Described is a technology by which driver safety technology such as collision detection is implemented via mobile device (e.g., smartphone) sensors and a cloud service that processes data received from vehicles associated with the devices. Trajectory-related data is received at the cloud service and used to predict collisions between vehicles and/or lane departures of vehicles. To operate the service in real-time with low latency, also described is dividing driving areas into grids, e.g., based upon traffic density, having parallel grid servers each responsible for only vehicles in or approaching its own grid, and other parallel/distributed mechanisms of the cloud service.