Traffic Engineering

 Question 1
The lane configuration with lane volumes in vehicles per hour of a four-arm signalized intersection is shown in the figure. There are only two phases: the first phase is for the East-West and the West-East through movements, and the second phase is for the North-South and the South-North through movements. There are no turning movements. Assume that the saturation flow is 1800 vehicles per hour per lane for each lane and the total lost time for the first and the second phases together is 9 seconds.

The optimum cycle length (in seconds), as per the Webster's method, is ____________. (round off to the nearest integer)
 A 12 B 45 C 37 D 65
GATE CE 2022 SET-2   Transportation Engineering
Question 1 Explanation:
From figure
\begin{aligned} y_{N-S}&=\left [ \frac{360}{1800},\frac{396}{1800} \right ]_{max}\\ &=0.22\\ y_{E-W}&=\left [ \frac{504+504}{2 \times 18},\frac{440}{1800} ,\frac{460}{1800}\right ]_{max}\\ &=0.28\\ &\text{Optimum cycle length}\\ &=\frac{1.5L+5}{1-y}\\ &=\frac{1.5 \times 9+5}{1-(y_{N-S}+y_{E-W})}\\ &=\frac{1.5 \times 9+5}{1-(0.22+0.28)}\\ C_o&=37secs. \end{aligned}
 Question 2
Assuming that traffic on a highway obeys the Greenshields model, the speed of a shockwave between two traffic streams (P) and (Q) as shown in the schematic is _______ kmph. (in integer)

 A 5 B 10 C 15 D 25
GATE CE 2022 SET-2   Transportation Engineering
Question 2 Explanation:
$\text{Speed of shock wave}=\frac{\text{Change in flow}}{\text{Change in density}}$
$\text{Flow}=\text{Speed} \times \text{Density}$
\begin{aligned} Density&=\frac{Flow}{speed}\\ &=\frac{q_Q-q_P}{\frac{q_Q}{V_Q}-\frac{q_P}{V_P}}\\ &=\frac{1800-1200}{\frac{1800}{30}-\frac{1200}{60}}\\ &=\frac{600}{60-20}\\ &=15Kmph \end{aligned}
 Question 3
A single-lane highway has a traffic density of 40 vehicles/km. If the time-mean speed and space-mean speed are 40 kmph and 30 kmph, respectively, the average headway (in seconds) between the vehicles is
 A 3 B 2.25 C $8.33 \times 10^{-4}$ D $6.25 \times 10^{-4}$
GATE CE 2022 SET-2   Transportation Engineering
Question 3 Explanation:
Given that,
Traffic density = 40 Veh/Km.
Time mean speed = 40 Kmph
Space mean speed = 30 kmph
We know that traffic volume
= Density x Space mean speed = 40x30 =1200 Veh hr.
and we also know that
$q=\frac{3600}{H_t}$
where $H_t$- average headway (sc)
$1200=\frac{3600}{H_t}$
$H_t=\frac{3600}{1200}=3$ secs.
 Question 4
For a traffic stream, $v$ is the space mean speed, $k$ is the density, $q$ is the flow, $v_f$ is the free flow speed, and $k_j$ is the jam density. Assume that the speed decreases linearly with density.
Which of the following relation(s) is/are correct?
 A $q=k_jk-\left ( \frac{k_j}{v_f} \right )k^2$ B $q=v_fk-\left ( \frac{v_f}{k_j} \right )k^2$ C $q=v_fv-\left ( \frac{v_f}{k_j} \right )v^2$ D $q=k_jv-\left ( \frac{k_j}{v_f} \right )v^2$
GATE CE 2022 SET-2   Transportation Engineering
Question 4 Explanation:
As per Greenshield's
\begin{aligned} V&=V_f\left ( 1-\frac{K}{K_j} \right )\\ q&=K \times V \\ &= K \left [ 1-\frac{K}{K_j} \right ]V_f\\ q&=V_fK-\left ( \frac{V_f}{K_j} \right )K^2\\ V&=V_f\left [ 1-\frac{K}{K_j} \right ] \end{aligned}
From above equation we can say that
\begin{aligned} K&=K_j\left ( 1-\frac{V}{V_f} \right )\\ q&=K \times V \\ q&= K_j \left [ 1-\frac{V}{V_f} \right ] \times V\\ q&=K_jV-\left ( \frac{K_j}{V_f} \right )V^2 \end{aligned}
 Question 5
For the dual-wheel carrying assembly shown in the figure, $P$ is the load on each wheel, $a$ is the radius of the contact area of the wheel, $s$ is the spacing between the wheels, and $d$ is the clear distance between the wheels. Assuming that the ground is an elastic, homogeneous, and isotropic half space, the ratio of Equivalent Single Wheel Load (ESWL) at depth $z=d/2$ to the ESWL at depth $z=2s$ is ___________. (round off to one decimal place) (Consider the influence angle to be $45^{\circ}$ for the linear dispersion of stress with depth)
 A 0.2 B 0.5 C 0.8 D 0.1
GATE CE 2022 SET-1   Transportation Engineering
Question 5 Explanation:
\begin{aligned} \text{ESWL @ depth }\frac{d}{2}&=P \\ \text{ESWL @ depth }2S&=2P \\ \text{Ratio }\frac{P}{2P}&=0.5 \\ \end{aligned}
 Question 6
At a traffic intersection, cars and buses arrive randomly according to independent Poisson processes at an average rate of 4 vehicles per hour and 2 vehicles per hour, respectively. The probability of observing at least 2 vehicles in 30 minutes is ______. (round off to two decimal places)
 A 0.52 B 0.64 C 0.8 D 0.44
GATE CE 2022 SET-1   Transportation Engineering
Question 6 Explanation:
\begin{aligned} \lambda _C&=4 \; vehical/hr=2 \; vehical /30 \;min\\ \lambda _C&=2 \; vehical/hr=1 \; vehical /30 \;min\\ \lambda _{Vehical}&=3 \; vehical/30 \;min\\ P(x \lt 2)&=1-P(x\leq 1)\\ &=1-[P(x=0)+P(x=1)]\\ &=1-\left [ \frac{e^{-\lambda }\lambda ^0}{0!} +\frac{e^{-\lambda }\lambda ^1}{1!}\right ]\\ &=1-e^{-3}(1+3)\\ &=1-\frac{4}{e^3}\\ &=0.8 \end{aligned}
 Question 7
A two-phase signalized intersection is designed with a cycle time of 100 s. The amber and red times for each phase are 4 s and 50 s, respectively. If the total lost time per phase due to start-up and clearance is 2 s, the effective green time of each phase is ______s. (in integer)
 A 96 B 56 C 82 D 48
GATE CE 2022 SET-1   Transportation Engineering
Question 7 Explanation:
Two phase signalized intersections,
Cycle time = 100 secs.
Amber time = 4 secs. [each phase]
Red time = 50 secs. [each phase]
Total lost time = 2 sec. [each phase]
Effective green time = ? [each phase]
Total Effective green = Cycle time - Lost time = 100-2x2 = 96 sec.
As there is symmetry in phases so effective green time per phase= 96/2=48 sec.
 Question 8
Consider the four points P, Q, R, and S shown in the Greenshields fundamental speed-flow diagram. Denote their corresponding traffic densities by $k_P,k_Q,k_R$ and $k_S$ respectively. The correct order of these densities is

