Q: What are the limitations of the Greenshields model?

The Greenshields (1935) linear model u = uf(1 − k/kj) gives capacity at k_opt = kj/2. While simple, real highways often show a non-linear speed drop near capacity. The Greenberg logarithmic and Underwood exponential models tend to fit measured data better for high-speed highways. All three models assume single-regime, homogeneous flow.

Question 1

What do LOS A through F mean in traffic engineering?

Accepted Answer

Level of Service (LOS) A through F is defined in the HCM (Highway Capacity Manual). LOS A is free-flow (v/c ≤ 0.35), B is reasonably free (≤ 0.54), C is stable flow (≤ 0.77), D is approaching capacity (≤ 0.90), E is at capacity (≤ 1.0), and LOS F is breakdown/oversaturated (v/c > 1.0). LOS D is typically the minimum acceptable level for design.

Question 2

What is a shockwave in traffic flow?

Accepted Answer

A shockwave is the boundary between two traffic states that propagates along the roadway. Its speed is w = (q₂ − q₁)/(k₂ − k₁). A stopping wave (back of queue) has a negative speed (travels upstream at −15 to −20 km/h). A recovery wave (dissolving queue) has a positive speed and moves downstream.

Question 3

What is Webster's optimal cycle length formula?

Accepted Answer

Webster's (1958) formula is C₀ = (1.5L + 5) / (1 − Y), where L is total lost time (sum of lost times per phase) and Y = Σ(yi) is the sum of critical flow ratios. The formula minimises average delay. Y < 1.0 is required for stable operation; as Y → 1.0, required cycle length approaches infinity.

Question 4

What are the limitations of the Greenshields model?

Accepted Answer

The Greenshields (1935) linear model u = uf(1 − k/kj) gives capacity at k_opt = kj/2. While simple, real highways often show a non-linear speed drop near capacity. The Greenberg logarithmic and Underwood exponential models tend to fit measured data better for high-speed highways. All three models assume single-regime, homogeneous flow.

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