To find the expected number of customers waiting in line (the average number of customers waiting in line), we can use Little's Law, which relates the average number of customers in a system to the arrival rate and the average time they spend in the system.
Little's Law states: L = λW
Where:
L = Average number of customers in the system (waiting in line + being served)
λ = Arrival rate of customers to the system (customers per unit of time)
W = Average time a customer spends in the system (waiting time + service time)
Given information:
- Arrival rate (λ) = 15 customers per hour
- Average time a customer spends in the system (W) = 12 minutes (convert to hours: 12 minutes / 60 minutes per hour = 0.2 hours)
Now, we can calculate the expected number of customers waiting in line (L) using Little's Law:
L = λW
L = 15 customers per hour * 0.2 hours
L = 3 customers
The expected number of customers waiting in line is 3. This means, on average, there are 3 customers waiting in line to buy tickets at any given time.