3 problems

Let $f:cmathbb{R}ctocmathbb{R}$ be convex and of class $C^h(cmathbb{R})$ for an even integer $h>0$, with unique minimizer $x^*$, satisfying $\lim_{x\to x^*}f^{(k)}(x)=0$ for…

Let $\widetilde{\bm{X}}^{(n)}(\infty)$ be the stationary random vector of the scaled finite system, and let $\bm{y}(\infty)$ denote the equilibrium point of the fluid model. Interc…

For each job class $i$, let $X^{(n)}_{i}(\infty)$ denote the number of class-$i$ jobs, including queued and in-service jobs, in steady state. Let $\lambda_i$ and $\mu_i$ be the cla…