List of top Transportation Engineering Questions on Fundamental relationships asked in GATE CE

For a given traffic stream, the speed-density relationship is given as:

\[ v = v_o \ln\left(\frac{k_j}{k}\right) \]

where \(v\) is the mean speed (in km/h), and \(k\) is the density (in veh/km).

Considering \(v_o\) as 45 km/h, and \(k_j\) as 200 veh/km, the maximum flow (in veh/h) for the given stream is (rounded off to the nearest integer).
A road is divided into four sections having varying widths as shown in the figure. Section-2 (S2) represents a capacity constrained condition with respect to the traffic flow passing through Section-1 (S1). Section-3 (S3) and Section-4 (S4) do not face any such capacity constraint with respect to the flow. A flow-density relationship for unconstrained and constrained flow conditions is shown in the figure.

If Section-1 observes density D2, the option representing the correct state of density in Sections 2, 3 and 4 is:

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 \(\frac{C_A}{C_B}\)? 

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: 
 

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 _________ \text{km/h}. (in integer)
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?

On a road, the speed – density relationship of a traffic stream is given by \( u = 70 - 0.7k \) where speed, u, is in km/h and density, k, is in veh/km.  At the capacity condition, the average time headway will be: