OK, let's take a very oversimplified scenario.
A post office has three counters, and it takes (an average of) 5 minutes
per customer per transaction. The counters are manned during opening
times for 10 hours per day (eg 8am to 6pm). That means 120 (12 per hour
x 10) transactions per day at each desk or 3 x 120 = 360 transactions
per day across all 3 desks. So the PO sets up to man the 3 desks for 10
hours per day.
But of course, that's the average - some transactions are longer, some
shorter. Also some customers carry out more than one transaction during
their visit. Now look at the queue lengths, customers don't arrive at
1.66 minute intervals (i.e. 5/3), they arrive randomly! So at opening
time there may be a rush, the doors open with a small queue outside, say
12 people, this is dealt with and arrival of customers may increase
until, say 11am, when the desks have caught up with the backlog. Then
things are quiet until the 1:00pm lunchtime rush and instead of the
'planned' 72 customers, only 48 arrive. The staff have a breather, but
they are 24 transactions short of the 'plan'. When the afternoon rush
brings the 'missing' 24 customer transactions. the queue length is now 8
per desk or 40 minutes! By the end of the day, counters are closed and
some customers asked to 'come back tomorrow'. The service efficiency is
judged at (360-24)/360 = 93.3% and a number of customers somewhat
disgruntled.
That may seem complicated (and easy to get round!) but of course real
life is much more random & unpredictable. In the situation described it
can be resolved by the manager manning a temporary desk during the peak
for 2 hours to deal with the 24 customers who might otherwise be turned
away.
My point was that waiting time will always increase, because as we
balance supply with demand, anytime a customer is late, the waiting time
increases, anytime an operative is off sick, the waiting time increases,
etc. If management 'MATCH' supply to demand - the waiting time will
always increase and never decrease! Indeed, I've heard of maternity
wards so busy that there's a 12 month waiting time for a bed! Geddit?
So once we get to the NHS, we have triage to sort out the different
urgencies and decide which can wait and which can't; and get them to the
right specialism. And there's no 'average time per transaction', AND no
'manager' to step in, we can see how difficult it is to balance supply
and demand.
Mike
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Mike Davis