00:01
For this problem, to begin, we know that customers arrive at a rate of six per hour, we know that customers are served, or i'll put it this way, it takes an average of 10 minutes per car repair, which means that the mechanics are able to serve about six customers per hour on average.
00:23
Okay, pardon me, i needed to pause for a second there.
00:26
So for part a, to find the probability of no cars waiting in the system p zero, we take one minus rho, where rho is equal to lambda over mu.
00:39
So that would be simply, since lambda and mu are equal to each other, this would be one minus one, which is equal to zero, immediately, we can recognize that there's going to be a problem here.
00:49
Since rho is equal to one, that means that the system is unstable, which means that only in the sort of ideal circumstance, will the singular mechanic actually be able to keep up with demand.
01:05
For part b, to find the average number of cars waiting in the system, well, this is the point where we start seeing why things basically start falling apart.
01:17
We have that the average number of cars waiting in the system l would be calculated as rho divided by one minus rho, which would be one divided by one minus one, which is undefined.
01:36
But we can say that in the limit, as rho approaches one, we have that rho over or not rho equals one in the limit as rho approaches one, we have rho over one minus rho will be approaching infinity...