Question

Question 1
A bank branch has two automatic teller machines (atms) that are accessible at all times (even when the branch is closed).
Customers arrive at the ATMs at a rate of 30 customers per hour with exponentially distributed interarrival times.
Each customer spends an average of 3 minutes to complete the service, where service time is also exponential.
When the branch is open, arriving customers refuse to join the ATM queue if it has 3 people or more waiting, and instead go to receive service
from human tellers.
On the other hand, when the branch is closed, customers have no choice but to join the queue regardless of its length

Q2
when the branch is open the probabilit that both ATMs are idle is (use three decimal places )

Q3
When the branch is open, find the fraction of customers that refuse to join the atm queue (use three decimal places )

Q4
When the branch is open, find the average queue length (use three decimal places )

Answer 1