yellow time is 3 seconds, the lost time is 4 seconds, saturation headway is 1.2 seconds, and degree of saturation is 0.9. Assume left turn adjustment factor 1.2 and right turn adjustment factor 1.3. Assume the left turn and right turn traffic proportion of 20% and 30% respectively. If the actual green time allotted for phase 1,2,3 and 4 is 30,28, 18 and 22 respectively, compute the delay for each lane and total intersection delay. 5. [57212] The phase plan and flows of a signalised intersection are given in Fig. 5. Design the cycle length using HCM method (xc =0.9) and green time for each phase. Compute also the average delay per vehicle using Webster’s model. Show these in a phase-time diagram. Assume lost time and amber time as 3 and 4 sec respectively for each phase. Ignore pedestrian requirements. All flows in veh./hr 1 = 300 2 = 400 3 = 180
12 11 10
10 = 120 11 = 365 12 = 170
P−1 P−2
1 2 3 9 8
P−3
7
4 = 185 5 = 450 6 = 360
4
5
7 = 210 8 = 410 9 = 110
6
P−4 Phase plan
Figure 3: Intersection flows and phase plan
6. [57213] A major road with four lane running E-W direction meets a minor road having two lane running in N-S direction. The E-W flow is 1670, W-E flow is 1550, N-S flow is 720, and S-N flow is 680 vehicles per hour. The intersection of the two road is controlled by a traffic signal with a cycle time of 60 seconds. Assume for all the phases the yellow time is 3 seconds, the lost time is 4 seconds, and saturation headway is 2.1 seconds. Ignore turning movements and pedestrian traffic. Compute the green time for each phase and total delay experienced by all vehicles in the intersection for one hour duration. 7. [57214] The phase plan and flows of a signalised intersection are given in Fig. 5. Design the cycle length using HCM method (xc =0.9) and green time for each phase. Compute also the average delay per vehicle using Webster’s model. Show these in a 25
phase-time diagram. Assume saturation headway, lost time and amber time as 2, 3 and 4 seconds respectively for each phase. Ignore pedestrian requirements. All flows in veh./hr 1 = 250 2 = 450 3 = 200
10
P−1
9 = 120 10 = 360
9
P−2
1 2 3 8
P−3
7 6
4 = 180 5 = 400
4
Phase plan
6 = 200 7 = 420 8 = 100
5
Figure 4: Intersection flows and phase plan
8. [57215] In the above problem, If the actual green time allotted for phase 1,2,3 and 4 is 30, 35, 8, and 9 respectively, compute the stopped delay for East-West movement (Assume uniform vehicle arrival). 9. [57216] For the data given in above problem (Q.6), if the actual green time alloted for phase 1, 2, 3 and 4 is 30, 28, 18 and 22 respectively, calculate the delay for lane 1 and lane 7. 10. [57222] The phase plan and flows of a signalised intersection are given in Fig. 5. Design the cycle length using HCM method (xc =0.9) and green time for each phase. Compute also the average delay per vehicle using Webster’s model. Show these in a phase-time diagram. Assume lost time and amber time as 3 and 4 sec respectively for each phase. Ignore pedestrian requirements. All flows in veh./hr 1 = 400 2 = 420 3 = 280
12 11 10
10 = 320 11 = 365 12 = 170
P−1 P−2
1 2 3 9 8
P−3
7
4 = 350 5 = 385 6 = 140
4
5
7 = 390 8 = 410 9 = 240
6
P−4
Phase plan
Figure 5: Intersection flows and phase plan
11. [57223] Traffic flow and phase plan for a four-arm intersection is shown in Figure 6. Assume the following: The yellow time is 3 seconds, the lost time is 4 seconds, saturation headway is 2.0 seconds for each phase; Left turn adjustment factor 1.1 and right turn adjustment factor 1.4; Left turn and right turn traffic proportions are 20 and 26
30 percent respectively; Through movements are distributed equally in all lanes; and There is no pedestrian traffic. Compute the critical flow for each phase and for the intersection. P−1 10
9
P−2
1 2 3
8
P−3
7 6
P−4 4
5
Phase plan
Figure 6: Intersection geometry and phase plan (FIGURE NEEDS CORRECTION)
12. [57224] Traffic flow and phase plan for a four-arm intersection is shown in Figure 7. If the actual green time is 18, 13, 15 and 9 respectively for phases 1-4, and the lane volumes are 150, 350, 250, 200, and 280 vph for lanes 1-5 respectively, compute the delay for the W-E and S-N approach. Assume the following: The yellow time is 3 seconds, the lost time is 4 seconds, saturation headway is 2.0 seconds for each phase;
All flows in veh./hr 1 = 400 2 = 420 3 = 280
12 11 10
10 = 320 11 = 365 12 = 170
P−1 P−2
1 2 3 9 8
P−3
7
4 = 350 5 = 385 6 = 140
4
5
7 = 390 8 = 410 9 = 240
6
P−4
Phase plan
Figure 7: Intersection geometry and phase plan (FIGURE NEEDS TO BE CORRECTED)
37 Special Requirement in Traffic Signal 1. [57311] The traffic flow and phase plan for a four-legged intersection is as shown in Figure 9. The E-W flow is 1420, W-E flow is 1150, N-S flow is 640, and S-N flow is 580 vehicles per hour. Assume for all the phases the yellow time is 3 seconds, the lost time is 4 seconds, saturation headway is 1.2 seconds, and degree of saturation is 0.9. Assume left turn adjustment factor 1.2 and right turn adjustment factor 1.3. Assume
27
the left turn and right turn traffic proportion of 20% and 30% respectively. Assuming no pedestrian traffic, compute signal timing and illustrate with a sketch. P1
(7)
N
P2
P3
P4
Figure 8: Intersection Geometry
2. [57312] The traffic flow and phase plan for a four-legged intersection is as shown in Figure 9. The E-W flow is 1000, W-E flow is 950, N-S flow is 850, and S-N flow is 750 vehicles per hour. Assume for all the phases the yellow time is 3 seconds, the lost time is 2 seconds, saturation headway is 1.8 seconds, and degree of saturation is 0.95. Assume the left turn and right turn traffic proportion is 15% and 20% respectively. Assuming no pedestrian traffic, compute the cycle time and green time for each phase.
P1
N 12
11 10
P2
1 P3
2 3 6 5
P4
4
7
8
9
Figure 9: Intersection Geometry
3. [57313] The traffic flow and phase plan for a four-legged intersection is as shown in Figure. The E-W flow is 800, W-E flow is 740, N-S flow is 450, and S-N flow is 490 vehicles per hour. Assume for all the phases the yellow time is 3 seconds, the lost time is 2 seconds, saturation headway is 1.8 seconds, and degree of saturation is 0.9. Assume left turn adjustment factor 1.10 and right turn adjustment factor 1.30. Assume 28
the left turn and right turn traffic proportion is 10% and 20% respectively. Assuming no pedestrian traffic, compute the cycle time and green time for each phase. Compute also the stopped delay for the traffic from north.
4. [57323] The traffic flow and phase plan for a four-legged intersection is as shown in Figure. The E-W flow is 780, W-E flow is 720, N-S flow is 430, and S-N flow is 470 vehicles per hour. Assume for all the phases the yellow time is 3 seconds, the lost time is 2 seconds, saturation headway is 1.8 seconds, and degree of saturation is 0.9. Assume left turn adjustment factor 1.15 and right turn adjustment factor 1.35. Assume the left turn and right turn traffic proportion is 10% and 20% respectively. Assuming no pedestrian traffic, compute the cycle time and green time for each phase. Compute also the stopped delay for the traffic from north (assume uniform vehicle arrival). P1
N
P2
P3
P4
38 Capacity and Los Analysis of a Signalized I/S 1. [57411] Calculate the delay and level of service using HCM method for a signalised intersection in South bound direction. Follow the terminology as per HCM 2000 and the intersection geometry is as shown in Figure 10. The intersection is located in CBD area and the traffic volume in each direction in vehicles/hour is given as East
West
North
South
bound
bound
bound
bound
Left turn
65
30
30
40
Through
620
700
370
510
Right turn
35
20
20
50
Pedestrian volume = 100 pedestrains/hour, Percentage of heavy vehicles = 5% in East and West approaches and 8% in North and 29
4.5 m N
3.3 m 3.3 m 3.3 m 3.3 m
Phase 1
Phase 2
4.5 m
