Related papers: Occupation times for the finite buffer fluid queue…
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…
We study the \emph{bounded-delay model} for Qualify-of-Service buffer management. Time is discrete. There is a buffer. Unit-length jobs (also called \emph{packets}) arrive at the buffer over time. Each packet has an integer release time, an…
We introduce a multiclass single-server queueing system in which the arrival rates depend on the current job in service. The system is characterized by a matrix of arrival rates in lieu of a vector of arrival rates. Our proposed model…
In this note we investigate geometric properties of invariant spatio-temporal random fields $X:\mathbb M^d\times \mathbb R\to \mathbb R$ defined on a compact two-point homogeneous space $\mathbb M^d$ in any dimension $d\ge 2$, and evolving…
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and…
Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and L\'evy processes. By contrast, two-time occupation statistics, which…
We give a simple derivation of the distribution of the maximum L of the length of the queue during a busy period for the M/M/1 queue with lambda<1 the ratio between arrival rate and service rate. We observe that the asymptotic behavior of…
We extend the measure-valued fluid model, which tracks residuals of patience and service times, to allow for time-varying arrivals. The fluid model can be characterized by a one-dimensional convolution equation involving both the patience…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…
We study the stationary sojourn time distribution in an M/G/1 queue operating under heavy traffic. It is known that the sojourn time converges to an exponential distribution in the limit. Our focus is on obtaining pre-asymptotic,…
Overlap times have been studied as a way of understanding the time of interaction between customers in a service facility. Most of the previous analysis relies on the single jump assumption for arrivals, which implies the queue increases by…
We prove functional limits theorems for the occupation time process of a system of particles moving independently in $R^d$ according to a symmetric $\alpha$-stable L\'evy process, and starting off from an inhomogeneous Poisson point measure…
We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. While saturated-buffer scenarios have been widely investigated and yield useful throughput estimates for…
In this paper, we study the following batch scheduling model: find a schedule that minimizes total flow time for $n$ uniform length jobs, with release times and deadlines, where the machine is only actively processing jobs in at most $k$…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
This work investigates the effect of finite buffer sizes on the throughput capacity and packet delay of line networks with packet erasure links that have perfect feedback. These performance measures are shown to be linked to the stationary…
One practical open problem is the development of a distributed algorithm that achieves near-optimal utility using only a finite (and small) buffer size for queues in a stochastic network. This paper studies utility maximization (or cost…
In this paper, a mixed integer linear formulation for problems considering time-of-use-type constraints for uninterruptible services is presented. Our work is motivated by demand response problems in power systems, in which certain devices…
We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in…
We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To…