Question

1 Approved Answer

Posted on May 17, 2024

Service Times 7.2 4.3 5.2 4.7 8.4 4.8 5.5 2.5 8.2 4.8 3.8 3.8 4.5 4.6 5.0 3.7 4.7 3.3 5.2 7.5 3.3 3.0 3.4

Service Times
7.2
4.3
5.2
4.7
8.4
4.8
5.5
2.5
8.2
4.8
3.8
3.8
4.5
4.6
5.0
3.7
4.7
3.3
5.2
7.5
3.3
3.0
3.4
3.9
4.0
3.3
4.6
3.2
1.4
5.5
4.6
6.7
3.6
6.8
5.0
4.7
4.0
4.5
3.9
5.7
7.0
3.7
9.0
5.2
10.0
5.8
4.0
2.9
3.0
4.2
8.0
5.6
4.3
7.0
4.2
2.8
4.0
5.3
3.8
5.3
6.0
2.9
5.3
4.9
6.0
3.1
5.5
2.8
5.0
4.1
3.9
4.7
6.5
5.2
5.6
3.8
4.3
6.4
6.0
3.7
3.8
2.9
7.0
3.0
5.5
5.5
5.1
6.5
4.5
5.9
3.3
4.9
5.7
4.6
4.0
6.9
3.4
8.0
4.5
3.2
5.3
5.3
5.7
4.4
4.1
3.7
3.9
2.7
3.0
3.6
5.6
3.2
3.4
3.2
3.4
4.8
4.2
2.3
2.3
3.6
6.7
1.8
2.0
6.0
4.3
4.4
6.4
3.4
9.1
3.9
5.7
3.6
2.6
2.2
6.5
2.6
5.6
4.6
4.9
5.1
3.5
2.5
7.1
4.6
3.9
3.5
5.1
1.8
8.1
3.6
6.7
5.8
1.5
4.3
6.4
3.4
6.5
4.0
2.9
6.2
2.2
5.0
4.4
3.1
4.7
3.7
2.0
3.9
3.3
4.5
3.6
6.7
5.4
3.4
5.4
5.2
5.4
6.8
2.5
6.6
3.6
2.8
4.9
4.3
3.7
3.8
4.2
2.8
2.1
2.4
5.1
3.1
1.9
4.6
3.9
3.1
6.5
6.3
5.5
2.2
3.3
3.1
7.8
4.5
3.5
5.8
4.4
4.3
7.6
3.2
1.6
1.8
5.8
4.0
1.7
5.7
2.9
4.0
2.0
3.3
3.9
4.3
4.5
4.2
5.3
5.7
5.7
4.4
4.3
2.8
5.8
2.8
5.0
3.3
4.5
4.3
4.7
7.4
3.3
3.7
3.1
3.7
4.5
2.4
3.9
3.6
5.0
4.5
8.0
3.4
4.6
4.2
5.3
2.6
7.3
3.6
4.2
5.2
5.2
4.2
1.8
2.0
2.2
3.8
5.4
2.9
2.9
5.0
3.4
2.5
5.6
2.9
6.2
2.3
4.8
6.8
2.3
3.3
4.8
3.3
5.0
3.3
5.2
5.4
4.5
4.2
2.8
7.1
0.9
4.4
5.5
3.6
5.2
3.7
4.2
8.0
2.9
3.1
5.3
1.4
5.7
2.5
1.1
3.9
6.1
7.8
5.1
3.3
4.7
8.2
1.7
5.7
5.1
4.5
3.3
1.5
3.6
4.5
5.2
1.6
3.1
3.2
3.5
3.7
1.5
5.3
3.3
4.4
2.0
4.1
5.9
3.6
4.6
1.6
4.5
2.3
4.1
3.7
6.6
1.7
5.7
3.8
1.6
5.2
5.7
2.7
4.4
2.8
3.8
4.4
3.7
5.6
5.5
4.6
3.4
2.0
1.3
5.4
5.3
4.1
4.7
5.1
2.2
5.3
6.9
2.6
6.1
4.9
3.8
4.1
1.7
1.2
3.5
6.1
2.0
2.0
2.9
5.0
5.3
3.2
1.2
6.5
6.0
2.6
4.4
2.7
3.6
4.1
5.7
3.4
3.9
4.2
1.7
4.6
5.8
3.1
1.7
2.2
3.2
3.1
5.3
3.0
4.1
2.4
5.0
8.2
4.9
3.4
3.7
5.1
4.4
3.4
3.4
3.7
2.9
3.3
5.8
3.0
5.1
3.6
4.3
4.5
6.7
8.0
3.9
4.3
3.0
5.5
1.3
5.3
3.2
3.6
2.2
3.3
4.0
3.2
3.8
4.1
4.8
4.5
3.7
4.2
3.7
3.6
3.7
1.7
4.1
2.3
3.6
6.0
3.7
1.3
1.5
2.2
1.9
4.9
4.4
4.8
6.6
4.4
6.0
3.7
4.5
2.6
3.1
3.0
4.7
3.9
5.5
4.4
5.8
4.3
4.6
2.7
3.2
4.3
3.0
2.7
1.9
7.1
2.9
1.9
6.4
6.3
2.4
4.3
5.1
2.1
4.2
7.3
3.5
4.6
4.5
3.6
2.8
3.1
4.5
3.1
4.1
4.7

The manager has asked you to predict the performance of the drive-thru service system during this time by simulating customer arrival and service for the system.

Assume the system there is one customer being serviced (service to be completed in 3 minutes) and there is one customer in the checkout queue at the beginning of the simulation.

Part I

Construct a simulation model to evaluate the above drive-thru problem for 40 customers.

Make ten independent replications, each of run length 40 customers. (Hint: Run each individual simulation trial using the "One Trial" worksheet in the Example2.5SingleServer.xls spreadsheet.) Record in a separate worksheet each of the ten independent replication results for the observed (1) mean amount of time customers spend waiting in the queue for each trial, and (2) number of instances in which the system is idle for more than 4 minutes for each trial.
Explain the observed differences between the ten trials with respect to the mean amount of time customers spend waiting in the queue, and number of instances in which the system is idle for more than 4 minutes.
Estimate long-run mean time customers spend waiting in the queue with a 95% confidence interval.
Using the results of part (a) and (b), estimate the total number of replications needed to estimate mean time customers spend waiting in the queue within 1 minute.

Part II

Run ten multi-trial replications of the simulation trials, with each replication consisting of 400 simulation trials. (Hint: Run each replication using the "Experiment" worksheet.) Record the observed (1) mean amount of time customers spend waiting in the system for each of the ten replications.
Explain the observed difference in the degree of variability between the mean amount of time customers spend waiting in the queue for the ten individual trials in Part I, and the degree of variability between the mean amount of time customers spend waiting in the queue for the ten multi-trial replications in Part II.