Dynamic behavior of interacting-particle systems with hard-core interaction

Summary The dynamic competition for shared resources among contending nodes in communication networks can commonly be modeled in terms of interacting-particle systems with hard-core interaction on a conflict graph.  High-load scenarios in communication networks, where resource contention is fierce, broadly correspond to a low-temperature regime in a statistical-physics sense, where the system is particularly prone to metastability effects.  The congestion levels, and hence the key performance metrics, in such communication networks can usually be expressed in terms of various integral functionals of the state process of the corresponding interacting-particle system.  In particular, the performance characteristics in high-load scenarios are severely impacted by the potential meta-stability effects.  Moreover, congestion control mechanisms in communication networks allow for the various nodes to have different temperatures, which are adapted in a distributed fashion based on the local values of the above-mentioned integral functionals.

The goal of this project is to examine the dynamic behavior of the relevant functionals in a low-temperature regime, and investigate how the impact of the potential metastability effects depends on the temperature adaptation mechanism as well as the size and structure of the conflict graph.  The key methodologies will involve concepts and techniques from statistical physics, large deviations and rare events, potential theory, fluid-limit scalings, and queues in random environments.

Supervisors Sem Borst (TU/e), Frank den Hollander (Leiden University), Francesca Nardi (TU/e)
PhD Student Matteo Sfragara
Location Leiden University (UL)