5 problems

Consider a fork-join network of four LLM agents indexed by $j\in\{0,1,2,3\}$. Requests arrive at agent $0$ with rate $\lambda$, fork into tasks processed by agents $1$ and $2$, and…

Large-system response-time conjecture. Provided that $\rho(\tau)<1$,

Let $B=(B_1,B_2)$ be the two-dimensional Brownian motion on a filtered probability space $(\mathnormal{\Omega},\mathcal{F},\{\mathcal{F}_t\}_{t\ge 0},\mathbb{P})$, and consider the…

Let $G(n,r)$ be the random graph model under consideration, with edge-probability parameter $r^2$, and let $\operatorname{LoP}$ denote the graph property that the local pooling fac…

Let $x$ be a fluid solution with initial condition $x(0)$, let ${\cal O}$ be the set of initial conditions whose trajectories oscillate indefinitely, and let $u^*$ denote a periodi…