If they get around to it, they would probably offer several subscription levels. Pay more, and you're guaranteed a swankier car, be frugal and it's a crapshoot, maybe you get a boring Tata, or you get a Jaguar.

Also, if the taxi fleet knows where everyone is going, they can easily organize a car-pool. If you're frugal then you'll be okay with pooling, pay more if you want the exclusivity (or, if you have the frugal plan, you can pay 10 bucks more this morning if you want to be left alone...).

The Jaguar vs Tata would make a fun algorithm. Say you're the frugal one, you order a car, and a Jaguar is heading your way. Suddenly your neighbor (on the premium plan) orders a car, and someone else a few minutes away cancelled their Tata. Oops, sorry, he gets the Jaguar.

Edit: Changed "Mercedes" to "Jaguar"