3 problems

Miyazawa's process-limit conjecture. A process limit of the diffusion-scaled queue-length process in heavy traffic is the solution $Z(\cdot)$ of the stochastic integral equation fo…

Miyazawa's conjecture. The process $Z(\bcdot)$ is the weak solution of a stochastic integral equation, and its stationary distribution agrees with the heavy-traffic limit of the sc…

A bandwidth sharing network has routes indexed by $i\in\mathbb{I}$ and resources indexed by $j\in\mathbb{J}$, with capacity-resource matrix $A$, service-rate vectors $\mu^r$ and…