12 problems

Similar-behavior conjecture. The AAoI $\overline{\Delta}$ of UORA networks with stochastic arrival of status updates and that of UORA networks with generate-at-will status updates…

Insignificant-deviation conjecture. The deviation between $\overline{\Delta}$ and $\overline{\Delta}_{LB}$ could be insignificant. This conjecture is based on numerical results sho…

Negative-drift conjecture. The same Lyapunov function as the one used in the proof of Theorem has negative drift in this asymmetric-routing scenario as well.

Necessity conjecture. If $\overline{\lambda}$ is strictly outside $\mathcal{C}$, then the queue-length process is transient.

Let $Q_1$ and $Q_2$ be the equilibrium queue lengths in the two-queue random walk, and let $Q$ be the equilibrium queue length in the corresponding $Geo/Geo/2$ model with one queue…

Stability conjecture. Since the scheme closely resembles Rivest's pseudo-Bayesian approach, stability should hold, and techniques similar to those used by Tsitsiklis should be appl…

Let $N$ denote the scaling parameter for the network, let $W_c^{(N)}$ be the waiting time for class $c$, and let $\tilde W_c^{(N)}$ be its empirical counterpart. For complete inter…

Consider the $2B\times 2B$ grid mentioned above, with … Here $H^*(\mathcal A)$ is the coefficient governing the lower bound on the mixing time and mean queue length, and $H_1,H_2$…

Random-capture throughput-optimality conjecture. The random-capture scheme is throughput-optimal in arbitrary network topologies.

Let $M$, $bc$, $bd$, and $\lambda$ be the system parameters, with $M\mu>(M-1)\nu>\mu$. Positive-throughput conjecture. The throughput of the system is positive when $\lambda$ is sm…

Consider a random access system with finitely many source nodes transmitting to a central station. Let the stable throughput region be the set of arrival-rate vectors for which the…

Consider a finite-user random-access network in which source nodes compete for access to a shared channel, and let the stability region and throughput region denote the sets of arr…