A system of linear equations was used to analyze the flow of traffic for a network of
Question:
A system of linear equations was used to analyze the flow of traffic for a network of four one-way streets in Lautoka, Fiji. The data was obtained by counting the number of vehicles that travelled around the four one-way streets between the hours of 6am to 10pm, and 2pm to 6pm during the midweek peak traffic hours. The arrows in the diagram indicate the direction of flow of traffic in and out of the network that is measured in terms of number of vehicles per hour (vph). The diagram below describes the four one-way streets in Lautoka under study in the model
Model Assumptions : The following assumptions were made in order to ensure the smooth flow of the traffic;
(i) Vehicles entering each intersection should always be equal to the num- ber of vehicles leaving the intersection.
(ii) The streets must all be one-way with the arrows indicating the direction of traffic flow.
(i) Setup and use the Gauss-Jordan elimination method to solve the system of equations for w, x, y, and z.
(ii) If we take a construction limit on road w to be 100vph, then the values of x, y, and z will be.
(iii) If all the directions are reversed in the figure above, discuss what hap- pens.
A Survey of Mathematics with Applications
ISBN: 978-0134112107
10th edition
Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde