Sense
Camera and field labels estimate queues, turns, stopped time, discharge, and downstream blockage.
Technology model
From traffic waves to safe signal recommendations.
PATC combines traffic-flow physics, probabilistic state estimation, and constrained optimization. Every recommendation is replayable, bounded, and explainable before it reaches an operator.
Model frame
Traffic is treated as a moving density field.
A road link changes state when arrivals, discharge, startup loss, and downstream capacity are not balanced. Bengaluru-style mixed traffic makes this stochastic: rain, buses, two-wheelers, lane friction, pedestrians, and office surges change the same junction from one window to the next.
PATC estimates the current state and predicts a short horizon. Only after the state is estimated does it ask what timing action is safe enough to recommend.
Core equations
The small set of equations that drive the replay.
Link conservation
rho_i(t + 1) = rho_i(t) + dt / L_i * (q_in - q_out)
Density rises when inflow exceeds outflow and falls when a green phase actually clears vehicles.
Fundamental diagram
q_i(t) = min(v_f * rho_i, w * (rho_jam - rho_i))
Flow increases in free movement, then drops as the link approaches jam density.
Startup-loss correction
q_eff = Pi_m(k) * q_i(t)
A green light does not instantly become moving traffic; drivers hesitate before discharge recovers.
Probabilistic state
x_t = [rho, queue, discharge, phase, blockage] + noise
The estimator keeps uncertainty visible instead of pretending sparse cameras see the full corridor perfectly.
What the math does
It scores the next action, then explains why.
min E[delay + queue + spillback + stops + safety_penalty]
Candidate signal windows are scored against predicted pressure, downstream blockage, startup loss, and safety constraints. The output is a shadow recommendation: action, reason, confidence, expected effect, and fallback trigger.
Measure
Camera and observer data estimate queues, phase state, movement, and blockage.
Predict
The estimator projects arrival waves and uncertainty over the next few windows.
Constrain
Minimum green, pedestrian windows, emergency priority, stale-data stops, and manual override remain hard rules.
Audit
Every recommendation stores the state, action, confidence, and counterfactual replay.
Model contract
What must be measured, bounded, and logged.
State variables
- rho
- vehicles per meter per lane, estimated from camera/observer counts
- queue
- vehicles waiting before each stop line and spillback point
- q
- vehicles per second leaving a lane group during effective green
- phase
- current signal group, elapsed green, minimum-green lockout
Estimator and weights
- Filter
- particle or ensemble Kalman estimator over the next 2-5 signal windows
- Delay
- dominant term, penalizes total stopped seconds
- Queue
- prevents one approach from starving while another clears
- Spillback
- high penalty when a green would feed a blocked downstream link
Hard constraints
- Safety
- minimum green, pedestrian windows, amber/all-red, emergency priority
- Data quality
- stale-camera, low-confidence, rain-glare, and occlusion fallbacks
- Control
- year one is shadow mode: recommend and replay, never write to controller
- Audit
- state, confidence, action, rejected actions, and fallback reason are logged
Validation path
The model earns trust through data, not claims.
Fit density, discharge, startup loss, and spillback behavior from HSR sector observations and labeled sessions.
Run recommendations in parallel without touching signal controllers; compare against observed outcomes and fixed-time baselines.
Only after replay safety gates, ask for an authority-reviewed pilot with before/after metrics.
References