1 IE 425 SUMMER 2022 QUIZ # 6: Take-home NAME: ______________________________________________ I have neither given nor received any unauthorized aid in completing this quiz. Signature _______________________________________________ Problem # 1 (10 points) NittanySoft (NS) is a software company that specializes in cloud-based analytics. NS is actually located in downtown State College, next to McDonalds. The owner loves Big Macs, especially the large combo. He believes that this is the perfect location for his business since the lunch break can be cut down to 15 min.: ordering on-line only takes 1 min., pick-up time for the combo never exceeds 4 min., and then he can enjoy this fantastic meal for 10 full min. Wow! What an amazing way to start the afternoon! NS has just set up a call center to provide technical assistance to customers on their software applications. Two technical associates are taking the calls, where the time required by either associate to answer a customer’s questions has an exponential distribution with a mean of 8 min. Calls arrive according to a Poisson process at a rate of 10 per hour. If both associates are busy, arriving customers don’t mind waiting for service while listening to entertaining songs, like “Sweet Caroline” or “Old McDonald had a farm”, and are served following the first-come first-served policy. (a) (1 point) Identify the customers and servers, number of servers, set a time unit for the rates, state the arrival and service rates, define the states of the system, draw the state transition diagram including the transition rates, classify this queueing system according to Kendall’s notation, and determine the utilization factor. (b) (2 points) Determine the steady state probabilities.2 (c) (2 points) Determine the average number of customers in the queueing system (L) and the average number of customers in queue (Lq). (d) (1 point) Compute the average time a customer spends in the system (W) and the average time a customer waits in queue (Wq). (e) (1/2 point) What is the utilization of an associate working in the call center?3 (f) (1 point) What is the probability that a new caller does not need to wait to talk to an associate? (g) (1/2 point) What is the fraction of time the call center is empty? (h) (1 point) If a customer finds both associates busy and there is only one customer in queue upon his/her arrival, what is his/her expected time in the queueing system? (i) (1 point) What is the average number of customers served in the morning (8.00 am to