In message , at 18:21:49 on Tue, 6 Oct 2015,
tim..... remarked:

It's not necessarily important for every private hire vehicle to
offer disability access, because the are pre-booked. As long as
each firm has some minimum number of such vehicles available if
requested, that should be sufficient.

That I understand

but unless that "minimum number" is somewhat larger than you might
first calculate, you either end up with the accessible cabs waiting
around all day for the one disabled passenger, or no accessible
cabs free at the time that passenger turns up.

It's queuing theory 101, not that difficult.

to a graduate level statistician perhaps,

You do Stats 101 in the first year!

In the first year of what?

The undergraduate course. I can't believe you really didn't know that.

to the average numpty who runs a cab office?

You think decisions about fleet procurement are done by a numpty in
the cab office?

Yep

That explains quite a lot.

What's likely to happen is that there's a ready reckoner, perhaps
even stipulated by the local authority, saying something like:
"fleets of 2-10 should have one accessible vehicle; 11-25 three;
26-50 four" or whatever.

But the numpty dispatcher can also use their experience to see how
often a person wanting an accessible car is kept waiting "too long",
and make recommendations to the owner.

btw, they don't sit around waiting for an accessible fare - they take
regular passengers if there's no booking in the queue for an
accessible ride.

so then the disabled pax might have an hour wait for a free cab

That's why you need a sensible ratio, but it's not 100% of the cars.

To wait an hour for the next accessible cab to be available would
indicate an *extremely* small fleet, of course.
--
Roland Perry