ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2010 April 14, 2010 Summary: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2010 H. Ayhan Homework 6 April 14, 2010 (Due: April 22) 1. Suppose there are two tellers taking customers in a bank. Service times at a teller are independent, exponentially distributed random variables, but the first teller has a mean service time of 3 minutes while the second teller has a mean of 6 minutes. There is a single queue for customers awaiting service. Suppose at noon, 3 customers enter the system. Customer A goes to the first teller, B to the second teller, and C queues. To standardize the answers, let us assume that TA is the length of time in minutes starting from noon until Customer A departs, and similarly define TB and TC. (a) What is the probability that Customer A will still be in service at time 12:05? (b) What is the expected length of time that A is in the system? (c) What is the expected length of time that A is in the system if A is still in the system at 12:05? (d) How likely is A to finish before B? (e) What is the mean time from noon until a customer leaves the bank? (f) What is the average time until C starts service? (g) What is the average time that C is in the system? (h) What is the average time until the system is empty? (i) What is the probability that C leaves before A given that B leaves before A? Collections: Engineering