Traffic Engineering

Traffic engineering studies how vehicles and people move and how to control them. Learn traffic stream parameters (flow, speed, density), the fundamental diagram, capacity and level of service, traffic studies, intersection control and signal timing (Webster), and ITS.

Congestion costs cities billions each year. Traffic engineers measure how traffic behaves, design intersections and signals, and manage roads to move people safely and efficiently.

Three variables — flow, speed and density — describe any traffic stream, linked by q = k·v.

An analogy

Traffic is like water in a pipe that can compress: as density rises, speed falls, and flow peaks at an in-between density before collapsing into a jam.

Traffic stream basics

Flow is vehicles passing a point per hour; density is vehicles per km at an instant; speed links them. Headway (time gap) and spacing are their microscopic counterparts. Passenger car units (PCU) convert trucks, buses and two-wheelers to equivalent cars.

Fundamental diagram and capacity

As density increases from zero, flow rises to capacity (≈ 1800–2200 veh/h/lane on freeways), then falls as speed collapses toward jam density. Level of service (A–F) grades operating conditions for design.

Intersections and signals

Control hierarchy: priority (give way/stop), roundabouts, signals, grade separation. Signal design: phases, saturation flows (≈ 1800 PCU/h green per lane), lost time, cycle length (Webster's formula minimises delay), green splits, pedestrian timing, coordination along corridors (green waves).

Studies, modelling and ITS

Volume counts, speed studies, origin–destination surveys and parking studies feed transport models (four-step: generation, distribution, mode choice, assignment). Microsimulation (VISSIM, SUMO) tests designs. ITS: adaptive signals (SCOOT/SCATS), ramp metering, variable speed limits and connected vehicles.

Formulas

• Fundamental relation: q = k · v
• Greenshields model: v = v_f(1 − k/k_j), q_max = v_f k_j/4
• Webster optimum cycle: C₀ = (1.5L + 5)/(1 − Y)
• Green split: g_i = (y_i/Y)(C₀ − L)
• Peak hour factor: PHF = V_hour / (4 × V_15,max)

Worked example: Capacity from Greenshields

Given: v_f = 100 km/h, k_j = 150 veh/km

Find: Capacity and optimum speed/density.

• k_opt = k_j/2 = 75 veh/km
• v_opt = v_f/2 = 50 km/h
• q_max = 100 × 150/4 = 3750 veh/h

Answer: 3750 veh/h at 50 km/h

Worked example: Webster cycle

Given: Lost time L = 12 s; Critical flow ratios Y = 0.6

Find: Optimum cycle.

• C₀ = (1.5 × 12 + 5)/(1 − 0.6) = 57.5 s → 60 s

Answer: ≈ 60 s

Common mistakes

• Wrong: Setting very long cycles to 'increase capacity'. — Right: Delay grows; Webster's optimum balances capacity and delay.
• Wrong: Using vehicle counts without PCU conversion in mixed traffic. — Right: Convert to PCUs for capacity analysis.

Applications

• Urban signals: Timing plans, coordination and adaptive control.
• Motorway management: Ramp metering, lane control and incident management.
• Transport planning: Demand modelling for new roads, transit and land use.

Key takeaways

• q = k·v; capacity at mid density.
• Greenshields: q_max = v_f k_j/4.
• Webster: C₀ = (1.5L + 5)/(1 − Y).
• Use PCUs, LOS and simulation for design.

Going further

• Shockwave theory: Speed of queue fronts: w = (q₂ − q₁)/(k₂ − k₁).
• Car-following models: Microscopic models (Gipps, IDM) drive microsimulation.
• Connected & automated vehicles: V2X communication could raise capacity and smooth flow.