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Unformatted text preview: Homework #2 Solution Waiting Lines Management BUAD311 Operations Management Fall 2011 1. (10 pts.) A small credit union has a small branch with two tellers. The arrival rate of customers to the branch is 12 customers per hour and the average service time is 6 minutes. Both interarrival time and service time follow exponential distributions (that is, the coefficient of variation is 1). a. What is the utilization rate? The average service time is given by: p = 6 minutes. The average interarrival time is given by: a = 1/12 hr = 5 minutes. We have two servers ( m =2), so the utilization is u = p /( am ) = 6 minutes / (5 minutes * 2) = 0.6 = 60% b. What is the average waiting time in line? Using the formula for the average waiting time in the line with CV a = CV p = 1, T q = p m u 2( m + 1) 1 1 u CV a 2 + CV p 2 2 = 6 2 0.6 2(2 + 1) 1 1 0.6 = 3.58 min c. What is the average number of customers in system (waiting and in service)? T = T q + p = 9.58 min I = T / a = 9.68/ 5 = 1.916 customers Alternatively, I q = T q / a = 0.716 customers; I p = m(u) (or p/a) = 1.2 customers and hence I = I q + I p = 1.916 customers 2. (25 pts.) Question 3.2 on page 81. a. What is the average time a customer has to wait for the response to his/her e mail, ignoring any transmission time? Note: This includes the time it takes the lawyer to start writing the email and the actual writing time. Since we have 10 emails per hour, the average interarrival time is given by: a = 6 minutes, and we are given that CV a = 1. From the problem, we have m = 1 (since only one lawyer is on call), and p = 5 minutes, with CV p = 4 minutes / 5 minutes = 0.8. This means that the utilization is u = 5/6 = 0.8333. And, the average waiting time for a customer is given by: 1 T q = p m u 2( m + 1) 1 1 u CV a 2 + CV p 2 2 = 5 1 5 6 2(1 + 1) 1 1 5 6 1 2 + 0.8 2 2 = 5 5 1.64 2 = 20.5 min Therefore, the total response time is given by: T = T q + p = 20.5 + 5 = 25.5 min b. How many emails will a lawyer have received at the end of a 10hour day?How many emails will a lawyer have received at the end of a 10hour day?...
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This note was uploaded on 04/01/2012 for the course BUAD 311 taught by Professor Vaitsos during the Fall '07 term at USC.
 Fall '07
 Vaitsos
 Management

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