10 problems

Consider a multiclass queue operating under the processor-sharing discipline, and suppose that the queue-length and workload processes are scaled in the heavy-traffic regime. Harri…

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…

Degirmenci's conjecture. The asymptotic result for the Markovian double-ended queue should continue to hold when arrivals are renewal processes and patience times have general dist…

Stationary-distribution conjecture. Based on the stationary density of the discrete-time Ornstein–Uhlenbeck approximation, the stationary distribution of $X^*$ can be approximated…

Diffusion approximation conjecture. Similar diffusion approximations should be obtainable for a GJN with an arbitrary number of nodes.

Grosjean's modified diffusion-length conjecture. The modified diffusion length can be obtained without Fourier transforms using only $\langle s^2\rangle$, and the complete Grosjean…

General-dimensional diffusion-coefficient conjecture. The formula $D=\langle s^2\rangle/(2d)$ holds in arbitrary spatial dimension $d$, with the dependence on $d$ as indicated.

Consider the proposed Gaussian-density approximation for non-stationary state-dependent queueing systems, and compare its covariance matrix with the covariance obtained from the em…

The paper considers empirical and Gaussian density approximations for the state of a non-stationary state-dependent queueing system, with covariance matrix entries computed from th…

Exact-order conjecture. Under some regularity assumptions, the exact order of this approximation is $k^{-3/2}$.