Question

we have a system, such as a bank, where customers arrive and wait on a
line until one of k tellers is available.Customer arrival is governed
by a probability distribution function, as is the service time (the
amount of time to be served once a teller is available). We are
interested in statistics such as how long on average a customer has to
wait or how long the line might be.

We can use the probability functions to generate an input stream
consisting of ordered pairs of arrival time and service time for each
customer, sorted by arrival time. We do not need to use the exact time
of day. Rather, we can use a quantum unit, which we will refer to as
a tick.

One way to do this simulation is to start a simulation clock at zero
ticks. We then advance the clock one tick at a time, checking to see
if there is an event. If there is, then we process the event(s) and
compile statistics. When there are no customers left in the input
stream and all the tellers are free, then the simulation is over.

The problem with this simulation strategy is that its running time
does not depend on the number of customers or events (there are two
events per customer), but instead depends on the number of ticks,
which is not really part of the input. To see why this is important,
suppose we changed the clock units to milliticks and multiplied all
the times in the input by 1,000. The result would be that the
simulation would take 1,000 times longer!

My question on above text is how author came in last paragraph what does author mean by ” suppose we changed the clock units to milliticks and multiplied all the times in the input by 1,000. The result would be that the simulation would take 1,000 times longer!” ?

Thanks!

Answer 1

With this algorithm we have to check every tick. More ticks there are the more checks we carry out. For example if first customers arrives at 3rd tick, then we had to do 2 unnecessary checks. But if we would check every millitick then we would have to do 2999 unnecessary checks.