Summary: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2010
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?