Two-piece suits are processed by a dry cleaner as follows. Suits arrive with exponential i...

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. 2.67. 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:

FIGURE 2.67 A dry-cleaning operation.

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. Observe the average and maximum time in the system for each type of outcome (damaged or not), separately, the average and maximum length of each queue, and the utilization of each server. What would happen if the arrival rate were to double (i.e., the interarrival-time mean were 5 minutes instead 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, where should it be?