Figure 10: Intersection Geometry South approaches, Base saturation flow rate = 1900 veh/h/lane, Peak hour factor= 0.9, Cross walk width = 3.0 m, Two phase signal with cycle time 70 seconds and North bound-South bound green time=36 s, East bound-West bound green time =26 s, Amber time= 4 s and Movement lost time =4 s, Arrival type 4 and Analysis duration = 15 min, Assume 0% grade with no parking maneuvers and no buses stopping. Consider Lane utilisation adjustment factor in North and South approaches= 1.00, East and West approaches = 0.95. Left turn pedestrian/bicycle adjustment factor= 0.999(N), 0.998(S), 0.997(E), 0.998(W), Right turn pedestrian/bicycle adjustment factor= 0.996(N), 0.994(S), 0.992(E), 0.995(W), Passenger car equivalent for heavy vehicle = 2.0, Left turn adjustment factor is 0.937(N), 0.951(S), 0.716(E), 0.901(W). Incremental delay factor= 0.5 and Initial queue delay= 0 s/veh. Progression adjustment factor = 1.000. 2. [57412] A major arterial is meeting a minor arteial and is located in the central business district (CBD) of a small urban area. Compute the delay and peak-hour LOS for west bound direction. Main Street has four lanes of 3.3 width, two in each direction and minor street has two lanes of 4.5m width, one in each direction. Heavy vehicle percentage is 5 % in east and west bound direction and 8 % in north and south bound. Assume no parking at intersection and no buses. Peak hour factor is 0.90. Pedestrian volume is 100 p/h in all approaches, Bicycle volume is 20 bicycles/h for all approaches, 30
Movement lost time is 4 s, yellow time is 4 s and terrain is level. Assume base saturation flow rate 1900 pc/h/lane, crosswalk width of 3.0 m, and heavy vehicle adjustment factor 2.0. Left turn adjustment factor in east bound direction is 0.716 and west bound direction is 0.901. Left turn pedestrian/bike adjustment factor is 0.998 and right turn pedestrian/bike adjustment factor is 0.995 for all approaches. The traffic volume is given in the input worksheet. Report the results in the capacity and LOS worksheet and submit alongwith the answer sheet 3. [57413] The intersection of Third Avenue (NB/SB) and Main Street (EB/WB) is located in the central business district (CBD) of a small urban area. Intersection geometry and flow characteristics are shown on the input worksheet. Facts/Data/Assumptions: (a) EB and WB HV = 5 percent, (b) NB and SB HV = 8 percemnt (c) PHF = 0.9, (d) Two-phase signal, (e) 70 sec cycle length, (f) NB-SB green = 36 s, (g) EB-WB green = 26 s, (h) Yellow =4 s, (i) Third avenue has two lanes, one in each direction, (j) Main street has four lanes, two in each direction, (k) No parking at intersection, (l) Pedestrian volume = 100 p/h, all approaches, (m) Bicycle volume = 20 bicycles/h, all approaches, (n) Movement lost time = 4s, (o) Level terrain, (p) Assume crosswalk width = 3.0 m for all approaches, (q) Assume base saturation flow rate = 1900 pc/h/lane, (r) AssumeET = 2.0, (s) No buses, (t) Left turn correction factor fLT = 0.937, (u) Pedestrian-Bicycle effects on turning fLpb = 0.999, and fRpb = 0.996 (v) Lane utilization factor fLU = 1.0 Compute the the delay and peak-hour LOS of the NB approach using HCM 2000 guidelines? Fill the relevant cells of the Exhibit 16-20,21, and 22. 4. [57414] The intersection of Third Avenue (NB/SB) and Main Street (EB/WB) is located in the central business district (CBD) of a small urban area. Intersection geometry and flow characteristics are shown on the input worksheet. Facts/Data/Assumptions: (a) EB and WB HV = 6 percent, (b) NB and SB HV = 9 percent (c) PHF = 0.85, (d) Twophase signal, (e) 76 sec cycle length, (f) NB-SB green = 40 s, (g) EB-WB green = 28 s, (h) Yellow =4 s, (i) Third avenue has two lanes, one in each direction, (j) Main street has four lanes, two in each direction, (k) No parking at intersection, (l) Pedestrian volume = 100 p/h, all approaches, (m) Bicycle volume = 20 bicycles/h, all approaches, (n) Movement lost time = 4s, (o) Level terrain, (p) Assume cross walk width = 3.0 m for all approaches, (q) Assume base saturation flow rate = 1900 pc/h/lane, (r) AssumeET = 2.0, (s) No buses, (t) Left turn correction factor fLT = 0.937, (u) Pedestrian-Bicycle effects on turning fLpb = 0.999, and fRpb = 0.996 (v) Vehicle arrival type (AT) is 4 (w) Type of control is pre-timed (P). The north bound flow is 420 ( Left 30, Through 370, and Right 20) Compute the saturation flow of the NB approach using HCM 2000 guidelines? 31
