Ergodic control of multi-class \(\mathrm{M}/\mathrm{M}/N+\mathrm{M}\) queues in the Halfin-Whitt regime

DOI10.1214/14-AAP1081zbMath1330.60108arXiv1404.1957OpenAlexW1868692815WikidataQ60167476 ScholiaQ60167476MaRDI QIDQ894815

Anup Biswas, Guodong Pang, Aristotle Arapostathis

Publication date: 24 November 2015

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.1957

zbMATH Keywords

diffusion approximationergodic controlasymptotic optimalityHalfin-Whitt regimespatial truncationstable Markov optimal controllong time-average controlmulti-class Markovian queues

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Stochastic scheduling theory in operations research (90B36) Optimal stochastic control (93E20) Diffusion processes (60J60) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20)

Related Items (13)

Optimal sizing of the sediment replenishment capacity based on robust ergodic control of subordinator-driven dynamics ⋮ Two‐class constrained optimization with applications to queueing control ⋮ Delay-Based Service Differentiation with Many Servers and Time-Varying Arrival Rates ⋮ Optimal Control of Markov-Modulated Multiclass Many-Server Queues ⋮ An ergodic control problem for many-server multiclass queueing systems with cross-trained servers ⋮ Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis ⋮ Optimal scheduling of critically loaded multiclass \(GI/m/n+m\) queues in an alternating renewal environment ⋮ Ergodicity of a Lévy-driven SDE arising from multiclass many-server queues ⋮ Infinite horizon asymptotic average optimality for large-scale parallel server networks ⋮ Infinite-Horizon Average Optimality of the N-Network in the Halfin–Whitt Regime ⋮ On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime ⋮ Uniform stability of some large-scale parallel server networks ⋮ Exponential ergodicity and steady-state approximations for a class of markov processes under fast regime switching

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Positive recurrence of piecewise Ornstein-Uhlenbeck processes and common quadratic Lyapunov functions
• Multiclass multiserver queueing system in the Halfin-Whitt heavy traffic regime: asymptotics of the stationary distribution
• Dynamic scheduling of a \(GI/GI/1+GI\) queue with multiple customer classes
• Diffusion models and steady-state approximations for exponentially ergodic Markovian queues
• Scheduling control for Markov-modulated single-server multiclass queueing systems in heavy traffic
• On the asymptotic optimality of the \(c \mu / \theta \) rule under ergodic cost
• Control of the multiclass \(\mathrm{G}/\mathrm{G}/1\) queue in the moderate deviation regime
• Optimal control of parallel server systems with many servers in heavy traffic
• Martingale proofs of many-server heavy-traffic limits for Markovian queues
• Degenerate variance control in the one-dimensional stationary case
• Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy traffic.
• Dynamic scheduling with convex delay costs: The generalized \(c\mu\) rule
• Existence of strong solutions for Itô's stochastic equations via approximations
• Validity of heavy traffic steady-state approximations in generalized Jackson networks
• Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic
• ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
• Ergodic Rate Control Problem for Single Class Queueing Networks
• The cμ/θ Rule for Many-Server Queues with Abandonment
• Ergodic Control of Diffusion Processes
• Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime
• Heavy-Traffic Limits for Queues with Many Exponential Servers
• On ergodic stochastic control
• Large Time Behavior of Solutions of Hamilton--Jacobi--Bellman Equations with Quadratic Nonlinearity in Gradients
• Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule
• Statistical Analysis of a Telephone Call Center
• Admission control for a multi-server queue with abandonment

This page was built for publication: Ergodic control of multi-class \(\mathrm{M}/\mathrm{M}/N+\mathrm{M}\) queues in the Halfin-Whitt regime