TAILIEUCHUNG - Choice of the control variables of an isolated intersection by graph colouring
This paper deals with the problem of grouping traffic streams into signal groups on a signalized intersection. Determination of the complete sets of signal groups, . the groups of traffic streams on one intersection, controlled by one control variable is defined in this paper as a graph-coloring problem. The complete sets of signal groups are obtained by coloring the complement of the graph of identical indications. | Yugoslav Journal of Operations Research 25 (2015), Number 1, 117-131 DOI: CHOICE OF THE CONTROL VARIABLES OF AN ISOLATED INTERSECTION BY GRAPH COLOURING Vladan BATANOVIĆ Mihailo Pupin Institute, Volgina 15, 11000 Belgrade, Serbia Slobodan GUBERINIĆ Mihailo Pupin Institute, Volgina 15, 11000 Belgrade, Serbia Radivoj PETROVIĆ Mihailo Pupin Institute, Volgina 15, 11000 Belgrade, Serbia Received: Аugust 2013 / Accepted: October 2013 Abstract: This paper deals with the problem of grouping traffic streams into signal groups on a signalized intersection. Determination of the complete sets of signal groups, . the groups of traffic streams on one intersection, controlled by one control variable is defined in this paper as a graph-coloring problem. The complete sets of signal groups are obtained by coloring the complement of the graph of identical indications. It is shown that the minimal number of signal groups in the complete set of signal groups is equal to the chromatic number of the complement of the graph with identical indications. The problem of finding all complete sets of signal groups with minimal cardinality is formulated as a linear programming problem where the values of variables belong to a set {0,1}. Keywords: Traffic control, Signalized intersection, Signal group, Graph coloring, Optimization. MSC: 90C35. 118 V. Batanović, S. Guberinić, R. Petrović / Choice of the Control Variables 1. INTRODUCTION Vehicles approaching an intersection are ready to perform certain "maneuver", . to drive straight through, turn left, or turn right at the intersection. The vehicles which perform the same maneuver and form the same queue on an approach, in one or several lanes, represent a flow component that can be considered separately from other flow components that perform other maneuvers [1], [2]. Such an arrival flow component is termed as a traffic stream. In
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