Завершено22 сентября 2022 года

Max-weight policies in stochastic matching models.

1961-е заседание (номер восстановлен по хронологии).

Nahuel Soprano-Loto
Max-weight policies in stochastic matching models.
We study a matching system where items arrive one by one at each node of a compatibility network according to Poisson processes and depart from it as soon as they are matched to a compatible item. The field of applications of this model is very wide, from housing applications to kidney exchange. The matching policy considered is a generalized max-weight policy where decisions can be noisy. Additionally, some of the nodes may have impatience, i.e. leave the system before being matched. Using specific properties of the max-weight policy, we construct a quadratic Lyapunov function. This allows us to establish stability results, to construct bounds for the stationary mean and variances of the total number of customers in the system, and to prove exponential convergence speed towards the stationary measure. We finally illustrate some of these results using simulations on toy examples. This is a work in collaboration with M. Jonckheere (LAAS, CNRS), P. Moyal (Universite de Lorraine), and C. Ramirez (Aristas SRL). Семинар пройдёт в 18:00 по НСК в онлайн-формате.