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Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…

Probability · Mathematics 2025-03-18 Anton Braverman , Ziv Scully

In multi-server queueing systems where there is no central queue holding all incoming jobs, job dispatching policies are used to assign incoming jobs to the queue at one of the servers. Classic job dispatching policies such as…

Systems and Control · Electrical Eng. & Systems 2021-06-11 Tuhinangshu Choudhury , Gauri Joshi , Weina Wang , Sanjay Shakkottai

Packet-dispersion based measurement tools insert pairs of probe packets with a known separation into the network for transmission over a unicast path or a multicast tree. Samples of the separation between the probe pairs at the…

Networking and Internet Architecture · Computer Science 2009-11-19 Bikash Kumar Dey , D. Manjunath , Supriyo Chakraborty

Queues that feature multiple entities arriving simultaneously are among the oldest models in queueing theory, and are often referred to as "batch" (or, in some cases, "bulk") arrival queueing systems. In this work we study the affect of…

Probability · Mathematics 2019-02-05 Andrew Daw , Jamol Pender

We consider a queue with renewal arrivals and n exponential servers in the Halfin-Whitt heavy traffic regime, where n and the arrival rate increase without bound, so that a critical loading condition holds. Server k serves at rate $\mu_k $,…

Probability · Mathematics 2007-11-15 Rami Atar , Adam Shwartz

This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…

Probability · Mathematics 2024-09-05 B. R. Vinay Kumar , Lasse Leskelä

We revisit the classical problem of minimizing the total flow time of jobs on a single machine in the online setting where jobs arrive over time. It has long been known that the Shortest Remaining Processing Time (SRPT) algorithm is optimal…

Data Structures and Algorithms · Computer Science 2025-08-26 Anupam Gupta , Haim Kaplan , Alexander Lindermayr , Jens Schlöter , Sorrachai Yingchareonthawornchai

We consider the FCFS $GI/GI/n$ queue in the Halfin-Whitt heavy traffic regime, and prove bounds for the steady-state probability of delay (s.s.p.d.) for generally distributed processing times. We prove that there exist $\epsilon_1,…

Probability · Mathematics 2016-09-02 David A. Goldberg

We consider the following distributed service model: jobs with unit mean, exponentially distributed, and independent processing times arrive as a Poisson process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched by a…

Probability · Mathematics 2017-09-14 David Gamarnik , John N. Tsitsiklis , Martin Zubeldia

In this paper, we present a stability criterion for Processor Sharing queues, in which the throughput may depend on the number of customers in the system (in such cases such as interferences between the users). Such a system is represented…

Probability · Mathematics 2008-03-18 Pascal Moyal

We consider the problem of simultaneous scheduling and resource allocation of an incoming flow of requests to a set of computing units. By representing each computing unit as a node, we model the overall system as a multi-queue scheme.…

Systems and Control · Electrical Eng. & Systems 2021-09-07 Eleftherios Vlahakis , Nikolaos Athanasopoulos , Sean McLoone

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…

Statistical Mechanics · Physics 2015-06-24 Bosiljka Tadic , Stefan Thurner

We investigate the steady-state diffusion-approximation error for continuous-time queueing systems with generally distributed primitives. Across four canonical systems -- the $G/G/1$ and $G/M/\infty$ queues, the join-the-shortest-queue…

Probability · Mathematics 2025-09-03 Anton Braverman , Ziv Scully

We consider a system of $N$ parallel single-server queues with unit exponential service rates and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to a server…

In this work, the achievable rate of three-node relay systems with selection relaying under statistical delay constraints, imposed on the limitations of the maximum end-to-end delay violation probabilities, is investigated. It is assumed…

Information Theory · Computer Science 2015-10-14 Deli Qiao

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…

Probability · Mathematics 2009-12-16 Josh Reed

In this paper we study the power-performance relationship of power-efficient computing from a queuing theoretic perspective. We investigate the interplay of several system operations including processing speed, system on/off decisions, and…

Performance · Computer Science 2013-03-08 Yanpei Liu , Stark C. Draper , Nam Sung Kim

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…

Statistical Mechanics · Physics 2026-05-18 José Giral-Barajas , Paul C. Bressloff

Maximizing throughput for heterogeneous parallel server queues has received quite a bit of attention from the research community and the stability region for such systems is well understood. However, many real-world systems have periods…

Dynamical Systems · Mathematics 2011-08-31 Carri W. Chan , Mor Armony , Nicholas Bambos

We consider a setting where qubits are processed sequentially, and derive fundamental limits on the rate at which classical information can be transmitted using quantum states that decohere in time. Specifically, we model the sequential…

Information Theory · Computer Science 2019-04-15 Avhishek Chatterjee , Krishna Jagannathan , Prabha Mandayam