Related papers: Polling systems and multitype branching processes …
The career of an employee can be described (under certain circumstances) by a random walk, where the states of the random walk are determined by the level and position of an employee. At each decision moment the state of the employee is…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital…
We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
Business processes are continuously evolving in order to adapt to changes due to various factors. One type of process changes are branching frequency changes, which are related to changes in frequencies between different options when there…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
We present an example of a single-server polling system with two queues and an adaptive service policy where the stability region depends on the expected values of all the primitives and also on a certain exponential moment of the…
We show that a simple mechanistic model of spatial dispersal for settling organisms, subject to parameter variability, can generate heavy-tailed radial probability density functions. The movement of organisms in the model consists of a…
Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by L\'{e}vy noise -…
Some aspects of applications of bunching parameters are discussed. It is investigated to what extent Monte-Carlo models, which have been tuned to reproduce global event-shape variables and single-particle inclusive distributions, agree with…
Since the first paper on polling systems, written by Mack in 1957, a huge number of papers on this topic has been written. A typical polling system consists of a number of queues, attended by a single server. In several surveys, the most…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
We analyse a generalisation of the Galam model of binary opinion dynamics in which iterative discussions take place in local groups of individuals and study the effects of random deviations from the group majority. The probability of a…