
Problem Title: Tollbooths 




Year: 2005 




Student Level: Undergraduate 




Source: MCM 




Commentary: Yes (1) 




Student Papers: Yes (7) 







Problem 


Heavilytraveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multilane divided highways that are interrupted at intervals by toll plazas. Because collecting tolls is usually unpopular, it is desirable to minimize motorist annoyance by limiting the amount of traffic disruption caused by the toll plazas. Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza. Upon entering the toll plaza, the flow of vehicles fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze back down to a number of travel lanes equal to the number of travel lanes before the toll plaza. Consequently, when traffic is heavy, congestion increases upon departure from the toll plaza. When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll.
Make a model to help you determine the optimal number of tollbooths to deploy in a barriertoll plaza. Explicitly consider the scenario where there is exactly one tollbooth per incoming travel lane. Under what conditions is this more or less effective than the current practice? Note that the definition of "optimal" is up to you to determine.








Commentary 




Judge's Commentary:
The Outstanding Tollbooths Papers
Kelly Black
Dept. of Mathematics
Union College










Student Papers 




The Booth Tolls for Thee
Duke University, Durham, NC








A SingleCar Interaction Model of
Traffic for a Highway Toll Plaza
Harvard University, Cambridge, MA








Lane Changes and Close Following:
Troublesome Tollbooth Traffic
Massachusetts Institute of Technology, Cambridge, MA








A QuasiSequential
CellularAutomaton Approach
to Traffic Modeling
Rensselaer Polytechnic Institute, Troy, NY








The Multiple Single Server
Queueing System
University of California, Berkeley, Berkeley, CA








Two Tools for Tollbooth
Optimization
University of California, Berkeley, Berkeley, CA








For Whom the Booth Tolls
University of Colorado, Boulder, CO









