dolution

Outcome: Students will analyze a waiting line system
and determine key operating characteristics of the
system.

A customer service center has customers call with questions
about the use of a product. The mean arrival rate of customer
calls is 20 per hour and follows a Poisson distribution. The
mean service rate (how long it takes the call center employee to
answer the customer’s question) is 30 customers per hour (most
customer questions can be answered rather quickly) and follows an
Exponential distribution.

1. What is the mean (average) time in hours that a customer spends
   in the system (waiting on hold, then having their question
   answered)?

1. What is the mean utilization percentage of the call center
   employee answering the phones (the server in this system)?

1. What is the mean number of customers that are on hold, waiting
   for their call to be answered?

d. If the company decides to hire a second person to
answer calls (there are now two “servers” in this system), the
waiting time should be faster. On average, how long will a
customer now wait on hold for their question to be answered?