Probability in the Engineering and Informational Sciences

Table of Contents - July 2012 - Volume 26, Issue 03  

Research Article

DELAYS AT SIGNALIZED INTERSECTIONS WITH EXHAUSTIVE TRAFFIC CONTROL*

M.A.A. Boona1, I.J.B.F. Adana1, E.M.M. Winandsa2 and D.G. Downa3

a1 EURANDOM and Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands E-mail: marko@win.tue.nl, iadan@win.tue.nl

a2 FNWIKorteweg de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, P.O. Box 942481090, GE AMSTERDAM, The Netherlands E-mail: emm.winands@few.vu.nl

a3 McMaster University, 1280 Main Street West, Hamilton, ON, Canada L8S 4L7 E-mail: downd@mcmaster.ca

Abstract

In this paper, we study a traffic intersection with vehicle-actuated traffic signal control. Traffic lights stay green until all lanes within a group are emptied. Assuming general renewal arrival processes, we derive exact limiting distributions of the delays under heavy traffic (HT) conditions. Furthermore, we derive the light traffic (LT) limit of the mean delays for intersections with Poisson arrivals, and develop a heuristic adaptation of this limit to capture the LT behavior for other interarrival-time distributions. We combine the LT and HT results to develop closed-form approximations for the mean delays of vehicles in each lane. These closed-form approximations are quite accurate, very insightful, and simple to implement.

Footnotes

* The research was done in the framework of the BSIK/BRICKS project, and of the European Network of Excellence Euro-NF.