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Transport networks in many cities are generally very seriously congested. Consequently, travel time, number of stops, unexpected delays, transport costs, level of air pollution, noise, and traffic accidents are increased. In addition to daily congestion, there may be congestion and traffic jams as a consequence of reconstruction of the roads' lanes. During the past decade, different strategies for transport demand management have been developed, with the aim to decrease existing traffic congestion. One of the available strategies is a ride matching (sharing) concept. This strategy means that several participants share only one private car when traveling from origin to destination. A model for grouping drivers into cars for ride matching, according to similarities of a place of living and working, working hours, and type of car license plate, is developed in this paper. The writers apply the ride matching concept on congested traffic during the reconstruction of the main bridge in Belgrade, Serbia, which is the Gazela Bridge. The basis of the proposed model is the K-means method and even-odd concept. To solve the ride matching problem, the writers present improvement of the traditional K-means algorithm, in which the numbers of centers is unknown in advance and the number of clusters may not be the same as the number of centers. This modification of the traditional K-means algorithm, called advanced K-means, for solving a specific ride matching problem is the main contribution of the paper. [ABSTRACT FROM AUTHOR]