Exact simulation of the stationary distribution of the FIFO M/G/c queue: the general case for ρ<c

We present an exact simulation algorithm for the stationary distribution of customer delay for FIFO M/G/c queues in which ρ = λ/μ < c. In Sigman (J. Appl. Probab. 48A:209–216, 2011) an exact simulation algorithm was presented but only under the strong condition that ρ < 1 (super stable case). We only assume that the service-time distribution G(x) = P(S ≤ x), x ≥ 0, with mean 0 < E(S) = 1/μ < ∞, and its corresponding equilibrium distribution Ge(x) = μ ∫ x 0 P(S > y)dy are such that samples of them can be simulated. Unlike the methods used in Sigman (J. Appl. Probab. 48A:209–216, 2011) involving coupling from the past, here we use different methods involving discrete-time processes and basic regenerative simulation, in which, as regeneration points, we use return visits to state 0 of a corresponding random assignment (RA) model which serves as a sample-path upper bound.