3. On average, 60 customers call per hour. The inter-arrival times are exponentially distributed. The customer first waits on hold until one of 20 Phone Technicians is available. The Phone Technicians works with customers an average of 15 minutes (exponentially distributed) to resolve the customer issue.

a) What is the utilization of the phone technicians?

b) How long do customers usually wait to speak to a phone technician (in minutes)?

c) For just the Phone Tech Support, how many customers are waiting and in process?

It turns out that of there are 60 requests coming in per hour (inter-arrival times are exponentially distributed), the Phone Tech Support agent solves 75% of the customer issues. The remainder require an onsite technician dispatched. There is typically an 8 hour wait time before the Onsite Technician arrives at the customers home. The technician works an average of 1 hour at the customer location and they resolve all customer issues they work on.

d) If the company target is to keep the onsite technicians busy 75% of the time, how many technicians need to be staffed?

e) Ignoring your answer to part (b), assume he wait time for a Phone Tech was 2 minutes. For the onsite work described above, recall the wait time was 8 hours and the average service time was 1 hour. What is the average time for all customers from initial call to resolution (in hours)?