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A traffic reconstruction and prediction algorithm based on probe vehicles is discussed in the present paper. Traffic information is provided by a set of probe vehicles circulating randomly on the network, in the form of average traffic intensity and correlations local in time and spatial position. The road network and the traffic are modeled as a queueing system on a planar graph with local interactions. Using statistical physics methods, a reconstruction algorithm is built and evaluated on a traffic toy model, where the queues have a finite capacity and specific state-dependent transitions rates are used to mimic typical situations of traffic-jams. The reconstruction algorithm consists of a message-passing procedure between sites corresponding to roads-segments at given day-time, which propagates both backward and forward in time, to reconstruct the past traffic and to make predictions. This work is partly funded by the European project REACT and is being implemented on a server for real tests with a fleet of probe cars.