 A $k_P \gt k_Q \gt k_R \gt k_S$ B $k_S \gt k_R \gt k_Q \gt k_P$ C $k_Q \gt k_R \gt k_S \gt k_P$ D $k_Q \gt k_R \gt k_P \gt k_S$
GATE CE 2022 SET-1   Transportation Engineering
Question 8 Explanation:

 Question 9
In a three-phase signal system design for a four-leg intersection, the critical flow ratios for each phase are 0.18, 0.32, and 0.22. The total loss time in each of the phases is 2s. As per Webster's formula, the optimal cycle length (in s, round off to the nearest integer) is _______________
 A 28 B 46 C 50 D 58
GATE CE 2021 SET-2   Transportation Engineering
Question 9 Explanation:
\begin{aligned} L &=2 \times 3=6 \text { seconds } \\ n &=3 \\ y &=(0.18+0.32+0.22) \\ C_{0} &=\left(\frac{1.5 L+5}{1-y}\right)=\left(\frac{1.5 \times 6+5}{1-(0.18+0.32+0.22)}\right) \\ &=50 \text { seconds } \end{aligned}
 Question 10
Relationship between traffic speed and density is described using a negatively sloped straight line. If $v_{f}$ is the free flow speed then the speed at which the maximum flow occurs is
 A 0 B $\frac{v_{f}}{4}$ C $\frac{v_{f}}{2}$ D $v_{f}$
GATE CE 2021 SET-2   Transportation Engineering
Question 10 Explanation:
Speed at maximum flow $=\frac{V_{f}}{2}$
There are 10 questions to complete.