You're the manager of a local bank where a teller provides service to customers. On average, the teller takes 5 minutes to serve a customer. Customers arrive, on average, at a rate of 10 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks you to evaluate the service system.
Assume that it be a M/M/1 system.
a. What is the average utilization of the service system?
b. What is the probability that no customers are being served in the system?
c. What is the average number of customers waiting in line?
d. On average, how long does a customer wait in line before being served?
e. On average, how many customers would be in the system (i.e., at the teller’s station and in line)?