Max-Pressure Traffic Signal Control — Microscopic 2D

Demand & Service

Boundary arrival rate 18 veh/min

Saturation flow rate 36 veh/min

Minimum green time 6 s

Signal Control

Live Network State

Vehicles in system

Avg queue / approach

0.0

Throughput (exiting network)

0.0 veh/min

How it works

This companion sim keeps the same 3×3 grid and the same real Max-Pressure control law as the 3D version, but replaces its continuous fluid-queue model with a genuine microscopic traffic model: every vehicle is an individual point mass with its own position, speed and acceleration, obeying a safe-stopping-distance car-following rule instead of an aggregate depletion equation.

v_safe = √(2·a_brake·gap)        (real kinematic stopping distance, d = v²/2a)
v_target = min(v_max, v_safe)
v += clamp(v_target − v, −a_brake·dt, a_accel·dt)

Each vehicle brakes exactly hard enough to stop at whatever is closest ahead — a red stop line or the car in front — and accelerates back up once the way clears. The saturation flow rate slider doesn't gate a timer; it sets the minimum bumper-to-bumper following distance at cruising speed via the standard traffic-engineering identity spacing = v_max × (60/satPerMin), so a released queue discharges nose-to-tail at a genuinely different mechanism than the 3D sim's fluid ODE, while still bounding throughput to the requested rate.

Signal control itself is identical maths to the 3D sim: every intersection computes a pressure per phase from its own vehicle counts and the counts immediately downstream,

P(phase) = Σ over movements m in phase of  [ q_upstream(m) − q_downstream(m) ]
switch to argmax P(phase)  whenever  time_in_phase ≥ min_green

Fixed-Time mode ignores queue state and just alternates EW/NS every min_green seconds. Because this version is microscopic, you can watch individual cars brake, queue bumper-to-bumper and pull away — including the real kinematic "start-up lag" every released queue pays, a car-following effect the 3D sim's fluid model cannot show.

Arrival rate — Poisson demand injected at each of the twelve boundary approaches; if entry is jammed, arrivals wait in an invisible off-grid backlog rather than vanishing, exactly like real traffic backing up beyond the modelled area.
Saturation flow rate — sets the following distance a released queue can sustain, i.e. the real capacity of a green lane.
Minimum green — the guaranteed green duration before a switch is even considered.

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