I'm saying you can keep track of all the riders and drivers, matchmake, start/progress/complete trips, with a single server, for the entire world.
Billing, serving assets like map tiles, etc. not included.
Some key things to understand:
* The scale of Uber is not that high. A big city surely has * The driver and rider phones participate in the state keeping. They send updates every 4 seconds, but they only have to be online to start a trip. Both mobiles cache a trip log that gets uploaded when network is available.
* Since driver/rider send updates every 4 seconds, and since you don't need to be online to continue or end a trip, you don't even need an active spare for the server. A hot spare can rebuild the world state in 4 seconds. State for a rider and driver is just a few bytes each for id, position and status.
* Since you'll have the rider and driver trip logs from their phones, you don't necessarily have to log the ride server side either. Its also OK to lose a little data on the server. You can use UDP.
Don't forget that in the olden times, all the taxis in a city like New York were dispatched by humans. All the police in the city were dispatched by humans. You can replace a building of dispatchers with a good server and mobile hardware working together.