Stochastic Manufacturing and Service Systems
November twenty-two, 2005
Because of at the start of sophistication on Thurs, December first.
1 . Assume there are two tellers acquiring customers in a bank. Service times at a teller are independent, exponentially sent out random parameters, but the п¬Ѓrst teller has a mean assistance time of four minutes as the second teller has a suggest of 7 moments. There is a solitary queue can be awaiting support. Suppose for noon, a few customers enter the system. Consumer A goes to the п¬Ѓrst teller, B to the second teller, and C queues. To standardize the answers, let us assume that TA is definitely the length of time in less than 10 minutes starting from noonday noontide, meridian until Customer A departs, and in the same way deп¬Ѓne TB and TC.
(a) What is the likelihood that Consumer A it's still in service for time doze: 05? (b) What is the expected period of time that A with the system? (c) What is the expected amount of time that A is in the system if A is still inside the system by 12: 05?
(d) How likely is actually a to п¬Ѓnish before B?
(e) Precisely what is the imply time by noon right up until a customer leaves the bank? (f) What is the regular time until C begins service?
(g) What is the typical time that C with the system?
(h) What is the average time before the system is clear?
(i) What is the likelihood that C leaves prior to A given that B leaves before A? (j) Exactly what the probabilities which a leaves last, B leaves last, and C leaves last? (k) Suppose D enters the program at doze: 10 and A, W, and C are still generally there. Let WD be time that G spends inside the system. Precisely what is the indicate time that D is in the system? installment payments on your Suppose all of us agree to deliver an order in one day. The contract states that if we offer the order within just one day all of us receive $1500. However , in the event the order is late, we lose money proportionate to the tardiness until we all receive absolutely nothing if the buy is 2 days late. The amount of time for us to complete the order is exponentially given away with suggest 0. eight days. For...