A bank has one drive in teller and room for one additional...

A bank has one drive-in teller and room for one additional customer to wait. Customers arriving when the queue is full park and go inside the bank to transact business. The time between arrivals and service time distributions are given below. Time Between Arrivals (Min) Probability 0 1 2 3 4 5 0.09 0.17 0.27 0.20 0.15 0.12 Service Time (Min) Probability 1 2 3 4 0.20 0.40 0.28 0.12 Simulate the operation of the drive-in teller for 10 new customers. The first of the 10 new customers arrives at a time determined at random. Start the simulation with one customer being served, leaving at time 3, and one in the queue. Assign random numbers for Inter-arrival Time and Service Time. (No need to show random number generation) 1. How many customers went into the bank to transact business? 2. What is the average time the customer spent in the drive-in bank?

Transcript

00:01 Alright, so for this problem, the first thing that i've done, as we can see here, i've copied down the probability tables, and i've added a column of the cumulative probabilities.

00:11 So the reason why i've done that is for doing the simulations in this case.

00:16 I'll be showing how to basically go through and do a by -hand simulation.

00:21 So figuring out the cumulative probabilities is going to be necessary.

00:25 Of course, it's not particularly difficult for the calculations.

00:29 Cumulative probability is always the equal to the probability for the first result, and then for the subsequent results, we would do the previous cumulative plus the current probability.

00:39 But the reason why we do that is because we want to use the cumulative probability to figure out the number range that would reflect a particular result in our simulation.

00:51 So we would have if the cumulative probability is 0 .09 for a result of 0, then a result.

00:58 Between 01 and 09 would reflect a time between arrival of 0.

01:05 Then we can see that we would have from 0 .1, from 10 up to 26 for 1, then from 27 up to 53 for 2, from 54 up to 73 for 3, from 74 up to 88 for 4, and then from 89 up to 0, zero, assuming that we're doing just two digits for a result of five.

01:31 Similarly, we can figure out the cumulative, or the number range for the service time.

01:40 All right, so there we have it shown.

01:43 So now moving along, what i'll do is i'm just going to bring up my preferred sort of software here for generating a bunch of two -digit random numbers.

01:52 So i'll say random integer, and let me just double check the syntax.

01:58 So, right, i want random integer from 0 ,0, up to 99, and i'm going to generate for, i'm going to generate a bunch of these just for the sake of having a large enough data set that i know that i'm not going to run out of values for the simulation.

02:21 All right, so we know that we're told that for our sort of starting point, let's see here, we have customers being served with a value of one.

02:35 Then we have...

02:39 Actually, for arranging the simulation, it's going to be best to basically set this up with a column of time and then a column of, we could say, it's state.

02:52 So we know that at time zero, we have one customer being served.

02:59 So i'll say one served, one in q.

03:03 We know that at time three we have one leaving.

03:14 So, all right, so we'll start going through our numbers.

03:18 For time between arrivals, our first result is that of an 80.

03:22 So we know that we're going to have four time units until our next arrival.

03:26 So that means that we have at time unit four, we have an arrival.

03:35 And for service time, i'll just go to my next two -digit number.

03:38 So we have a result of 34.

03:40 So we can see that the service time falls into the range of two.

03:44 So we know that the when the one who is currently in the queue goes into service, so we have queued is served.

04:03 We know that when we have the, that for the person who enters the queue, or pardon me, who enters service, we have that it's going to take two times, units for them to leave.

04:16 So we have one departure.

04:21 Then from the time of that next arrival, we need to figure out what or how long it will be until the subsequent arrival...

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