#### Event Title

#### Location

Parker-Reed, SSWAC

#### Start Date

1-5-2014 2:00 PM

#### End Date

1-5-2014 3:00 PM

#### Project Type

Poster

#### Description

When designing a toll plaza, many factors have to be considered, especially the number of toll booths to build. In this paper, we try to determine the optimal number of toll booths by creating a model for car movement at a toll plaza. We define optimal as the number of toll booths that minimizes the waiting time, particularly at a high congestion time (i.e. rush hour). To model the movement of cars through a toll booth plaza, we break the problem into two parts: time spent waiting in line and then time spent merging back into traffic. Because each of these depend on the number of lanes, toll booths, and traffic, we derive model based upon these parameters. We then apply Queue theory, as each part can be simulated using a queue system. We then simulated multiple runs with a range of number of toll booths, lane numbers and service times. We explicitly consider the conditions where the number of toll booths and lanes were the same as well. We found that the number of toll booths plateaued at the optimal number that provided the shortest time spent going through the plaza and changed based upon the highway lane number.

#### Faculty Sponsor

Lu Lu

#### Sponsoring Department

Colby College. Mathematics and Statistics Dept.

#### CLAS Field of Study

Natural Sciences

#### Event Website

http://www.colby.edu/clas

#### ID

203

Modeling the Optimization of a Toll Booth Plaza

Parker-Reed, SSWAC

When designing a toll plaza, many factors have to be considered, especially the number of toll booths to build. In this paper, we try to determine the optimal number of toll booths by creating a model for car movement at a toll plaza. We define optimal as the number of toll booths that minimizes the waiting time, particularly at a high congestion time (i.e. rush hour). To model the movement of cars through a toll booth plaza, we break the problem into two parts: time spent waiting in line and then time spent merging back into traffic. Because each of these depend on the number of lanes, toll booths, and traffic, we derive model based upon these parameters. We then apply Queue theory, as each part can be simulated using a queue system. We then simulated multiple runs with a range of number of toll booths, lane numbers and service times. We explicitly consider the conditions where the number of toll booths and lanes were the same as well. We found that the number of toll booths plateaued at the optimal number that provided the shortest time spent going through the plaza and changed based upon the highway lane number.

http://digitalcommons.colby.edu/clas/2014/program/254