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Diffusion approximations for open queueing networks with service interruptions

Abstract

This paper establishes functional central limit theorems describing the heavy-traffic behavior of open single-class queueing networks with service interruptions. In particular, each station has a single server which is alternatively up and down. There are two treatments of the up and down times. The first treatment corresponds to fixed up and down times and leads to a reflected Brownian motion, just as when there are no service interruptions, but with different parameters. To represent long rare interruptions, the second treatment has growing up and down times with the up and down times being of ordern andn 1/2, respectively, when the traffic intensities are of order 1-n−1/2. In this case we establish convergence in the SkorohodM 1 topology to a multidimensional reflection of multidimensional Brownian motion plus a multidimensional jump process.

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Chen, H., Whitt, W. Diffusion approximations for open queueing networks with service interruptions. Queueing Syst 13, 335–359 (1993). https://doi.org/10.1007/BF01149260

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Keywords

  • Service interruptions
  • vacations
  • limit theorems
  • heavy traffic
  • queueing networks
  • oblique reflection mapping
  • Skorohod topologies
  • jump-diffusion processes