Related papers: Many-Server Asymptotics for Join-the-Shortest-Queu…
We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…
We continue the development, started in of the asymptotic description of certain stochastic neural networks. We use the Large Deviation Principle (LDP) and the good rate function H announced there to prove that H has a unique minimum mu_e,…
It is known that simulation of the mean position of a Reflected Random Walk (RRW) $\{W_n\}$ exhibits non-standard behavior, even for light-tailed increment distributions with negative drift. The Large Deviation Principle (LDP) holds for…
We consider a class of multi-agent distributed synchronization systems, which are modeled as $n$ particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in [15], employing so-called…
In many service systems, especially those in healthcare, customer waiting times can result in increased service requirements. Such service slowdowns can significantly impact system performance. Therefore, it is important to properly account…
A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…
We consider multi-component matching systems in heavy traffic consisting of $K\geq 2$ distinct perishable components which arrive randomly over time at high speed at the assemble-to-order station, and they wait in their respective queues…
We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…
A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time…
We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
We study the load balancing system operating under Join the Shortest Queue (JSQ) in the many-server heavy-traffic regime. If $N$ is the number of servers, we let the difference between the total service rate and the total arrival rate be…
This paper studies the heavy-traffic joint distribution of queue lengths in two stochastic processing networks (SPN), viz., an input-queued switch operating under the MaxWeight scheduling policy and a two-server parallel server system…
The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…
In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…
In cyber-physical systems such as automobiles, measurement data from sensor nodes should be delivered to other consumer nodes such as actuators in a regular fashion. But, in practical systems over unreliable media such as wireless, it is a…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…
We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits.…
Motivated by emerging applications in online matching platforms and marketplaces, we study a matching queue. Customers and servers that arrive in a matching queue depart as soon as they are matched. While state-dependent control is an…