Location

Parker-Reed, SSWAC

Start Date

1-5-2014 1:00 PM

End Date

1-5-2014 2:00 PM

Project Type

Poster

Description

One of the biggest woes of highway drivers is the amount of tolls along the road that require each vehicle to not only slow down significantly, but also pay sometimes up to -8 to the State. This inconvenience is protested on various levels, but since its clear that the government must institute some type of toll system, we have decided to find a model that will at least optimize the time for each driver while still saving the State as much money as possible. Our report constructs a model of the ideal amount of tollbooths for any number of highway lanes, taking a multitude of factors into consideration. We have made a set of equations that calculates the optimal number of tollbooths needed in order to minimize the arrival, waiting, and merging time it takes for customers to move through the system while also taking into account the cost of each added tollbooth, considering the price of building and maintaining a new booth. We specifically modeled the arrival rates of cars coming into tollbooth plazas, the amount of time customers have to wait in line for service, the service time, and the merging/departure time through various diagrams, highway data, and personal experiences. These combined sources have led us to assume that each driver will find the shortest line to optimize their own personal waiting time before going through the booth at a constant service time of about 30 seconds. Based on the data weve collected, we used the Poisson Random Process to model both the arrival rates and waiting times. Our answer to this original concern can therefore be applied to a wide range of highways and interstates, and in turn will decrease the amount of traffic congestion while creating a convenient and profitable tollbooth system.

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

248

Included in

Mathematics Commons

Share

COinS
 
May 1st, 1:00 PM May 1st, 2:00 PM

The Highway Game: Optimizing the Number of Tollbooths

Parker-Reed, SSWAC

One of the biggest woes of highway drivers is the amount of tolls along the road that require each vehicle to not only slow down significantly, but also pay sometimes up to -8 to the State. This inconvenience is protested on various levels, but since its clear that the government must institute some type of toll system, we have decided to find a model that will at least optimize the time for each driver while still saving the State as much money as possible. Our report constructs a model of the ideal amount of tollbooths for any number of highway lanes, taking a multitude of factors into consideration. We have made a set of equations that calculates the optimal number of tollbooths needed in order to minimize the arrival, waiting, and merging time it takes for customers to move through the system while also taking into account the cost of each added tollbooth, considering the price of building and maintaining a new booth. We specifically modeled the arrival rates of cars coming into tollbooth plazas, the amount of time customers have to wait in line for service, the service time, and the merging/departure time through various diagrams, highway data, and personal experiences. These combined sources have led us to assume that each driver will find the shortest line to optimize their own personal waiting time before going through the booth at a constant service time of about 30 seconds. Based on the data weve collected, we used the Poisson Random Process to model both the arrival rates and waiting times. Our answer to this original concern can therefore be applied to a wide range of highways and interstates, and in turn will decrease the amount of traffic congestion while creating a convenient and profitable tollbooth system.

http://digitalcommons.colby.edu/clas/2014/program/305