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We obtain asymptotic bounds for the tail distribution of steady-state waiting time in a two server queue where each server processes incoming jobs at a rate equal to the rate of their arrivals (that is, the half-loaded regime). The job…

Probability · Mathematics 2016-04-05 Jose Blanchet , Karthyek Murthy

In this paper, we investigate the number of customers that overlap or coincide with a virtual customer in an Erlang-A queue. Our study provides a novel approach that exploits fluid and diffusion limits for the queue to approximate the mean…

Probability · Mathematics 2025-07-02 Young Myoung Ko , Jamol Pender , Jin Xu

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…

Probability · Mathematics 2019-05-01 Zhenghua Long , Jiheng Zhang

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…

Probability · Mathematics 2025-08-28 Hoang Huy Nguyen , Sushil Mahavir Varma , Siva Theja Maguluri

This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters.…

Information Theory · Computer Science 2021-03-26 Parimal Parag , Jean-Francois Chamberland , Henry D. Pfister , Krishna R. Narayanan

We consider the problem of managing a bounded size First-In-First-Out (FIFO) queue buffer, where each incoming unit-sized packet requires several rounds of processing before it can be transmitted out. Our objective is to maximize the total…

Networking and Internet Architecture · Computer Science 2012-04-25 Kirill Kogan , Alejandro López-Ortiz , Sergey I. Nikolenko , Alexander V. Sirotkin , Denis Tugaryov

We consider the $N$-model queueing system with a waiting time dependent threshold on the diagonal: the service discipline is First--Come--First--Served, but type-1 jobs can only be served by server 2 if their waiting time exceeds a…

Probability · Mathematics 2025-11-17 Sanne van Kempen , Elene Anton , Fiona Sloothaak

This work develops a methodology for studying the effect of an offload zone on the ambulance ramping problem using a multi-server, multi-class non-preemptive priority queueing model that can be treated analytically. A prototype model for…

Systems and Control · Electrical Eng. & Systems 2024-02-01 Josef Zuk , David Kirszenblat

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…

Probability · Mathematics 2012-03-14 Tomasz Bojdecki , Luis G. Gorostiza , Anna Talarczyk

One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue…

Probability · Mathematics 2009-11-19 David Gamarnik , Dmitriy Katz

We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two…

Performance · Computer Science 2013-05-16 Fabrice Guillemin , Alain Simonian

Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…

Probability · Mathematics 2017-01-13 Angelos Aveklouris , Maria Vlasiou , Jiheng Zhang , Bert Zwart

We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions…

Probability · Mathematics 2019-03-19 Asaf Cohen

With respect to a class of long-range exclusion processes on $\mathbb{Z}^d$, with single particle transition rates of order $|\cdot|^{-(d+\alpha)}$, starting under Bernoulli invariant measure $\nu_\rho$ with density $\rho$, we consider the…

Probability · Mathematics 2014-07-31 Cédric Bernardin , Patrícia Gonçalves , Sunder Sethuraman

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

Probability · Mathematics 2012-10-12 Bojan Basrak , Danijel Krizmanić , Johan Segers

E-commerce Web-servers often face overload conditions during which revenue-generating requests may be dropped or abandoned due to an increase in the browsing requests. In this paper we present a simple, yet effective, mechanism for overload…

Performance · Computer Science 2007-05-23 Naresh Singhmar , Vipul Mathur , Varsha Apte , D. Manjunath

We study the steady-state delay performance of load balancing in large-scale systems with heterogeneous servers in the heavy-traffic regimes. The system consists of $N$ servers, each with a local buffer of size $b-1$, serving jobs in the…

Probability · Mathematics 2026-02-27 Xin Liu , Lei Ying

Let $\tau(x)$ be the epoch of first entry into the interval $(x,\infty)$, $x>0$, of the reflected process $Y$ of a L\'evy process $X$, and define the overshoot $Z(x) = Y(\tau(x))-x$ and undershoot $z(x) = x - Y(\tau(x)-)$ of $Y$ at the…

Probability · Mathematics 2013-07-29 Aleksandar Mijatović , Martijn Pistorius

In this work, we analyze the steady-state maximum overlap time distribution in a single-server queue by introducing a dependence structure between service and interarrival times under the Farlie-Gumber-Morgenstern copula. We provide…

Probability · Mathematics 2025-09-18 Ioannis Dimitriou

In a superscalar processor, instructions of various types flow through an execution pipeline, traversing hardware resources which are mostly shared among many different instruction types. A notable exception to shared pipeline resources is…

Performance · Computer Science 2018-07-24 Shane Carroll , Wei-Ming Ling