Eva H. Loeser

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math.PR2026

Fluid and Diffusion Approximation of a Multiclass Proportional Processor Sharing Queue with Reneging and General Distributions

Eva Loeser

In this paper, we resolve the long open problem of the diffusion approximation for a generally distributed processor sharing queue with reneging. In particular, we first extend the…

math.PR2026

Rank Based Routing in Large Server Systems under Extreme Congestion

Sayan Banerjee, Amarjit Budhiraja, Eva Loeser

We study $n$ parallel queues in an extreme heavy-traffic regime: each server works at rate $n$ , while jobs arrive to a dispatcher at rate $n^{2} - (a - b) n$ , with fixed $a > b > 0$ . A…

math.PR2025

Diffusive Scaling limit of stochastic Box-Ball systems and PushTASEP

David Keating, Minjun Kim, Eva Loeser +1

We introduce the Stochastic Box-Ball System (SBBS), a probabilistic cellular automaton that generalizes the classic Takahashi-Satsuma Box-Ball System. In SBBS, particles are transp…

math.PR2025

Diffusion Limits for Measure-Valued Queueing Models, With Application to General Random Order of Service Queues

Eva H Loeser

Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one…