22 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…

Approximate-behavior conjecture. The function $\tilde{\Delta}_{LB}(W)$ also tends to have the same behavior on $(0,+\infty)$ as $\hat{\Delta}_{LB}(W)$.

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

Exponential degradation conjecture. The rate of information degradation is exponential in the age of information for all gossip networks.

Let $\mathbb{Z}_m^d$ be the $d$-dimensional discrete torus with $n:=m^d$ nodes, and consider the age of information (AoI) under the gossiping model. Srivastava–Ulukus conjecture. T…

In the variable-length stop-feedback coding setting, feedback is received only after a transmission decision can be made, and sufficiently long packets may be attempted after the t…

M/M/1-PS AAoI conjecture. The average age of information is

Best-systems conjecture. Regardless of the message-size distribution,

The $\mathcal{P}_2$-versus-$\mathcal{B}_1$ conjecture. The age of information of $\mathcal{P}_2$ should be lower than that of $\mathcal{B}_1$, in the relevant sense of age comparis…

Let a cache unit store sensing data, and let $[?]$ denote the frequency of cache updates. Cache-update conjecture. Cache updates could happen less frequently, such that the sensing…

Let $N>1$, let $E$ denote the energy state, let $T_1,\ldots,T_N$ denote the ages of information of the $N$ processes, and define … Let $E_p$ and $E_s$ be the probing and sampling e…

Let $M>2$ and let $N$ be the number of channels. For a problem instance $(M,N,\boldsymbol\mu)$, consider all possible permutations of arms in the set $\mathcal{S}(M)$ and the round…

Content-update conjecture. The update of content becomes less frequent, resulting in more outdated content items cached at ENs.

Data-freshness conjecture. The decrease in transmission energy consumption and fronthaul traffic loads is a result of worsening data freshness.

Let $cpi$ be a scheduling policy and let $cpi_{\rm I}$ denote its informative version; an informative policy prioritizes informative updates and discards non-informative updates wh…

Consider the scheduling policies described above for a single-server queue, including size-based policies such as SJF, preemptive SJF, and SRPT, and let AoI denote age of informati…

Let $I_k$, $W_{k-1}$, and $\hat{Z}_{k-1}$ denote the random variables used in the derivation of the upper bound $\Phi_2$, with the inequality … used to obtain that bound. Looseness…

Consider an infinite-buffer FIFO system and a single-server pushout system ${\mathcal P}_2$ with buffer size $2$, obtained as a variation of the pushout system ${\mathcal P}$. Buff…

Optimality conjecture. The optimality of the proposed policies can be extended from the considered subset to all online policies.

In an age-of-information scheduling system with energy harvesting, finite battery capacity, and age-based threshold policies, let the highest energy state denote the battery state…

Myopic-policy conjecture. The myopic policy with GSI is close to optimal with infinite horizon.

Let $n$ be the number of nodes, and let $k$ denote the pre-selected number of nodes participating in selective multicast. Write $\Delta^S_{(k)}$ for the original average age functi…