Journal of Applied Probability

Exact simulation of the stationary distribution of the FIFO M/G/c queue

Karl Sigman


We present an exact simulation algorithm for the stationary distribution of the customer delay D for first-in--first-out (FIFO) M/G/c queues in which ρ=λ/μ<1. We assume that the service time distribution G(x)=P(Sx),x≥0 (with mean 0<E(S)=1/μ<∞), and its corresponding equilibrium distribution Ge(x)=μ∫0x P(S>y)dy are such that samples of them can be simulated. We further assume that G has a finite second moment. Our method involves the general method of dominated coupling from the past (DCFTP) and we use the single-server M/G/1 queue operating under the processor sharing discipline as an upper bound. Our algorithm yields the stationary distribution of the entire Kiefer--Wolfowitz workload process, the first coordinate of which is D. Extensions of the method to handle simulating generalized Jackson networks in stationarity are also remarked upon.

Article information

J. Appl. Probab., Volume 48A (2011), 209-213.

First available in Project Euclid: 18 October 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65C05: Monte Carlo methods
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 60J05: Discrete-time Markov processes on general state spaces 68U20: Simulation [See also 65Cxx]

Exact simulation coupling from the past processor sharing queueing theory


Sigman, Karl. Exact simulation of the stationary distribution of the FIFO M/G/ c queue. J. Appl. Probab. 48A (2011), 209--213. doi:10.1239/jap/1318940466.

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