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Filtration, flow in narrow channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. If the blockage is temporary, which means that after a finite time the channel…

Statistical Mechanics · Physics 2018-08-01 G. Page , J. Resing , P. Viot , J. Talbot

The combination of boundary flow control and variable speed limit (VSL) is a widely used strategy for highway corridors to maintain safety and throughput when the capacity downstream is dropped. However, most proposed models assume fixed…

Optimization and Control · Mathematics 2021-10-28 Hao Liu , Suyash Vishnoi , Christian Claudel

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 load balancing system comprised of a fixed number of single server queues, operating under the well-known Join-the-Shortest Queue policy, and where jobs/customers are impatient and abandon if they do not receive service after…

Probability · Mathematics 2023-04-05 Prakirt Raj Jhunjhunwala , Martin Zubeldia , Siva Theja Maguluri

We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…

Probability · Mathematics 2020-09-01 Lun Yu , Ohad Perry

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

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service…

Optimization and Control · Mathematics 2022-03-04 Melis Boran , Bahar Cavdar , Tugce Isik

Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current…

Performance · Computer Science 2016-05-11 Taoyu Li , Minghua Chen , Tony Lee , Xing Li

Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…

Probability · Mathematics 2025-04-25 Bernardo D'Auria , Ivo J. B. F. Adan , René Bekker , Vidyadhar Kulkarni

In this paper we analyze the quasi-stationary workload of a L\'evy-driven storage system. More precisely, assuming the system is in stationarity, we study its behavior conditional on the event that the busy period $T$ in which time 0 is…

Probability · Mathematics 2011-10-19 Michel Mandjes , Zbigniew Palmowski , Tomasz Rolski

We study a queueing network with a strictly upper-triangular routing matrix, where each column contains at most one non-negative entry, and the root node receives input from a spectrally positive L\'{e}vy process. Our aim is to characterize…

Probability · Mathematics 2026-02-05 Krzysztof Dȩbicki , Nikolai Kriukov , Michel Mandjes

The performance of non-preemptive M/M/1 queueing system with two priority is analyzed. By using complementary variable method to make vector Markov process and analyzing the state-change equations of the queueing system, the generating…

Optimization and Control · Mathematics 2009-02-13 Zhao Guo-xi , Hu Qi-Zhou

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

In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of $N$ servers and the distance of arrival rate to…

Probability · Mathematics 2020-04-28 Xingyu Zhou , Ness Shroff

We develop a fluid-flow model for routing problems, where fluid consists of different size particles and the task is to route the incoming fluid to $n$ parallel servers using the size information in order to minimize the mean latency. The…

Performance · Computer Science 2025-09-29 Runhan Xie , Esa Hyytiä , Rhonda Righter

This work considers a server that processes $J$ classes using the generalized processor sharing discipline with base weight vector $\alpha=(\alpha _1,...,\alpha_J)$ and redistribution weight vector $\beta=(\beta_1,...,\beta_J)$. The…

Probability · Mathematics 2008-01-28 Kavita Ramanan , Martin I. Reiman

In a carsharing system, a fleet of cars is distributed at stations in an urban area, customers can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio…

Data Structures and Algorithms · Computer Science 2015-11-10 Sahar Bsaybes , Alain Quilliot , Annegret K. Wagler , Jan-Thierry Wegener

Distributed load balancing is the act of allocating jobs among a set of servers as evenly as possible. There are mainly two versions of the load balancing problem that have been studied in the literature: static and dynamic. The static…

Performance · Computer Science 2020-11-04 Nitish K. Panigrahy , Thirupathaiah Vasantam , Prithwish Basu , Don Towsley

We study an ordinary differential equation (ODE) arising as the many-server heavy-traffic fluid limit of a sequence of overloaded Markovian queueing models with two customer classes and two service pools. The system, known as the X model in…

Probability · Mathematics 2010-08-10 Ohad Perry , Ward Whitt

This paper calculates transient distributions of a special class of Markov processes with continuous state space and in continuous time, up to an explicit error bound. We approximate specific queues on R with one-sided L\'evy input, such as…

Probability · Mathematics 2025-04-03 Fabian Michel , Markus Siegle