Generic equivalence conjecture for 0-RJF and G-RDS

From papers

Fix a network and a tail-exponent vector γ{\boldsymbol{\gamma}}. Let λ{\boldsymbol{\lambda}}^* range over nonnegative nominal arrival vectors, and let 0-RJF and G-RDS denote the conditions defined in the paper. Generic 0-RJF–G-RDS conjecture. The set

{λ0:  0-RJF holds but G-RDS does not hold}\left\{ {\boldsymbol{\lambda}}^*\succeq {\bf 0}:\; 0\text{-RJF holds but G-RDS does not hold}\right\}

has Lebesgue measure zero. Thus, although the two conditions may differ on a boundary, they should be generically equivalent. This is posed as an open conjecture motivated by the apparent closedness of the 0-RJF region and openness of the G-RDS region.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

Arsalan Sharifnassab and John N. Tsitsiklis, “Jumping Fluid Models and Delay Stability of Max-Weight Dynamics under Heavy-Tailed Traffic”, arXiv:2111.07420 (2023).

Solutions 0

No solutions have been posted yet.