Related papers: Sojourn time in a $M^{[X]}/M/1$ Processor Sharing …
We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…
We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The…
This paper provides a mathematical framework for estimation of the service time distribution and the expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process, in the case of partial…
The distribution of electron waiting times is useful to characterize quantum transport in mesoscopic structures. Here we consider a generic quantum-coherent conductor consisting of a mesoscopic scatterer in a two-terminal setup. We extend…
We present new, simple, fully distributed, practical algorithms with linear time communication cost for irregular gather and scatter operations in which processors contribute or consume possibly different amounts of data. In a linear cost…
We consider a discrete population of users with homogeneous service demand who need to decide when to arrive to a system in which the service rate deteriorates linearly with the number of users in the system. The users have heterogeneous…
We prove limit theorems for rescaled occupation time fluctuations of a (d,alpha,beta)-branching particle system (particles moving in R^d according to a spherically symmetric alpha-stable Levy process, (1+beta)-branching, 0<beta<1, uniform…
Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…
In this paper, we introduce a nonlinear stochastic model to describe the propagation of information inside a computer processor. In this model, a computational task is divided into stages, and information can flow from one stage to another.…
We consider the FCFS G/G/n queue in the Halfin-Whitt regime, in the presence of heavy-tailed distributions (i.e. infinite variance). We prove that under minimal assumptions, i.e. only that processing times have finite 1 + epsilon moment and…
The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…
We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the…
Join-the-Shortest-Queue (JSQ) is the scheduling policy of choice for many network providers, cloud servers and traffic management systems, where individual queues are served under processor sharing (PS) queueing discipline. A numerical…
We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…
We provide power series approximations for a structured batch arrival single server retrial system with two infinite capacity weighted fair orbit queues, i.e., the re-transmission rate of an orbit depends on the state of the other orbit…
We compute the stationary performance metrics of a single server $M^X/G/1$ queue under a class of generalized processor-sharing scheduling policies that are proposed by Grishechkin. This class of processor-sharing policies allow service…
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or…
We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…
In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…
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…