Traffic Engineering: Flow, Capacity and Signal Design
Traffic stream parameters, fundamental relation q = kv, Greenshields model, capacity, spot and journey speed studies, PCU, and traffic signal design by Webster's method.
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
A road has free speed 60 km/h and jam density 160 veh/km. What is its capacity in veh/h by Greenshields' model?
Show answer and explanation
Answer: 2400q_max = v_f k_j/4 = 60 × 160/4 = 2400 veh/h.
Two phases have critical flow ratios 0.3 and 0.25; total lost time is 10 s. What is Webster's optimum cycle length in seconds? (Give 1 decimal place.)
Show answer and explanation
Answer: 44.4C₀ = (1.5 × 10 + 5)/(1 − 0.55) = 20/0.45 = 44.4 s.
Spot speeds of three vehicles are 30, 40 and 60 km/h. What is the space-mean speed in km/h?
Show answer and explanation
Answer: 40Space-mean speed = harmonic mean = 3/(1/30 + 1/40 + 1/60) = 3/0.075 = 40 km/h (time-mean is 43.3 km/h).
Which percentile of spot speed is generally used to set the speed limit?
Show answer and explanation
Answer: CThe 85th percentile speed is the upper safe limit used for speed regulation.