5. [57423] The intersection of Third Avenue (NB/SB) and Main Street (EB/WB) is located in the central business district (CBD) of a small urban area. Intersection geometry and flow characteristics are shown on the input worksheet. Facts/Data/Assumptions: (a) EB and WB HV = 6 percent, (b) NB and SB HV = 9 percent (c) PHF = 0.85, (d) Twophase signal, (e) 76 sec cycle length, (f) NB-SB green = 40 s, (g) EB-WB green = 28 s, (h) Yellow =4 s, (i) Third avenue has two lanes, one in each direction, (j) Main street has four lanes, two in each direction, (k) No parking at intersection, (l) Pedestrian volume = 100 p/h, all approaches, (m) Bicycle volume = 20 bicycles/h, all approaches, (n) Movement lost time = 4s, (o) Level terrain, (p) Assume cross walk width = 3.0 m for all approaches, (q) Assume base saturation flow rate = 1900 pc/h/lane, (r) AssumeET = 2.0, (s) No buses, (t) Left turn correction factor fLT = 0.716, (u) Pedestrian-Bicycle effects on turning fLpb = 0.997, and fRpb = 0.992 (v) Vehicle arrival type (AT) is 4 (w) Type of control is pre-timed (P) (x) East bound flow is 750 ( Left 70, Through 640, and Right 40) Compute the the delay and peak-hour LOS of the EB approach using HCM 2000 guidelines? Fill the relevant cells of the Exhibit 16-20,21, and 22.
39 Coordinated Traffic Signal 1. [57511] A North-South corridor has three junctions namely A, B, and C. Junction A is on the south end of the corridor and junction C is on the north end. These junctions are coordinated in the north direction. All the junctions are having two phase signals with a cycle of 80 sec. The juctions A, B, and C have green times of 40, 50, and 30 sec respectively in the coordinated direction. The distance between A and B is 600 meters and B and C is 900 meters. The junctions are coordinated considering a speed of 15 m/sec. (a) What will be the resulting band width? (b) While the corridor is operating under the above control conditions, if the vechiles could travel only at a speed of 12 m/sec, what bandwidth will be achieved? 2. [57512] The distance between two intersections is 0.75 km and the average vehicle speed in the northbound direction is 50 kmph and south bound direction is 54 kmph. If the cycle time is 100 seconds and north bound and south bound traffic volume is 950 vehicles/hour. (a) Compute the offset if south bound direction is ignored. (b) Compute the offset if both directions are considered. Illustrate the result using timespace diagram. 3. [57513] An urban arterial with 2 signalized intersections 400 m apart is to be coordinated in both directions with a design speed of 20 m/s and a cycle of 60 seconds. Determine the optimal offset at the second intersection with respect to both directions. 32
4. [57522] The distance between two intersections is 0.75 km and the average vehicle speed in the northbound direction is 45 kmph and south bound direction is 50 kmph. If the cycle time is 90 seconds, split is 50 percent, and north bound and south bound traffic volume is 900 vehicles/hour, compute offset and band width, if: (a) only north bound traffic is considered, and (b) both directions are considered. Illustrate the result using time-space diagram. 5. [57532] The distance between two intersections is 0.75 km and the average vehicle speed in the northbound direction is 40 kmph and south bound direction is 60 kmph. If the cycle time is 120 seconds, split is 50 percent, and north bound traffic is 1000 vph and south bound traffic is 800 vph, compute offset and band width, if: (i) only north bound traffic is considered, and (ii) both directions are considered. Illustrate the result using time-space diagram.
40 Vehicle Actuated Signals 1. [57601] Describe the working principle and various control parameters of a vehicle actuated controller and its limitations.
41 Area Traffic Control 1. [57701] Compare and contrast SCOOT and SCAT system for area traffic control 2. [57702] What are the various building blocks of area traffic control system SCOOT. 3. [57703] Highlight the broad principle of SCOOT system and its implementation issues for Indian cities.
42 Parking Studies 1. [58101] Illustrate with a sketch 300 on-street parking facility and derive the length required to park N number of vehicles with the help of neat diagrams. Assume the dimensions of vehicle as 5.5m X 2.5m. 2. [58102] Calculate the length required to park N number of vehicles in the case of 600 on-street parking facility with the help of neat diagrams. Assume the dimensions of vehicle as 5.5m X 2.5m.
