Many urban areas face traffic congestion. Automatic traffic management systems and congestion pricing are getting prominence in recent research. An important stage in such systems is lane prediction and on-road self-positioning. We introduce a novel problem of vehicle self-positioning which involves predicting the number of lanes on the road and localizing the vehicle within those lanes, using the video captured by a dashboard camera. To overcome the disadvantages of most existing low-level vision-based techniques while tackling this complex problem, we formulate a model in which the video is a key observation. The model consists of the number of lanes and vehicle position in those lanes as parameters, hence allowing the use of high-level semantic knowledge. Under this formulation, we employ a lane-width-based model and a maximum-likelihood-estimator making the method tolerant to slight viewing angle variation. The overall approach is tested on real-world videos and is found to be effective.