IS23: Inference in Stochastic Networks

Organizer: Michel Mandjes (Leiden University)

Inference in dynamic random graphs

Michel Mandjes

The bulk of the random graph literature concerns models that are of an inherently static nature, in that features of the random graph at a single point in time are considered. There are strong practical motivations, however, to consider random graphs that are stochastically evolving, so as to model networks’ inherent dynamics. In this talk I’ll start by briefly discussing a set of dynamic random graph mechanisms and their probabilistic properties. Key results cover functional diffusion limits for subgraph counts (describing the behaviour around the mean) and a sample-path large-deviation principle (describing the rare-event behaviour, thus extending the seminal result for the static case developed by Chatterjee and Varadhan). The main part of my talk will be about estimation of the model parameters from partial information. We for instance demonstrate how the model’s underlying parameters can be estimated from just snapshots of the number of edges. We also consider settings in which particles move around on a dynamically evolving random graph, and in which the graph dynamics are inferred from the movements of the particles (i.e., not observing the graph process).

Inference in infinite-server queueing networks with Poisson sampling

Liron Ravner

In this work, we study a network of n stations, each modeled as an infinite-server queue, where all arriving customers receive service in parallel. The network dynamics are governed by three key elements: external arrivals, per-station sojourn times, and the routing mechanism. Our objective is to estimate the system parameters based on periodic, noisy observations of customer counts at each station. These observations are collected through a Poisson sampling process. We derive the covariance structure of the observed counts and leverage it to develop consistent estimators for the system parameters.