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This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…

Probability · Mathematics 2019-06-12 Anton Braverman

We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…

Probability · Mathematics 2018-09-17 Maria Clara Fittipaldi , Matthieu Jonckheere , Sergio I. Lopez

We consider optimal control of a multi-class queue in the Halfin--Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide…

Probability · Mathematics 2012-03-09 Baris Ata , Itai Gurvich

Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…

Optimization and Control · Mathematics 2022-10-03 Marc Abeille , Bruno Bouchard , Lorenzo Croissant

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…

Optimization and Control · Mathematics 2023-05-22 Jodi Dianetti , Giorgio Ferrari

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…

Probability · Mathematics 2014-03-28 Alexander Stolyar

In this paper we consider a single-server cyclic polling system. Between visits to successive queues, the server is delayed by a random switch-over time. The order in which customers are served in each queue is determined by a priority…

Probability · Mathematics 2014-08-05 Marko Boon , Ivo Adan , Onno Boxma

The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…

Probability · Mathematics 2014-06-03 Anatolii A. Puhalskii

Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity $D(x)$. We investigate the ergodic and non-ergodic behavior of these processes in an arbitrary potential well $U(x)$…

Statistical Mechanics · Physics 2019-05-01 Xudong Wang , Weihua Deng , Yao Chen

This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…

Probability · Mathematics 2009-06-15 Rami Atar , Gennady Shaikhet

We consider an arbitrary network of $M/M/\infty$ queues with controlled transitions between queues. We consider optimal control problems where the costs are linear functions of the state and inputs over a finite or infinite horizon. We…

Optimization and Control · Mathematics 2025-09-11 Giovanni Pugliese Carratelli , Ioannis Lestas

We consider a large-scale flexible service system with two large server pools and two types of customers. Servers in pool 1 can only serve type 1 customers, while server in pool 2 are flexible -- they can serve both types 1 and 2. (This is…

Probability · Mathematics 2014-12-24 Alexander L. Stolyar

This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process. The uncontrolled process is assumed to be ergodic but, unlike the extant literature, the…

Optimization and Control · Mathematics 2024-02-06 Jan Palczewski , Lukasz Stettner

This paper studies a diffusion control problem motivated by challenges faced by public health agencies who run clinics to serve the public. A key challenge for these agencies is to motivate individuals to participate in the services…

Applications · Statistics 2023-12-06 Baris Ata , Deishin Lee , Mustafa H. Tongarlak

In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…

Probability · Mathematics 2015-11-13 Andrei Sleptchenko , Jori Selen , Ivo Adan , Geert-Jan van Houtum

We consider the heavy-traffic approximation to the $GI/M/s$ queueing system in the Halfin-Whitt regime, where both the number of servers $s$ and the arrival rate $\lambda$ grow large (taking the service rate as unity), with…

Probability · Mathematics 2013-02-14 Brian H. Fralix , Charles Knessl , Johan S. H. van Leeuwaarden

This self-contained discussion relates the long-run average holding cost per unit time to the long-run average response time per customer in a $G/G/1$ queue with no assumption made on the order of service. The only restriction established…

Performance · Computer Science 2021-08-18 Dylan Solms

Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…

Probability · Mathematics 2008-08-22 Rami Atar

This paper studies a 2-class, 2-server parallel server system under the recently introduced extended heavy traffic condition, which states that the underlying 'static allocation' linear program (LP) is critical, but does not require that it…

Optimization and Control · Mathematics 2022-07-19 Rami Atar , Eyal Castiel , Marty Reiman

In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and the special queue skipping policy. Customers arrive in batches, but are served one by one according to any conservative discipline. The…

Probability · Mathematics 2020-12-01 A. Zeifman , R. Razumchik , Y. Satin , I. Kovalev