00:01
For this problem, we are told that at a service counter of a fast food joint, the customers arrive at the average interval of six minutes.
00:08
So our arrival rate, lambda, is equal to 1 per 6 minutes.
00:16
So that would be 10 per 60 minutes.
00:23
So that would then be 10 per hour.
00:29
Let's see here.
00:30
And the counter clerk takes on average five minutes for preparation of bill and delivery of the item.
00:38
So the service rate, mu, is 1 per 5 minutes, which would be 12 per 60, or that's 12 per hour.
00:48
Whereas to calculate the following, first, the counter -utilization level.
00:53
So that is typically used or given by the symbol s, which is going to be equal to lambda over mu.
01:00
That's 10 over 12, or is a decimal value that's 0 .833 repeating.
01:06
For part 2, average waiting time of the customers at the fast food joint or the system.
01:13
So that's the average waiting for the system, which is 1 over mu minus lambda.
01:18
That's 1 over 12 minus 10, which is then going to be 1 over 2 or 0 .5.
01:25
Part 3, we're asked for the expected average waiting time in the line.
01:31
So wq is equal to lambda divided by mu times mu minus lambda...