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We study ergodic properties of Markovian multiclass many-server queues which are uniform over scheduling policies, as well as the size n of the system. The system is heavily loaded in the Halfin-Whitt regime, and the scheduling policies are…

Optimization and Control · Mathematics 2019-11-25 Ari Arapostathis , Hassan Hmedi , Guodong Pang

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…

Probability · Mathematics 2011-05-04 David Gamarnik , Alexander Stolyar

A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time…

Probability · Mathematics 2018-05-02 Rami Atar , Asaf Cohen

The Join-the-Shortest-Queue (JSQ) load balancing scheme is known to minimise the average response time of jobs in homogeneous systems with identical servers. However, for {\em heterogeneous} systems with servers having different processing…

Probability · Mathematics 2024-10-22 Sanidhay Bhambay , Burak Büke , Arpan Mukhopadhyay

We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy…

Probability · Mathematics 2012-10-04 H. Christian Gromoll , Łukasz Kruk , Amber L. Puha

We develop Bellman equation based approach for infinite time horizon optimal impulsive control problems. Both discounted and time average criteria are considered. We establish very general and at the same time natural conditions under which…

Networking and Internet Architecture · Computer Science 2013-11-28 Konstantin Avrachenkov , Oussama Habachi , Alexei Piunovskiy , Zhang Yi

We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs (i.e., abandonment costs and holding costs) with server utilization costs. To solve the control problem, we…

Optimization and Control · Mathematics 2023-11-08 Yueyang Zhong , Amy R. Ward , Amber L. Puha

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

This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite…

Optimization and Control · Mathematics 2026-02-06 Kai Ding , Xun Li , Siyu Lv , Xin Zhang

We present discrete-time approximation of optimal control policies for infinite horizon discounted/ergodic control problems for controlled diffusions in $\Rd$\,. In particular, our objective is to show near optimality of optimal policies…

Optimization and Control · Mathematics 2025-02-11 Somnath Pradhan , Serdar Yuksel

We study $n$ parallel queues in an extreme heavy-traffic regime: each server works at rate $n$, while jobs arrive to a dispatcher at rate $n^2-(a-b)\sqrt{n}$, with fixed $a>b>0$. Arrivals are routed by a marginal join-the-shortest-queue…

Probability · Mathematics 2026-05-19 Sayan Banerjee , Amarjit Budhiraja , Eva Loeser

We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of [SIAM J. Control Optim. 57 (2019), no. 2, 1516-1540] to running costs that are not…

Optimization and Control · Mathematics 2021-01-01 Ari Arapostathis , Guodong Pang , Yi Zheng

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

We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by $N$ identical parallel servers in a…

Probability · Mathematics 2017-12-06 Reza Aghajani , Kavita Ramanan

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

Probability · Mathematics 2019-01-25 Sayan Banerjee , Debankur Mukherjee

This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…

Optimization and Control · Mathematics 2026-02-17 Mohamed Naveed Gul Mohamed , Abhijeet , Aayushman Sharma , Raman Goyal , Suman Chakravorty

We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual…

Probability · Mathematics 2022-04-13 Rami Atar , Eyal Castiel , Yonatan Shadmi

We adopt an optimal-control framework for addressing the undiscounted infinite-horizon discrete-time restless $N$-armed bandit problem. Unlike most studies that rely on constructing policies based on the relaxed single-armed Markov Decision…

Optimization and Control · Mathematics 2024-03-19 Chen YAN

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

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