Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays.
What is the system utilization?
A) 0.6
B) 0.7
C) 0.8
D) 0.9
E) 1

Question

Quizplus · Accepted Answer

System utilization ($ρ$) in a queuing system is calculated as $ρ = \lambda / \mu$, where $\lambda$ is the arrival rate and $\mu$ is the service rate. Here, $\lambda = 14$ customers per hour and the service time is 3 minutes per customer, which translates to 20 customers per hour ($60 / 3 = 20$). Thus, $ρ = 14 / 20 = 0.7$.

Customers Arrive at a Suburban Ticket Outlet at the Rate