Teaching Mathematics and its Applications Advance Access originally published online on February 17, 2009
Teaching Mathematics and its Applications 2009 28(1):38-42; doi:10.1093/teamat/hrp002
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Minimizing the delay at traffic lights
Department of Applied Engineering Sciences, University College Ghent, Schoonmeersstraat 52, 9000 Gent, Belgium
Email: tanja.vanhecke{at}hogent.be
Submitted November 2008; accepted January 2009
Vehicles holding at traffic lights is a typical queuing problem. At crossings the vehicles experience delay in both directions. Longer periods with green lights in one direction are disadvantageous for the vehicles coming from the other direction. The total delay for getting through the traffic point is what counts. This article presents an expression to calculate the optimal time periods of red lights and green lights starting from a fixed-cycle time. The solution is optimal if it makes the traffic jam delay at the road crossing minimal. As these solutions depend on the number of cars arriving in the different directions, which is not constant during the day, the application can be enlarged to a system where the time periods of red and green lights change during the day.
Tanja Van Hecke obtained the master degree in applied mathematics in 1995 at the University of Ghent. In 1998 she finished her doctoral theses in numerical analysis. Since 2000 she works at the Faculty of Applied Engineering Sciences at the University College Ghent where she gives several courses in mathematics ands statistics.