a) Consider an M/M/1 queue in steady state. Assume λ = /µ 0 that the system is in state i at time t and that i j departures occur before the next arrival. b) Find the PMF of the state immediately...

a) Consider an M/M/1 queue in steady state. Assume λ = /µ <> 0 that the system is in state i at time t and that i j departures occur before the next arrival.

b) Find the PMF of the state immediately before the first arrival after time t.

c) There is a well-known queueing principle called PASTA, standing for “Poisson arrivals see time-averages”. Given your results above, give a more precise statement of what that principle means in the case of the M/M/1 queue.