This project applies solving systems of equations into solving and analyzing traffic flow problem at the intersection of Poplar Way, Alderwood Mall Parkway, and Interstate 5 in Lynnwood, Washington. Using traffic data provided by Snohomish County Traffic Operations during the AM peak hour on December 4th 2024, this study conducts a network diagram and system of equations representing the traffic movement. By solving the system using Gaussian elimination and reduced row echelon form (RREF), the study comes up with possible traffic distribution to balance the inflow and outflow of the intersection.

Our project analyzes data from a roundabout on Rhodes Road, Jameson St, and SR-9 in Sedro-Woolley to find the average cars/day that travel through the roundabout. The counts of the roundabout depend on a certain part of the roundabout (F₈), which is at minimum 4566 vehicles/day. Based on this minimum value, we can find the minimum average vehicle count for the other parts of the roundabout.

We analyzed the average daily traffic (ADT) at the intersection of Main Street and 104th Ave, Bothell, from June 24, 2024. Given the traffic count collected from the City of Bothell Geographic Information System Services, and using the fact that the incoming and outgoing traffic will add up to zero, we used matrices to calculate the number of vehicles entering and exiting the intersection Southbound from 104th Ave. In addition to this information, we also calculated the vehicle count on Valley View Road connecting to the intersection from the South to show that the total incoming and outgoing flow of traffic adds up to zero.

In this project, we will use matrix of linear equations to calculate and analyze the traffic flow of the one-way street system in downtown Seattle. We will set up a matrix based on equations getting from intersections, and then transform it to Gaussian-Jordan elimination. After that, we will get free variables to determine how important some specific roads are when they are closed, so we can calculate how the vehicle should commute to balance the consistent traffic flow. This approach helps to predict congestion, and identify solutions to reduce pressure on roads in a whole traffic network.

Most of those who have driven through Downtown Seattle have experienced the backed up streets and bottlenecks. In this project, we sought to understand why these problems occur and how they can be addressed. In the process, we found large inconsistencies in the data that the City of Seattle collected and shared, which form barriers to understanding the traffic flow in the area. Following our analysis, which utilized linear algebra methods to solve for the traffic flow along streets between intersections, our primary recommendations to the City of Seattle and the WSDOT are to more carefully collect data and to be more transparent about the way the data is collected. This will ensure accuracy of the data and allow researchers to better understand the nuances of the data, leading to better understanding and the opportunity to improve traffic for the area. 

Government agencies need to understand how traffic flows through their system of roads in order to plan future improvements. As part of these efforts, they collect traffic count information for road segments, and then analyze this data to understand road usage. To better understand these processes and the mathematics involved, we have identified a traffic circle in Skagit county, modeled its network of roads, and performed an analysis revealing the unknowns. This included accounting for inaccuracy in the count data that affected solutioning, and we conclude with interpretation of the system of equations for the unknown and it’s free variable, and suggestion for how such data may be used by a government agency in the future.

Seattle Convention Center on Pike St and 7th Ave experiences long traffic jams during events. Seattle GeoData has total traffic flow for the surrounding streets but no directional traffic. The design of streets in the area dictates how people enter the convention center, pass through the area, and visit the surrounding stores.  Using the total traffic we will using linear algebra to determine the directional traffic around the Seattle Convention Center. The results will influence new design decisions to optimize traffic flow to relieve backups. Patrons of the convention center will have easier access while people driving through will have a faster trip.