Question:
A small filling station in a rural area provides diesel for agricultural machines. It has one diesel pump and waiting capacity for 5 machines. On average, 8 machines per hour arrive for diesel. An arriving machine immediately leaves the station without fuel if pump and all waiting places are occupied. The mean time a machine occupies the pump is 5 minutes. It is assumed that the station behaves like an M/M/s/mqueueing system.
(1) Determine the stationary loss probability.
(2) Determine the stationary probability that an arriving machine waits for diesel.