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The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…

Probability · Mathematics 2021-07-01 Vyacheslav M. Abramov

A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs…

Probability · Mathematics 2020-12-21 Seva Shneer , Alexander Stolyar

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

Randomized load-balancing algorithms play an important role in improving performance in large-scale networks at relatively low computational cost. A common model of such a system is a network of $N$ parallel queues in which incoming jobs…

Probability · Mathematics 2020-08-20 Pooja Agarwal , Kavita Ramanan

We consider large fluctuations, namely overload of servers, in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers, the messages of any flow are distributed…

Probability · Mathematics 2008-03-19 E. A. Pechersky , N. D. Vvedenskaya

We consider a system with several job types and two parallel server pools. Within the pools the servers are homogeneous, but across pools possibly not in the sense that the service speed of a job may depend on its type as well as the server…

Performance · Computer Science 2020-05-28 Youri Raaijmakers , Sem Borst , Onno Boxma

We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit…

Probability · Mathematics 2010-01-14 Anatolii A. Puhalskii , Josh E. Reed

In most service systems, the servers are humans who desire to experience a certain level of idleness. In call centers, this manifests itself as the call avoidance behavior, where servers strategically adjust their service rate to strike a…

Probability · Mathematics 2025-05-28 Burak Büke , Goncalo dos Reis , Vadim Platonov

We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the…

Optimization and Control · Mathematics 2025-07-18 Bowen Xie , Haoyu Yin

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…

Probability · Mathematics 2017-05-02 Marko Boon , Onno Boxma , Offer Kella , Masakiyo Miyazawa

In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…

The large-time behavior of a nonlinearly coupled pair of measure-valued transport equations with discontinuous boundary conditions, parameterized by a positive real-valued parameter $\lambda$, is considered. These equations describe the…

Probability · Mathematics 2021-07-13 Rami Atar , Weining Kang , Haya Kaspi , Kavita Ramanan

A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…

Computer Science and Game Theory · Computer Science 2021-12-21 Roberto Cominetti , José Correa , Neil Olver

In large-scale distributed systems, balancing the load in an efficient way is crucial in order to achieve low latency. Recently, some load balancing policies have been suggested which are able to achieve a bounded maximum queue length in…

Performance · Computer Science 2022-01-12 Tim Hellemans , Grzegorz Kielanski , Benny Van Houdt

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…

Probability · Mathematics 2020-01-01 Michel Mandjes , Nicos Starreveld , René Bekker

In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account…

Probability · Mathematics 2020-04-13 Harsha Honnappa , Yiran Liu , Samy Tindel , Aaron Yip

This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…

Probability · Mathematics 2020-04-21 Onno Boxma , Mariska Heemskerk , Michel Mandjes

We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first two terms in the asymptotic expansions of the moments of L…

Probability · Mathematics 2011-07-11 Patrick Eschenfeldt , Ben Gross , Nicholas Pippenger

Traffic to any server is rarely constant over time. In addition, the workload brought by each service request is typically unknown in advance, and each request may bring a different workload to the server. Cha and Lee (2011) proposed a…

Probability · Mathematics 2015-11-16 Rachel Traylor

A fundamental problem in distributed computing is the distribution of requests to a set of uniform servers without a centralized controller. Classically, such problems are modeled as static balls into bins processes, where $m$ balls (tasks)…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-03-08 Petra Berenbrink , Tom Friedetzky , Peter Kling , Frederik Mallmann-Trenn , Lars Nagel , Chris Wastell