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This paper presents a Cloud-based system computing customized and practically fast driving routes for an end user using (historical and real-time) traffic conditions and driver behavior. In this system, GPS-equipped taxicabs are employed as mobile sensors constantly probing the traffic rhythm of a city and taxi drivers' intelligence in choosing driving directions in the physical world. Meanwhile, a Cloud aggregates and mines the information from these taxis and other sources from the Internet, like Web maps and weather forecast. The Cloud builds a model incorporating day of the week, time of day, weather conditions, and individual driving strategies (both of the taxi drivers and of the end user for whom the route is being computed). Using this model, our system predicts the traffic conditions of a future time (when the computed route is actually driven) and performs a self-adaptive driving direction service for a particular user. This service gradually learns a user's driving behavior from the user's GPS logs and customizes the fastest route for the user with the help of the Cloud. We evaluate our service using a real-world dataset generated by over 33,000 taxis over a period of 3 months in Beijing. As a result, our service accurately estimates the travel time of a route for a user; hence finding the fastest route customized for the user.