solution

Consider a box office at a movie theater where three identical workers sell tickets. Assume that customers arrive at the box office according to a Poisson distribution at a rate of 3 per minute and the service time of each worker is exponentially distributed with a mean of 40 seconds.

a. What type of queue is described here according to Kendall-Lee notation?

b. What is the utilization of each worker? Is this a stable queueing system?

c. What is the steady-state probability that there are no customers at the box office?

d. What is the steady-state probability that all workers are busy?

e. What is the long-run average number of all customers at the box office?

f. What is the long-run average number of customers waiting in line at the box office?

g. What is the long-run average time that a customer spends in the system?

h. What is the long-run average time that a customer spends waiting in line?