5 problems

Let $z$ be a fluid limit with initial condition $z(0)=x$, where $x=\lim_n x^n/|x^n|$, and let $V_i$ denote the neighborhood associated with coordinate $i$. The right derivative at…

Consider the queueing system with on-demand servers and its fluid limits, and let $\gamma$ be the parameter governing the invitation scheme. Large-$\gamma$ global-stability conjectu…

Consider the fluid-limit dynamics of the on-demand agent service system with system matrix $A^{-}$. Non-Hurwitz parameter-dependence conjecture. If $A^{-}$ is not Hurwitz, the syst…

Consider the fluid-limit dynamics of the on-demand agent service system, represented by switched linear systems with system matrices $A^{-}$ and $A^{+}$. A matrix is Hurwitz when a…

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…