Monte Carlo Commute Time Simulator
Problem Context
The Problem: Calculate the time it takes to commute from home to the office.
We are trying to answer:
- How much time do I need to allow in order to have 75% confidence that I will arrive on time?
- How much time should I allow in order to have 99.5% confidence that I will arrive on time (on days that start with an important meeting)?
The Situation:
- Drive 2 miles on a highway (Segment 1): 90% probability of averaging 65 MPH, 10% probability of averaging 20 MPH due to a traffic jam.
- Intersection: Encounter a traffic light that is red for 90 seconds and green for 30 seconds.
- Travel 2 more miles on a surface street (Segment 2): 70% probability of averaging 30 MPH, 10% probability of 20 MPH, 10% probability of 40 MPH, and 10% probability of a traffic jam taking 30 minutes for this segment.
Simulation Parameters
Highway Segment (2 miles)
Traffic Light
Surface Street (2 miles)
Teaching Notes
This Monte Carlo simulation demonstrates:
- How to model uncertainty in a commute using probability distributions
- The importance of understanding tail events in risk management
- The difference between planning for regular days (75% confidence) vs. critical days (99.5%)
- How to identify which segment contributes most to the overall variability
Simulation Results
Run the simulation to see results
Mean Time
Min Time
Max Time
75% Confidence
99.5% Confidence
Distribution of Commute Times
Key Insight:
Segment Contribution to Variance
Highway
Traffic Light
Surface Street
Simulation Tool