# Seminario di Probabilità e Finanza Matematica: “Diffusion limits for queues and their applications to random graphs”

## Martedì 26 Luglio 2016, ore 11:00 - Aula 2AB40 - Gianmarco Bet

ARGOMENTI: Seminari

Martedì 26 Luglio 2016 alle ore 11:00 in Aula 2AB40, Gianmarco Bet (Politecnico di Eindhoven) terrà una conferenza dal titolo: “Diffusion limits for queues and their applications to random graphs”.

Abstract
Classical queueing theory is the study of models in which customers demand service from a resource-constrained system. The stochastic input of these models are the random arrival times, and the service times.
Typically, the arrival process is assumed to be ergodic and stationary, since this provides a convenient framework to prove long-term, or average, results on the relevant performance metrics. In fact, the time-dependent behaviour of queueing systems is often too complicated to be amenable to direct analysis. We consider a class of queueing models, including the so-called $\Delta/G/1$ queue, for which only the transient behaviour is of interest. Indeed, the signature characteristics of the $\Delta/G/1$ queue is that only a finite number of customers can potentially request service. To analyse these, we resort to asymptotic techniques, such as functional central limit theorems. We will show that, perhaps surprisingly, there is a connection between the $\Delta/G/1$ queue and a certain class of random graphs. Some interesting properties of the latter can be derived exploiting our queueing-theoretic results.