Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory

DOI10.1214/12-AAP861zbMath1274.60244arXiv1001.0895OpenAlexW3104995436MaRDI QIDQ1950259

Malwina J. Luczak, James R. Norris

Publication date: 10 May 2013

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

Full work available at URL: https://arxiv.org/abs/1001.0895

zbMATH Keywords

law of large numberscorrectorsfast variablessupermarket modeljoin the shortest queueexponential martingale inequalitiesfluid limits for Markov chainssupermarket model with memory

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (6)

Scalable Load Balancing in Networked Systems: A Survey of Recent Advances ⋮ The Power of Filling in Balanced Allocations ⋮ Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms ⋮ The supermarket model with bounded queue lengths in equilibrium ⋮ Power-of-d-Choices with Memory: Fluid Limit and Optimality ⋮ Unnamed Item

Cites Work

• Differential equation approximations for Markov chains
• Asymptotic analysis of multiscale approximations to reaction networks
• Queueing system with selection of the shortest of two queues: An asymptotic approach
• Functional central limit theorems for a large network in which customers join the shortest of several queues
• Asymptotic distributions and chaos for the supermarket model
• On the maximum queue length in the supermarket model
• Strong approximation for the supermarket model
• Chaoticity on path space for a queueing network with selection of the shortest queue among several

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