Related papers: Effectively tailoring fluid and diffusion models f…

In this paper, we consider modeling time-dependent multi-server queues that include abandonments and retrials. For the performance analysis of those, fluid and diffusion models called "strong approximations" have been widely used in the…

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 path for deriving diffusion limit equations of queueing…

Diffusion approximations have been a popular tool for performance analysis in queueing theory, with the main reason being tractability and computational efficiency. This dissertation is concerned with establishing theoretical guarantees on…

Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…

Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

We introduce a framework and develop a theory of transitory queueing models. These are models that are not only non-stationary and time-varying but also have other features such as the queueing system operates over finite time, or only a…

In this paper, we analyze a discrete-time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count…

The article describes the diffusion approximation and the method of its use for evaluation of the effectiveness of active queue management (AQM) mechanisms. The presented model combines the approximation and simulation approaches. The…

A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…

Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…

We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience…

A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…

This paper proposes the DnD Filter, a differentiable filter that utilizes diffusion models for state estimation of dynamic systems. Unlike conventional differentiable filters, which often impose restrictive assumptions on process noise…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…