Antonio Gómez-Corral

TL;DR: In this paper, the authors considered a population of individuals that grows stochastically according to a batch Markovian arrival process and is subject to renewal generated geometric catastrophes, and presented tractable formulae for a variety of probabilistic descriptors of the population, including the equilibrium distribution of population size and the distribution of the time to extinction for present units at post-catastrophe epochs.

TL;DR: In this paper, the authors presented a more detailed description of the underlying PDMP, from which they analyzed the population transmission number and the infection probability of a certain susceptible individual, and showed how SIR epidemics in which individuals' infection periods are not necessarily exponentially distributed may be modeled in terms of a piecewise-deterministic Markov process (PDMP).

TL;DR: A regenerative approach is used to derive a numerically stable recursion scheme for the stare probabilities that can be employed to analyze the behaviour of a buffer in computers with virus infections.

TL;DR: In this paper, the authors considered multi-server queues with a finite buffer of size N in which units waiting for service generate into priority at a constant rate, independently of other units in the buffer.

TL;DR: This approach uses matrix calculus and exploits the specific structure of the infinitesimal generator, which allows us to obtain additional information during the perturbation analysis of the LD‐QBD process by dealing with specific matrices carrying probabilistic insights of the dynamics of the process.