Related papers: Technical Note for Discrete-Time Diffusion Approxi…
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…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
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…
This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue. This model is motivated by an energy saving problem for a…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
Motivated by call center practice, we propose a tractable model for $\mbox{GI}/\mbox{GI}/n+\mbox{GI}$ queues in the efficiency-driven (ED) regime. We use a one-dimensional diffusion process to approximate the virtual waiting time process…
Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps…
In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic…
In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion…
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…
We study a sequence of single server queues with customer abandonment (GI/GI/1+GI) under heavy traffic. The patience time distributions vary with the sequence, which allows for a wider scope of applications. It is known ([20, 18]) that the…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…