#### Project Title

### Modeling Traffic at an Intersection

#### Disciplines

Numerical Analysis and Computation | Other Applied Mathematics | Probability | Statistical Models | Theory and Algorithms

#### Abstract (300 words maximum)

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program we compute: the number of vehicles in the queue every time a vehicle arrives and leaves the intersection, the service time, and the total time the vehicle spends in the queue, or the sojourn time. We describe the probability distribution of the queue length in the long run and analyze its dependence on and the durations of the green and red light. Using regression we build a model for the dependence of the average queue length and the average service time on and the durations of the green and red light.

Based on the regression results we propose traffic models that achieve optimal queue lengths and sojourn times.

#### Academic department under which the project should be listed

CSM - Mathematics

#### Primary Investigator (PI) Name

Anda Gadidov

#### Included in

Numerical Analysis and Computation Commons, Other Applied Mathematics Commons, Probability Commons, Statistical Models Commons, Theory and Algorithms Commons

Modeling Traffic at an Intersection

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program we compute: the number of vehicles in the queue every time a vehicle arrives and leaves the intersection, the service time, and the total time the vehicle spends in the queue, or the sojourn time. We describe the probability distribution of the queue length in the long run and analyze its dependence on and the durations of the green and red light. Using regression we build a model for the dependence of the average queue length and the average service time on and the durations of the green and red light.

Based on the regression results we propose traffic models that achieve optimal queue lengths and sojourn times.