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Fluctuation bounds for the max-weight policy with applications to state space collapse

Sharifnassab, A ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1287/stsy.2019.0038
  3. Publisher: INFORMS Inst.for Operations Res.and the Management Sciences , 2020
  4. Abstract:
  5. We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under nonMarkovian arrivals and, for the case of independent and identically distributed arrivals, an additive SSC result over an exponential time scale. © 2020 The Author(s)
  6. Keywords:
  7. Fluid model ; Max-weight scheduling policy ; Sensitivity to cumulative perturbations ; State space collapse
  8. Source: Stochastic Systems ; Volume 10, Issue 3 , 2020 , Pages 223-250
  9. URL: https://pubsonline.informs.org/doi/10.1287/stsy.2019.0038