A simplified game server is modelled as follows. Players arrive to the server according to a Poisson process with rate of one every 2 minutes. Arrivals wait until three players have arrived, at which point the game immediately starts. The game takes an exponentially distributed period of time with mean 20 minutes. When the game is complete, all of the players leave the system. This infinitely repeats, i.e. another game is started after three more players arrive. Potential players that arrive when a game is in progress leave without waiting. (a) Calculate the limiting probability that a game is being played. (b) Suppose that we add room so that one player can wait for the next game while the current game is in progress (three players are still required for a game). Determine the limiting probability that a game is being played