We provide tech support to all our computer users, both inside Central and for vendors and customers who use our integrated systems. We operate that support center with one consultant. We take calls and live online chats. If the consultant is busy when a new call arrives, the caller will hear a recorded message stating that all consultants are busy but to hold and a consultant will be with them as soon as possible. The incoming calls follow a Poisson distribution with an arrival rate of 5 per hour. On average, it takes 7.5 minutes for the consultant to answer the questions. The service time is well approximated by an exponential probability distribution. Powers wants a report on the facts of our current system and to anticipate what we will need to do with the anticipated growth.
1. What is our current service rate in terms of customers per hour?
2. What is the probability that NO customers are in the system and that the consultant could be using the time on other tasks?
3. What is the average number of customers waiting for the consultant?
4. We don’t want any customer to wait more than two minutes for a consultant. Are we achieving that?
5. What is the probability that a customer will have to wait for a consultant?
6. Our policy is that no customer should wait more than 2 minutes. If demand increases to an arrival rate of 7 per hour, can we achieve that goal by adding just one more consultant who services at the same speed?