# Traffic Engineering

 Question 1
The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements are true? A Speed is higher in Region $\mathrm{R}$ than in Region $\mathrm{P}$ B Volume is lower in Region $Q$ than in Region $P$ C Volume is higher in Region $\mathrm{R}$ than in Region $\mathrm{P}$ D Density is higher in Region $\mathrm{Q}$ than in Region $\mathrm{R}$
GATE CE 2023 SET-2   Transportation Engineering
Question 1 Explanation:
Any vertical line drawn in the graph which cuts arrow lines give positions of vehicles in different regions at a particular time.
Slope of a line in a region represents speed of vehicles in that particular region.

From the Plot :
1. Distance between position of vehicles in region ' $P$ ' is greater than that in region $R \Rightarrow$ Density in region ' $P$ ' is greater than that in region ' $R$ '.
2. Slope of lines in region ' $Q$ ' $=0 \Rightarrow$ Speed of vehicles in region ' $\mathrm{Q}$ ' is zero.
3. Slope of lines in region ' $P$ ' is greater than in region ' $R$ ' $\Rightarrow$ speed of vehicles in region ' $P$ ' is greater than in region ' $R$ '.
4. Since vehicles in region ' $Q$ ' are stationary, flow or volume in region ' $Q$ ' is zero and hence lower than in region $\mathrm{P}$ or region $\mathrm{R}$. And density in region ' $\mathrm{Q}$ ' is higher than in region $\mathrm{P}$ or region $\mathrm{R}$.
5. Boundary between region ' $P$ and ' $R$ ' represents 'forward moving slope wave' means slope is positive.
i.e. $\quad$ slope $=\frac{q_{R}-q_{P}}{K_{R}-K_{P}} \gt 0$
q - Flow
$\mathrm{K}$ - Density.
Since $\mathrm{K}_{\mathrm{R}} \gt \mathrm{K}_{\mathrm{P}}$
$\Rightarrow \mathrm{q}_{\mathrm{R}}$ should be greater than $\mathrm{q}_{\mathrm{P}}$.
$\Rightarrow$ Volume/flow in region ' $R$ ' is higher than in Region 'P'.
 Question 2
A plot of speed-density relationship (linear) of two roads (Road $A$ and Road $B$ ) is shown in the figure. If the capacity of Road $A$ is $C_{A}$ and the capacity of Road $B$ is $C_{B}$, what is $\frac{C_{A}}{C_{B}}$ ?
 A $\frac{k_A}{k_B}$ B $\frac{u_A}{u_B}$ C $\frac{k_Au_A}{k_Bu_B}$ D $\frac{k_Au_B}{k_Bu_A}$
GATE CE 2023 SET-1   Transportation Engineering
Question 2 Explanation:
\begin{aligned} \mathrm{v}_{\mathrm{f}} & =\mathrm{u}_{\mathrm{A}}, \quad \mathrm{k}_{\mathrm{j}}=\mathrm{k}_{\mathrm{A}} \\ \mathrm{c}_{\mathrm{A}} & =\frac{\mathrm{u}_{\mathrm{A}} \mathrm{k}_{\mathrm{A}}}{4} \\ \mathrm{c}_{\mathrm{A}} & =\text { Capacity of road, } \end{aligned}

\begin{aligned} & v_{f}=\text { Free flow speed }=u_{B} \\ & k_{j}=\text { Jam density }=k_{B} \end{aligned}

Capacity of Road 'B' $\left(c_{B}\right)=\frac{u_{B} k_{B}}{4}$
$\therefore \quad \frac{\mathrm{C}_{\mathrm{A}}}{\mathrm{c}_{\mathrm{B}}}=\frac{\mathrm{u}_{\mathrm{A}} \mathrm{k}_{\mathrm{A}}}{4\left(\frac{\mathrm{u}_{\mathrm{B}} \mathrm{k}_{\mathrm{B}}}{4}\right)}=\frac{\mathrm{u}_{\mathrm{A}} \mathrm{k}_{\mathrm{A}}}{\mathrm{u}_{\mathrm{B}} \mathrm{k}_{\mathrm{B}}}$

 Question 3
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 3 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 4
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 4 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 5
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 5 Explanation:
Given that,
Traffic density = 40 Veh/Km.
Time mean speed = 40 Kmph
Space mean speed = 30 kmph
$q=\frac{3600}{H_t}$
where $H_t$- average headway (sc)
$1200=\frac{3600}{H_t}$
$H_t=\frac{3600}{1200}=3$ secs.