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

  • Authors:

  • Karl Sigman

  • Affiliations:

  • Department of Industrial Engineering and Operations Research, Columbia University, New York, USA 10027

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2012

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Abstract

We present an exact simulation algorithm for the stationary distribution of customer delay for FIFO M/G/c queues in which 驴=驴/μc. In Sigman (J. Appl. Probab. 48A:209---216, 2011) an exact simulation algorithm was presented but only under the strong condition that 驴G(x)=P(S驴x), x驴0, with mean 0E(S)=1/μ $G_{e}(x)=\mu\int_{0}^{x} P(Sy)\,dy$ 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.