5 papers
Only Segmented Heavy Tails Can Produce a Light-Tailed Minimum
Sergey Foss, Michael Scheutzow, Anton Tarasenko
A random variable has a {\it light-tailed} distribution (for short: is light-tailed) if it possesses a finite exponential moment, $\E \exp (λξ) <\infty$ for some , and…
On Recurrence of the Infinite Server Queue
Sergey Foss, Peter Glynn
This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in t…
On the instability of local learning algorithms: Q-learning can fail in infinite state spaces
Urtzi Ayesta, Sergey Foss, Matthieu Jonckheere +1
We investigate the challenges of applying model-free reinforcement learning algorithms, like online Q-learning, to infinite state space Markov Decision Processes (MDPs). We first i…
Heavy-tail asymptotics for the length of a busy period in a Generalised Jackson Network
Sergey Foss, Masakiyo Miyazawa, Linglong Yuan
We consider a Generalised Jackson Network with finitely many servers, a renewal input and service times at each queue. We assume the network to be stable and, in addition,…
Last passage percolation and limit theorems in Barak-ErdÅs directed random graphs and related models
Sergey Foss, Takis Konstantopoulos, Bastien Mallein +1
We consider directed random graphs, the prototype of which being the Barak-ErdÅs graph , and study the way that long (or heavy, if weights are present) paths…