Choosing FreewaysMS&E 220 Project

David Andrew HarjuShan LiuXi Wang

Huangxuan Ying

Problem Introduction

• The main goal of this project is to examine the driving preference of the average local driver in a daily choice between Route 101 and Route 280. This research should be pertinent to traffic planners, highway patrol, and any driver who is conscious about travel time.

The Probability Model

• Equation I:

P101(n, k) = P101(n) x P(n - 1; k - 1) + P280(n) x P(n - 1; k)

P101(n) : The probability of choosing route 101 on the nth dayP280(n) : The probability of choosing route 280, which is equal to

1- P101(n).

The Probability Model

• Equation II:P101(n) = If (T280 < T101, 0, If(H < Hlow, 0.9, If(H < Hhigh, 0.5, 0.1)))

T280: historical traffic count of Route 280 T101: historical traffic count of Route 101 H: current humidity Hlow: a lower bound on humidity Hhigh: a higher bound on humidity

Results

P(72, k) for Peak Hours on Route 101. Mean: 1.90 SD: 1.05

Sensitivity Analysis

• Vary the humidity threshold, Hlow and Hhigh. This kind of changes did not significantly change our results, only slightly shifting the distribution of P101(72, k), using Hlow = 60 and Hhigh = 90.

• Vary the parameters in the P101(n) dynamic equation. More specifically, instead of 0, we set P101(n) to a positive value even when T280 < T101, assuming people are less than perfectly rational in their choice:

• Vary drivers' initial route preference. Given various initial conditions for P101 (1, 0), which is the probability of driving on 101 on the first day, we can simulate various distribution of driving pattern for a local population.

Sensitivity Analysis

• P(72, k) for Peak Hours on Route 101, with new preference probabilities. Mean: 10.1 SD: 2.71

Conclusion and Recommendation

• The analysis shows for an individual driver, using route 280 is usually a quite good option. The model did not predict what people would do, but what they ought to do on an individual basis. However, the model is dynamic—if every driver with given historical traffic information, decide to choose 280, then 280 is no longer attractive, the aggregate model breaks down. Fortuitously, the irrationality of people keeps the system alive. The well informed and rational drivers would benefit from such a system.

• Even through our base case result shows that more than 90% of the time people should take 280, it does not mean that 280 is much better than 101 every single time—280 can be only slightly better than 101 for each time. Therefore, the difference can be unnoticeable by drivers. The data does not capture the reasons behind why 280 being less crowed than 101 on most of the days in a year. We also don’t know the percentage of local drivers verse one-time travelers and their impacts on the system.

• Furthermore, weather data is the only “current” factor people would consider in their freeway choice in the model. In reality, real time accident report and other current road information may be more relevant than weather in people’s decision process.