What are the density states of S2, S3, and S4 in GATE Civil 2026 Set-1 Q42?

S2→D4, S3→D3, S4→D1. S1 is at density D2 on the unconstrained branch. S2 is a bottleneck and operates on the constrained (congested) branch at the same flow rate, corresponding to density D4. S3 downstream of S2 re-accelerates to free flow at density D3. S4 further downstream spreads further to density D1 — the lowest density free flow state at that flow rate.

Why is S2 at density D4 in GATE Civil 2026 Set-1 Q42?

S2 is capacity constrained (narrower than S1). Traffic from S1 cannot pass freely, causing congestion in S2. S2 operates on the constrained (descending/congested) branch of the flow-density curve. At the same flow rate as S1's operating point, the constrained branch gives density D4 — much higher density than D2, reflecting the congested, slow-moving traffic in the bottleneck.

Why does density decrease from D3 to D1 going from S3 to S4 in GATE Civil 2026 Set-1 Q42?

Both S3 and S4 are unconstrained (wider sections) and operate on the free flow branch. The flow rate is conserved throughout. As traffic moves into progressively wider sections with more capacity, it accelerates and spreads out, reducing density. S3 is at D3 on the unconstrained branch and S4, being even less constrained, is at D1 — the lowest density corresponding to the same flow rate on the free flow branch.

Traffic Flow Density Constrained Unconstrained Sections S1 S2 S3 S4 | GATE Civil 2026 Set-1 Q42

Civil Engineering > GATE 2026 SET-1 > Traffic Flow Theory

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:

S2 → D4 ; S3 → D3 ; S4 → D2

S2 → D3 ; S3 → D2 ; S4 → D1

S2 → D3 ; S3 → D4 ; S4 → D2

S2 → D4 ; S3 → D3 ; S4 → D1

Correct : d

S1 is at density D2 on the unconstrained (free flow) branch — point 2 on the diagram. The flow rate at this operating point is marked by the horizontal dashed line.
S2 is a bottleneck (narrower, capacity constrained). Traffic from S1 cannot pass freely through S2, causing congestion. S2 operates on the constrained (congested) branch at the same flow rate. On the constrained branch this corresponds to point 4 at density D4 — high density, low speed. S2 → D4.
S3 is downstream of S2 and wider — no capacity constraint. Traffic discharging from the constrained S2 re-accelerates into free flow. On the unconstrained branch at the same flow rate, this is point 3 at density D3. S3 → D3.
S4 is further downstream and also unconstrained. With even more road space, the traffic continues to spread out and accelerate further. On the unconstrained branch the same flow rate corresponds to point 1 at density D1 — very low density, high speed. S4 → D1.
Correct answer: D — S2→D4, S3→D3, S4→D1 ✓

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