The Output of an M/D/1 Queue

In this paper we investigate the output process of the M/D/1 queuing system. We derive expressions for the distributions and first two moments, in both steady-state and transient conditions, of the following random variables: (1) the time until the nth departure measured from a departure epoch, T₀, (2) the time between the n − 1st and nth departures after T₀, and (3) the number of departures in (T₀, T₀ + t]. Further we study the autocorrelation functions of random variables (1) and (2) in the steady state.