Related papers: Buffer occupancy asymptotics in rate proportional …
In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we show that $N_\alpha(N_\beta(t))…
Neurons process sensory stimuli efficiently, showing sparse yet highly variable ensemble spiking activity involving structured higher-order interactions. Notably, while neural populations are mostly silent, they occasionally exhibit highly…
A fine-grained analysis of network performance is crucial for system design. In this paper, we focus on the meta distribution of the signal-to-interference-plus-noise-ratio (SINR) in the mmWave heterogeneous networks where the base stations…
This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…
This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…
We consider the problem of determining asymptotic bounds on the capacity of a random ad hoc network. Previous approaches assumed a link layer model in which if a transmitter-receiver pair can communicate with each other, i.e., the Signal to…
The occupation time of an age-dependent branching particle system in $\Rd$ is considered, where the initial population is a Poisson random field and the particles are subject to symmetric $\alpha$-stable migration, critical binary branching…
This paper investigates the asymptotic behavior of the Multi-set Allocation Occupancy (MAO) distribution, which models the count vector $X=(X_{=0},\ldots,X_{=T})$ from $T$ independent rounds of sampling without replacement of size $m$ from…
Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous…
Exponential backoff (EB) is a widely adopted collision resolution mechanism in many popular random-access networks including Ethernet and wireless LAN (WLAN). The prominence of EB is primarily attributed to its asymptotic throughput…
We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…
This work investigates the effect of finite buffer sizes on the throughput capacity and packet delay of line networks with packet erasure links that have perfect feedback. These performance measures are shown to be linked to the stationary…
We consider base-$\beta$ expansions of Parry's type, where $a_0 \geq a_1 \geq 1$ are integers and $a_0<\beta <a_0+1$ is the positive solution to $\beta^2 = a_0\beta + a_1$ (the golden ratio corresponds to $a_0=a_1=1$). The map $x\mapsto…
The on-line nearest-neighbour graph on a sequence of $n$ uniform random points in $(0,1)^d$ ($d \in \N$) joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this…
We investigate asymptotics of the tail distribution of sojourn time $$ \int_0^T \mathbb{I}(X(t)> u)dt, $$ as $u\to\infty$, where $X$ is a centered stationary Gaussian process and $T$ is an independent of $X$ nonnegative random variable. The…
We study the performance of wireless links for a class of Poisson networks, in which packets arrive at the transmitters following Bernoulli processes. By combining stochastic geometry with queueing theory, two fundamental measures are…
As the demand for low-latency services grows, ensuring the delay performance of random access (RA) networks has become a priority. Existing studies on the queueing delay performance of the Aloha model universally treat packets as atomic…
We consider Ewens random permutations of length $n$ conditioned to have no cycle longer than $n^\beta$ with $0<\beta<1$ and to study the asymptotic behaviour as $n\to\infty$. We obtain very precise information on the joint distribution of…
This paper addresses an interference channel consisting of $\mathbf{n}$ active users sharing $u$ frequency sub-bands. Users are asynchronous meaning there exists a mutual delay between their transmitted codes. A stationary model for…