Traffic Engineering: Flow, Capacity and Signal Design

Traffic engineering studies how vehicles move and how roads and junctions should be controlled. GATE asks about traffic flow models and signal timing.

Traffic stream parameters

• Flow (volume) q: vehicles per hour. Density k: vehicles per km. Speed v: km/h.
• Fundamental relation: q = k × v (with v the space-mean speed).
• Time-mean speed (average of spot speeds) ≥ space-mean speed (harmonic mean of spot speeds).
• Headway h = 1/q; spacing s = 1/k.

Greenshields model

Speed falls linearly with density: v = v_f (1 − k/k_j) (v_f = free speed, k_j = jam density).

• Then q = v_f (k − k²/k_j), a parabola.
• Maximum flow (capacity): q_max = v_f k_j/4, at k = k_j/2 and v = v_f/2.

Speed and volume studies

• Spot speed: 85th percentile speed is used for speed limits; 98th for geometric design; 15th for minimum speed limits.
• Journey speed and delay studies: moving observer method.
• PCU (passenger car units) convert mixed traffic to equivalent cars.
• Origin–destination studies for planning.

Traffic signals (Webster's method)

• Critical flow ratio for each phase: y = q/s (q = design flow, s = saturation flow).
• Optimum cycle length: C₀ = (1.5 L + 5)/(1 − Y), with Y = Σy (critical ratios of all phases) and L = total lost time per cycle (s).
• Effective green for each phase is shared in proportion to y: gᵢ = (yᵢ/Y)(C₀ − L).
• Pedestrian crossing time and amber (2–4 s) are added.

Other control: rotaries (weaving sections), grade separation, channelisation.

Accident studies

Collision and condition diagrams; accident rates per million vehicle-km.

Worked example

A road has v_f = 80 km/h and k_j = 120 veh/km (Greenshields).

• Capacity = 80 × 120/4 = 2400 veh/h, at 60 veh/km and 40 km/h.

Practice