A small call center, staffed by only one operator (server), has 20 customers calling every hour with a standard deviation of inter-arrival times of 3 minutes. (This results in a ca2 = 1.) The activity time for a call center operator to process each call (by addressing the caller’s queries) is, on average, 2.5 minutes with a standard deviation of 5 minutes (or a ce2 = 4), primarily because of the wide variety of caller queries. (Hint: Consider these processing times to be General not Exponential.)
a. What is the average time that a caller has to wait in line before getting served by the call center operator?
b. What is the average number of callers who are in the call center system (either waiting or being served by the operator)?
c. What is the probability that the server will be busy as a %, i.e. what percentage of the time will the staff members be busy?