33
3. [58103] (a) Any two longitudinal and transverse road markings. (b) A diamond interchange with movement of all flows. (c) Elements involved in the design of a rotary. (d) Zone and zoning principles. (e) Show all the relevant dimensions of a 450 angle parking for a car. 4. [58111] From an in-out survey consiting of 50 bays, the initial count was 18. The number of vehicles coming in and out of the parking lot for a time interval of 5 minutes is shown below. Find the accumulation, total parking load, average occupancy, and efficiency of parking lot. Time
5 10 15
20 25 30
In
7
6
3
3
7
4
Out
2
4
5
2
8
3
43 Accident Studies 1. [58201] Illustrate with a numerical example of your choice how energy theory is used in the accident reconstruction of a collinear impact. 2. [58211] Vehicle A is approaching from west and vehicle B from south. After collision A skids 600 north of east and B skids 300 south of east. Skid distance before collision for A is 18 m and B is 26 m. The skid distances after collision are 30m and 15 m respectively. Weight of A and B are 4500 and 6000 respectively. Skid resistance of pavement is 0.55 m. Determine the pre-collision speed.
44 Fuel Consumption and Emission Studies 1. [58311] A bus stalled at a signal emits pollutants at the rate of 20000 g/s. The exhaust pipe is situated at height of 0.75 m from the Ground level. What will be the concentration of pollutants inhaled by a man living on the first floor of a building with storey height 3.5 m? The building is situated at a lateral distance of 5 m from the main road and longitudinal distance of 4 m downwind of the source. Assume a wind velocity of 10 m/s, σy = 375 m and σz = 120 m. The concentration of the emission is given by C(x, y, z) =
Q 2∗π∗u∗σy ∗σz
2
2
2
−(z−h) −y + exp −(z+h) ) ∗ exp 2∗σ 2 ∗ (exp 2∗σ2 2∗σ2 y
z
z
2. [58312] What is the total fuel consumption of a vehicle travelling on a 10 km stretch of road if the average stopped delay is 6 s and it stops thrice during its journey. Assume that the fuel consumption rate per unit distance while cruising is 0.0045, the fuel consumption rate per unit time while idling is 0.0035, and the excess fuel used in 34
decelerating to stop and accelerating back to cruise speed is 0.002. If the vehicle is cruising throughout the stretch of the road, what is the decrease in fuel consumption?
45 Congestion Studies 1. [58401] Describe in detail how congestion can be quantified. Illustrate with equations and sketches. 2. [58402] Describe congestion management measures: both demand and supply side. 3. [58411] On a 2.8km long link of road, it was found that the vehicle demand was 1000, mean speed of the link 12 km/hr, and free flow speed 27 km/hr. Assuming the Average vehicle occupancy as 1.2 person/vehicle, calculate congestion intensity in terms of total person hours of delay.
46 Queuing Analysis 1. [58511] Vehicles arrive at a toll booth at an average rate of 300 per hour. Average waiting time at the toll booth is 10 s per vehicle. If both arrival and departures are markovian events, what is the average number of vehicles in the system, average queue length, average delay per vehicle, average time in the system?
47 Toll Operation 1. [58611] Calculate the optimum number of tollbooths to be installed on a toll plaza, proposed to be built on a two-lane highway. The total traffic flow is 1200 veh/hr. Assume the following data: service rate of Tollbooth = 350 veh/hr; service rate when merging of vehicles takes place = 1184.9 veh/hr; and service rate when no merging of vehicles takes place = 3017.1 veh/hr.
48 Pedestrian Studies 1. [58711] Calculate time gap for a platoon of 27 school children 5 in a row, consecutive time 2 sec width of crossing section is 7.5 m and walking speed of children 0.9 m/s start up time 3 sec.
35
49 Intelligent Transportation System - I 1. [59101] Show a typical ITS architecture and write briefly on the communications involved. 2. [59102] Discuss briefly any three services offered and their respective implementation challenges for each of the following ITS user service components (i) travel and traffic management, and (ii) public transport operations.
50 Intelligent Transportation System - II 1. [59201] Describe how RP & SP surveys can be used for ITS evaluation.
51 Advanced ITS 1. [59301] Write notes on: Smart road, smart car, V2V, and V2I.
52 General 1. [59401] As a traffic engineer, discuss various traffic management measures that you will recommend to your local authorities for our college campus (Make brief and specific points, with simple sketches).
Acknowledgments I wish to thank several of my students and staff of NPTEL for their contribution in this lecture. I also appreciate your constructive feedback which may be sent to
[email protected] Prof. Tom V. Mathew Department of Civil Engineering Indian Institute of Technology Bombay, India
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