Monte Carlo Simulation for Traffic Light Optimization

Introduction

Imagine sitting in traffic, watching the light turn red just as you pull up—frustrating, right? As an engineering student fascinated by how cities work, I wanted to tackle this everyday problem using Monte Carlo simulation, a cool statistical method that uses random sampling to predict uncertain outcomes. In this experiment, I simulated traffic at a single intersection to find the best light timing that reduces wait times and keeps cars moving smoothly.

By modeling random car arrivals (like how traffic ebbs and flows unpredictably), I tested different light cycles over a one-hour period. This isn't just theory—it's a practical way to make roads more efficient, cutting down on wasted time and fuel. Drawing from basic queue theory and real traffic data, my goal was to see if computer simulations could beat traditional fixed timings, and the results were eye-opening!

How I Did the Experiment

I built the simulation in Google Colab using Python—it's free and easy to share. The setup mimics a four-way intersection with east-west (EW) and north-south (NS) directions. Cars arrive randomly following a Poisson process (think of it as bursts of traffic with quiet spells), at rates of 0.8 cars per minute EW and 0.6 NS—realistic for a suburban spot.

The key was a TrafficLightSimulator class that cycles through green (cars go) and yellow (caution) phases for each direction. I tested four simple scenarios, changing how long each side gets green:

• Short Cycle: 30s EW green, 25s NS green (total 61s cycle)

• Medium Cycle: 45s EW green, 40s NS green (total 93s)

• Long Cycle: 60s EW green, 55s NS green (total 125s)

• Rush Hour Setup: 70s EW green, 30s NS green (total 110s, favoring busier EW)

For reliability, I ran each scenario 100 times (Monte Carlo magic!), tracking metrics like average wait time, queue length, cars processed per hour (throughput), and an efficiency score (throughput divided by wait time). I also compared results to Webster's formula, a classic equation for ideal cycle time:

Theoretical Benchmark

• Webster’s Formula:

  • Theoretical optimal cycle time: 17.8 seconds

  • Theoretical green (EW): 5.6 seconds

  • Theoretical green (NS): 4.2 seconds

  • Critical flow ratio: 0.047

These theoretical values favor shorter cycles under moderate flows, consistent with the simulation’s preference for the Short Cycle configuration.

Probability Analysis of Arrivals

• Average vehicles per minute: 0.69

• Standard deviation: 0.83

• Probability of high traffic (> ~1.5 vehicles/min): 0.150

• Probability of zero arrivals per minute: 0.506

This variability explains why shorter cycles reduce excessive waiting during random lulls and spikes.

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