A bus is a large vehicle which carries a lot of people on a specified route
to a specified destination at a specified time for a specified cost.
A taxi is a smaller vehicle which carries a few people to where they
want to go at a time which suits them for a specified cost.
So what if we combine
the two ideas;
A large vehicle which takes a lot of people to where they want to go for
a specified cost.
The taxibus would begin at a designated point in a city/airport. People
would get on and tell it where they wanted to go at which point it
would begin taking them to the destination. Along the way, anyone
who wanted to jump on could hail the bus (like you hail a taxi) and ask
to be taken to another destination.
If the second destination is on the way, so much the better, the people
who just got on are taken there. If it's not then the people who got on
first are taken where they want to go and then the taxibus proceeds to
the second destination.
At any point people can jump on and request destinations, and in each
case if the destination is nearer or on the way they get dropped off
first, if it's not theirs becomes the second destination.
I think there would need to be computer controlled prioritising for the
destinations based on the amount of time diverting would add to the
current journey (no more than 5% say) weighted against how long
someone has been on the taxibus. Someone who has been on the
taxibus for a while might be allocated a 10% or 15% diversion
allowance, for example. The whole route could be controlled by satnav
and instructions relayed to the driver.
Once there are no passengers the taxibus returns to the nearest starting
zone, or the zone with the most waiting passengers, etc.
I would also argue that system would make more money than a bus or
taxi because it would be a little more expensive than a route bus
(though not much more) and it would not spend very much time running