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We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing…

Probability · Mathematics 2014-10-10 A. B. Dieker , Tonghoon Suk

We consider a class of multi-agent distributed synchronization systems, which are modeled as $n$ particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in [15], employing so-called…

Probability · Mathematics 2026-02-13 Alexander Stolyar

We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic…

Probability · Mathematics 2017-11-20 Pascal Moyal

The non-stationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large scale multi-server service systems that may experience customer abandonments, such as call centers, hospitals, and…

Probability · Mathematics 2026-01-14 Andrew Daw , Jamol Pender

In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this…

Probability · Mathematics 2014-08-04 Marko Boon , Sandra van Wijk , Ivo Adan , Onno Boxma

Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\lambda:[0,\infty)\rightarrow[0,\lambda_h ]$ for some…

Probability · Mathematics 2025-03-18 Shreehari Anand Bodas , Royi Jacobovic

Motivated by applications such as urban traffic control and make-to-order systems, we study a fluid model of a single-server, on-off system that can accommodate multiple queues. The server visits each queue in order: when a queue is served,…

Computer Science and Game Theory · Computer Science 2025-04-01 Yanwei Sun , Zhe Liu , Chiwei Yan

This paper investigates a partially observable queueing system with $N$ nodes in which each node has a dedicated arrival stream. There is an extra arrival stream to balance the load of the system by routing its customers to the shortest…

Probability · Mathematics 2021-01-01 Qihui Bu , Liwei Liu , Jiashan Tang , Yiqiang Q. Zhao

We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by…

Probability · Mathematics 2013-05-24 Sem Borst , Florian Simatos

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…

Probability · Mathematics 2018-08-21 Philip Ernst , Søren Asmussen , John Hasenbein

We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy…

Probability · Mathematics 2014-03-24 Rami Atar , Itai Gurvich

This paper proposes a totally asymmetric simple exclusion process on a traveling lane, which is equipped with a queueing system and functions of site assignments along the parking lane. In the proposed system, new particles arrive at the…

Cellular Automata and Lattice Gases · Physics 2018-10-10 Satori Tsuzuki , Daichi Yanagisawa , Katsuhiro Nishinari

We consider an acyclic network of single-server queues with heterogeneous processing rates. It is assumed that each queue is fed by the superposition of a large number of i.i.d. Gaussian processes with stationary increments and positive…

Probability · Mathematics 2020-09-01 Martin Zubeldia , Michel Mandjes

We study a continuous-time, infinite-horizon dynamic bipartite matching problem. Suppliers arrive according to a Poisson process; while waiting, they may abandon the queue at a uniform rate. Customers on the other hand must be matched upon…

Data Structures and Algorithms · Computer Science 2025-06-03 Alireza AmaniHamedani , Ali Aouad , Amin Saberi

In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…

Machine Learning · Statistics 2025-05-07 Jung-hun Kim , Min-hwan Oh

We consider a dynamic model of traffic that has received a lot of attention in the past few years. Infinitesimally small agents aim to travel from a source to a destination as quickly as possible. Flow patterns vary over time, and…

Computer Science and Game Theory · Computer Science 2024-02-08 Neil Olver , Leon Sering , Laura Vargas Koch

Motivated by applications in online marketplaces such as ride-hailing platforms and payment channel networks, we study a single-server queue with state-dependent arrival control. The service operator dynamically chooses the arrival rate as…

Optimization and Control · Mathematics 2026-02-03 Tianze Qu , Sushil Mahavir Varma

We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…

Probability · Mathematics 2026-03-20 Nicos Georgiou , Enrico Scalas , Vladislav Vysotsky

We study a token-based central queue with multiple customer types. Customers of each type arrive according to a Poisson process and have an associated set of compatible tokens. Customers may only receive service when they have claimed a…

Probability · Mathematics 2019-02-07 U. Ayesta , T. Bodas , J. L. Dorsman , I. M. Verloop

We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding…

Probability · Mathematics 2009-12-10 Rishi Talreja , Ward Whitt