Exercise 1
Two-piece suits are processed by a dry cleaner as follows. Suits arrive with exponential interarrival times having mean 10 minutes, and are all initially served by server 1, perhaps after a wait in a FIFO queue; (see Fig bellow). Upon completion of service at server 1, one piece of the suit (the jacket) goes to server 2, and the other part (the pants) to server 3. During service at server 2, the jacket has a probability of 0.05 of being damaged, and while at server 3 the probability of a pair of pants being damaged is 0.10. Upon leaving server 2, the jackets go into a queue for server 4; upon leaving server 3, the pants go into a different queue for server 4. Server 4 matches and reassembles suit parts, initiating this when he is idle and two parts from the same suit are available. If both parts of the reassembled suit are undamaged, the suit is returned to the customer. If either (or both) of the parts is (are) damaged, the suit goes to customer relations (server 5). Assume that all service times are exponential, with the following means (in minutes) and use the indicated stream assignments:
|
Server number
|
Mean service time, in minutes
|
Stream
|
|
1
|
6
|
1
|
|
2
|
4
|
2
|
|
3
|
5
|
3
|
|
4
|
5 (undamaged)
|
4
|
|
4
|
8 (damaged)
|
5
|
|
5
|
12
|
6
|
In addition, use stream 7 for interarrival times, and streams 8 and 9 for determining Whether the pieces are damaged at servers 2 and 3, respectively. The system is initially empty and idle, and runs for exactly 12 hours. Describe in details how you calculate the average and maximum time in the system for each type of outcome (damaged or not), separately, describe how you calculate the average and maximum length of each queue, and the utilization of each server. Describe what need to be done to simulate the system if the arrival rate were to double (i.e., the interarrival-time mean were 5 minutesinstead of 10 minutes)? In this case, if you could place another person anywhere in the system to help out with one of the 5 tasks, how do you figure out where should it be?
Exercise 2
In the following hand simulation of the simple processing system which was discussed in the class.The original Arrival, Interarrival and service time of parts is shown bellow
|
Part Number
|
Arrival Time
|
Interanival Time
|
Service Time
|
|
1
|
0.00
|
1.73
|
2.90
|
|
2
|
1.73
|
1.35
|
1.76
|
|
3
|
3.08
|
0.71
|
3.39
|
|
4
|
3.79
|
0.62
|
4.52
|
|
5
|
4.41
|
14.28
|
4.46
|
|
6
|
18.69
|
0.70
|
4.36
|
|
7
|
19.39
|
15.52
|
2.07
|
|
8
|
34.91
|
3.15
|
3.36
|
|
9
|
38.06
|
1.76
|
2.37
|
|
10
|
39.82
|
1.00
|
5.38
|
|
11
|
40.82
|
|
|
Suppose that a constant setup time of 3 minutes was required once a part entered the drill press but before its service could actually begin. When a setup is going on, regard the drill press as being busy. (Hint: Simply add 3 to each service time).Plot the total number of parts in system as a function of simulated time. As numerical output performance measures, report the total production (number of parts produced), the average and maximum waiting time in queue, the average and maximum total time in system, the time-average and maximum number of parts in queue, and the drill-press utilization. Redo the hand simulation and discuss the results.
The original record of the hand simulation is shown bellow which needs to be updated based on new data:
