Our head and founder, Anton Esin, delivered a talk entitled
“Cylindrical Reflected Ornstein–Uhlenbeck Model for High-Speed Mobile Networks”.

From 15 to 17 July 2025, the 6th International Conference on Mathematics and its Applications in Science and Engineering (ICMASE 2025) took place in Plovdiv, Bulgaria, in a hybrid format. The conference brought together researchers working across a wide spectrum of mathematics, including applied mathematics, analysis, stochastic processes, geometry, and computational methods.
Conference website
Book of Abstracts (PDF)

The presentation introduced an analytically tractable model for signal dynamics in quasi-one-dimensional propagation environments typical of high-speed trains and vehicular platoons. Specifically, the model employs a two-dimensional reflected Ornstein–Uhlenbeck diffusion on the cylinder, where the longitudinal signal component QtQ_t is subject to a Doppler-modified drift field and reflection at hard signal boundaries, while the angular component StS_t models the periodic movement of the receiver within a cell.

An explicit stationary distribution πv0(q,s)\pi_{v_0}(q, s) is derived in closed form for each fixed speed v0>0v_0 > 0, enabling precise evaluation of signal-dependent performance metrics. In particular, the model provides a necessary and sufficient stability condition for a coupled queueing system with Poisson arrivals and signal-level-dependent service rates. This yields a natural buffer-dimensioning rule for high-mobility scenarios.

The approach unifies path-loss geometry, Doppler-aware signal degradation, and stochastic fluctuation within a mathematically rigorous framework. The work demonstrates how advanced diffusion models can be fruitfully applied to performance analysis in modern mobile networks, including 5G/6G scenarios involving mobile aggregators and edge devices operating under high-speed conditions.

A full-length research article is currently in preparation.