Consider an M/M/1 queuing system in which customers arrive according to a Poisson process with rate λ, and service times are exponential with mean 1/λ. We know that, in the long run, such a system...

Consider an M/M/1 queuing system in which customers arrive according to a Poisson process with rate λ, and service times are exponential with mean 1/λ. We know that, in the long run, such a system will not be stable. For i ≥ 0, suppose that at a certain time there are i customers in the system. For j > i, find the expected length of time until the system has j customers.