The number of customers arriving at a bank counter is in accordance with a Poisson distribution with mean rate of 5 customers in 3 minutes. Service time at the counter follows exponential distribution with mean service rate of 6 customers in 2 minutes. If there were 20 customers waiting in the line just before opening the counter, what is the probability that more than 20 customers will be waiting in the line, 2 hours after opening the counter? Assume that no customers leave the line without service.
Here arrival rate is $\lambda=5/3$ and service rate is $\mu=3$. If $W$ is the average number of people waiting in the line then $W= \lambda/(\mu - \lambda)$ . But I don't know how to calculate number of waiting customer using a given time span. I didn't find any formula to do it in the book. Please help.