Related papers: Diffusion Approximations for $\text{Cox}/G_t/\inft…
We consider an automatic overload control for two large service systems modeled as multi-server queues, such as call centers. We assume that the two systems are designed to operate independently, but want to help each other respond to…
We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion…
In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We study load balancing under the Batch Sampling routing scheme for a network of $n$ servers storing a set of files using the…
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…
Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through self-excitation of the arrival process. In this paper, we analyze an…
We investigate the light-cone-like spread of electronic correlations in a laser-driven quantum chain. Using the time-dependent density matrix renormalization group, we show that high-frequency driving leads to a Floquet-engineered spread…
Recent advancements in diffusion models have notably improved the perceptual quality of generated images in text-to-image synthesis tasks. However, diffusion models often struggle to produce images that accurately reflect the intended…
We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…
In this paper, we develop a stochastic algorithm based on the Euler--Maruyama scheme to approximate the invariant measure of the limiting multidimensional diffusion of $G/Ph/n+GI$ queues in the Halfin-Whitt regime. Specifically, we prove a…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
We study infinite-horizon asymptotic average optimality for parallel server network with multiple classes of jobs and multiple server pools in the Halfin-Whitt regime. Three control formulations are considered: 1) minimizing the queueing…
In this paper we study the distributed average consensus problem in multi-agent systems with directed communication links that are subject to quantized information flow. Specifically, we present and analyze a distributed averaging algorithm…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…
We consider the Halfin-Whitt diffusion process $X_d(t)$, which is used, for example, as an approximation to the $m$-server $M/M/m$ queue. We use recently obtained integral representations for the transient density $p(x,t)$ of this diffusion…
Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
In geographically-distributed systems, communication latencies are non-negligible. The perceived processing time of a request is thus composed of the time needed to route the request to the server and the true processing time. Once a…