Continuing Problem 10.5.5, suppose each service time is either one minute or two minutes equiprobably, independent of the arrival process or the other service times What is the PMF of the number of customers N(t) in service at the bank at time t?
Problem 10.5.5
Customers arrive at the Veryfast Bank as a Poisson process of rate λ customers per minute. Each arriving customer is immediately served by a teller. After being served, each customer immediately leaves the bank. The time a customer spends with a teller is called the service time. If the service time of a customer is exactly two minutes, what is the PMF of the number of customers N(t) in service at the bank at time t?