7 problems

Let $n$ be the number of nodes, and let a sub-TVG be a randomly sampled sub-temporal visibility graph of the STARLINK satellite system. Let $r$ denote the convergence radius of its…

Reshuffling hydrodynamic-limit conjecture. Under these assumptions, the process $\phi^N_{\mathrm{RS}}(\cdot,\cdot)$ converges, in an appropriate sense, to the hydrodynamic model…

Reshuffling stage-profile conjecture. As $N\to\infty$, $\phi^N_{\mathrm{RS}}(\cdot,\infty)$ converges in probability to the deterministic linear function

Large reshuffling-system conjecture. As $N\to\infty$: (i) the number of useful packets on a link at a communication epoch converges in distribution to…

Limiting slowdown conjecture. As $N\to\infty$, the expected steady-state sojourn time under OU or RU, normalized by the expected free-system sojourn time, converges to a finite con…

Delay-profile convergence conjecture. For $D=\mathrm{OU}$ or $D=\mathrm{RU}$, and for a given load $\lambda<1$, as $N\to\infty$,

Let $(L_j(t),0\leq j\leq J)$ be the Markov process describing the numbers of requests at the nodes of the star network, and let $\rho_0,\rho_1,\ldots,\rho_J$ denote the correspondi…