1 citations · 1 across the 6 of their papers we have counts for
6 papers
Mean field limits of large Jackson networks in heavy traffic
Rami Atar
We consider an open Jackson network with exchangeable single-server stations and weak all-to-all interaction through routing: upon service completion at station , a job is r…
High-dimensional limits for reflected Brownian motion in the orthant
Rami Atar
We study interacting Brownian particles on the half-line whose interaction occurs through boundary local times at the origin. The particle system is given by \[ X_i^n(t)=X^n_{0,i}+…
Trimmed branching random walk and a free obstacle problem
Rami Atar, Leonid Mytnik, Gershon Wolansky
Consider particles performing random walks on the -grid , with branching and density-dependent selection: When one of the particles branches, a particle is rem…
Heavy traffic limit with discontinuous coefficients via a non-standard semimartingale decomposition
Rami Atar, Masakiyo Miyazawa
This paper studies a single server queue in heavy traffic, with general inter-arrival and service time distributions, where arrival and service rates vary discontinuously as a func…
Rank-based stochastic differential inclusions and diffusion limits for a load balancing model
Rami Atar, Tomoyuki Ichiba
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream…
Invariance principle and McKean-Vlasov limit for randomized load balancing in heavy traffic
Rami Atar, Gershon Wolansky
We consider a load balancing model where a Poisson stream of jobs arrive at a system of many servers whose service time distribution possesses a finite second moment. A small fract…