How does the tolling system detect when a vehicle has exited the excluded roadways and should therefore be charged a toll? 

The tolling system in Manhattan uses a combination of advanced technologies to detect when a vehicle exits the excluded roadways and enters the tolled Congestion Relief Zone: 
 
Electronic Tolling Gantries: These are strategically placed at entry and exit points of the tolled zone. They use cameras and sensors to capture the license plates of vehicles as they pass through. 
GPS Tracking: Some vehicles, especially commercial ones, may be equipped with GPS devices that communicate with the tolling system to provide real-time location data. This helps in determining if a vehicle has entered the tolled area. 
Automatic Number Plate Recognition (ANPR): This technology is used to read and record the license plates of vehicles. The system cross-references this data with the entry and exit points to determine if a vehicle has traveled within the tolled zone. 
 
By using these technologies, the tolling authority can effectively monitor and charge vehicles that leave the excluded roadways and enter the congestion pricing zone.