Related papers: Distribution-valued heavy-traffic limits for the $…
We carry out a delay stability analysis (i.e., determine conditions under which expected steady-state delays at a queue are finite) for a simple 3-queue system operated under the Max-Weight scheduling policy, for the case where one of the…
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…
We consider a load balancing system consisting of $n$ single-server queues working in parallel, with heterogeneous service rates. Jobs arrive to a central dispatcher, which has to dispatch them to one of the queues immediately upon arrival.…
We discuss weak convergence of the number of busy servers in a $G/G/\infty$ queue in the $J_1$-topology on the Skorokhod space. We prove two functional limit theorems, with random and nonrandom centering, respectively, thereby solving two…
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…
In this paper, we consider five models of heavy-tailed queues involving Mittag-Leffler distributions that generalize the classical $M/M/1$ queues. These models are suitable modifications of previously defined models in such a way that the…
For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system…
Customers arrive at rate N times alpha on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate beta. We let N go to infinity.We prove a functional…
Front propagation in time dependent laminar flows is investigated in the limit of very fast reaction and very thin fronts, i.e. the so-called geometrical optics limit. In particular, we consider fronts evolving in time correlated random…
The subject of this paper is the problem of estimating service time distribution of the $M/G/\infty$ queue from incomplete data on the queue. The goal is to estimate $G$ from observations of the queue--length process at the points of the…
The paper examines a class of first order linear hyperbolic systems, proposed as a generalization of the Goldstein-Kac model for velocity-jump processes and determined by a finite number of speeds and corresponding transition rates. It is…
Diffusion based generative models have achieved unprecedented fidelity in synthesizing high dimensional data, yet the theoretical mechanisms governing multimodal generation remain poorly understood. Here, we present a theoretical framework…
The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular…
We study distributed load balancing in bipartite queueing systems where frontends route jobs to heterogeneous backends with workload-dependent service rates. The system's connectivity -- governed by compatibility constraints such as data…
We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete time grid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component, or node.…
We develop a general approach to Stein's method for approximating a random process in the path space $D([0,T]\to R^d)$ by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as…
First-passage time (FPT) of an Ornstein-Uhlenbeck (OU) process is of immense interest in a variety of contexts. This paper considers an OU process with two boundaries, one of which is absorbing while the other one could be either reflecting…
Service systems like data centers and ride-hailing are popularly modeled as queueing systems in the literature. Such systems are primarily studied in the steady state due to their analytical tractability. However, almost all applications in…
Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…