7 problems

Let $cmathbf{N}_k$ be a subnetwork arising in a realization constructed by the simplex method. Stability conjecture for the subnetworks. The subnetworks $cmathbf{N}_k$ usually poss…

Let a network be created by the simplex method, and suppose it contains at least one equilibrium with a higher-dimensional unstable manifold, of dimension at least $2$. The generat…

Let $J$ be the number of stations, let $\rho_j$ denote the traffic intensity at station $j$, and let denote the network stability condition … for $i\in\{0,\ldots,I-1\}$. Stability…

Let $X$ be the queue-length vector and, for $b1>0$, consider the scheduling policy that chooses a feasible departure vector by maximizing the pressure-weighted expression with queu…

Let $\Gamma$ be a graph with $N$ vertices, let $\Gamma_+$ denote its positive-edge subgraph, and let $t^\star(\Gamma)$ be the critical interaction strength at which stability is lo…

Let GFS denote the greedy link scheduler introduced for wireless networks with fading channels, and let GMS denote Greedy Maximal Scheduling. The performance of a scheduler is meas…

Bonald's vanishing-access-rate conjecture. Capacity in acyclic networks increases as access rates tend to $0$ and, in the limit, is determined only by the optimal per-link stabilit…