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Extreme events appear in many physics phenomena, whenever the probability distribution has a ''heavy tail'', differing very much from the equilibrium one. Most unusual are the cases of power-law (Pareto) probability distributions. Among…
Expansion planning problems refer to the monetary and unit investment needed for energy production or storage. An inherent element in these problems is the element of stochasticity in various aspects, such as the generation output of the…
The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…
Consider the communication of a single-user aided by a nearby relay involved in a large wireless network where the nodes form an homogeneous Poisson point process. Since this network is interference-limited the asymptotic error probability…
We analyze randomized dynamic load balancing schemes for multi-server processor sharing systems when the number of servers in the system is large and the servers have heterogeneous service rates. In particular, we focus on the classical…
In randomly connected networks of pulse-coupled elements a time-dependent input signal can be buffered over a short time. We studied the signal buffering properties in simulated networks as a function of the networks state, characterized by…
An almost ubiquitous assumption made in the stochastic-analytic study of the quality of service in cellular networks is Poisson distribution of base stations. It is usually justified by various irregularities in the real placement of base…
In this paper, the asymptotic behaviour of the distribution tail of the stationary waiting time $W$ in the $GI/GI/2$ FCFS queue is studied. Under subexponential-type assumptions on the service time distribution, bounds and sharp asymptotics…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
In this work, we study the effects of finite buffers on the throughput and delay of line networks with erasure links. We identify the calculation of performance parameters such as throughput and delay to be equivalent to determining the…
We consider a spectrum-sharing network where n secondary relays are used to increase secondary rate and also mitigate interference on the primary by reducing the required overall secondary emitted power. We propose a distributed relay…
Motivated by the recent advances in the Internet of Things (IoT) and in Wireless Power Transfer (WPT), we study a network architecture that consists of power beacons (PBs) and passive backscatter nodes (BNs). The PBs transmit a sinusoidal…
Random unitary circuits have become a model system to investigate information scrambling in quantum systems. In the literature, mostly random circuits with Haar-distributed gate operations have been considered. In this work, we investigate…
We derive the asymptotic first passage time (FPT) distribution for space-dependent variable-order time-fractional diffusion, where the fractional exponent $\alpha(x)$ varies with position. For any sufficiently smooth $\alpha(x)$ on a finite…
We study a general $k$ dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index $\alpha\in (0,1)$. When the arrival rate is sped up by a factor $n^\gamma$, the…
In Part I of this paper, we presented a mathematical model for communication subject to both network interference and noise, where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a…
This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…
In this paper, we provide a general method to obtain the exact solutions of the degree distributions for RBDN with network size decline. First by stochastic process rules, the steady state transformation equations and steady state degree…
The Join-the-Shortest-Queue routing policy is studied in an asymptotic regime where the number of processors $n$ scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as $n\to \infty$, in…
This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted)…