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

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

Quizplus · Accepted Answer

To find the system utilization, we need to calculate the average service time and the average time between customer arrivals.

The average service time is given as 3 minutes per customer.

The average time between customer arrivals can be calculated as 1/14 (since there are 14 customers arriving per hour). This is approximately 4.3 minutes.

Using Little's Law, we can calculate the system utilization as the ratio of the average service time to the average time between customer arrivals:

System utilization = (average service time) / (average time between customer arrivals)
System utilization = 3 / 4.3
System utilization ≈ 0.7

Therefore, the answer is B.

Customers Arrive at a Suburban Ticket Outlet at the Rate