Abstract
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 \(G_{e}(x)=\mu\int_{0}^{x} P(S>y)\,dy\) 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.
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References
Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003)
Asmussen, S., Glynn, P.W.: Stochastic Simulation. Springer, New York (2007)
Asmussen, S., Glynn, P.W., Thorisson, H.: Stationary detection in the initial transient problem. ACM Trans. Model. Comput. Simul. 2, 130–157 (1992)
Foss, S.G.: Approximation of mutichannel queueing systems. Sib. Math. J. 21, 132–140 (1980)
Foss, S.G., Chernova, N.I.: On optimality of the FCFS discipline in mutiserver queueing systems and networks. Sib. Math. J. 42, 372–385 (2001)
Sigman, K.: Exact simulation of the stationary distribution of the FIFO M/G/c queue. J. Appl. Probab. 48A, 209–216 (2011). Special Volume: New Frontiers in Applied Probability
Wolff, R.W.: Poisson arrivals see time averages. Oper. Res. 30, 223–231 (1982)
Wolff, R.W.: Upper bounds on work in system for multi-channel queues. J. Appl. Probab. 14, 547–551 (1987)
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Sigman, K. Exact simulation of the stationary distribution of the FIFO M/G/c queue: the general case for ρ<c . Queueing Syst 70, 37–43 (2012). https://doi.org/10.1007/s11134-011-9266-6
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DOI: https://doi.org/10.1007/s11134-011-9266-6