Topic: Continuous-Time Markov Chains

Question:Customers arrive in a government office with three service windows at a rate of 10 per hour. Transactions in each service window takes 15 minutes, on average. Moreover, customers would only be willing to wait 30 minutes, on average, in line or they would leave the office without being served. Assume that the number of customers in the office at any given time follows a birth and death process. Find the expected amount of time (in hours) needed for the office to go from having 2 customers to 5 customers.