On the maximum queue length in the supermarket model

DOI10.1214/00911790500000710zbMath1102.60083arXivmath/0605639OpenAlexW3101587807MaRDI QIDQ2496955

Malwina J. Luczak, Colin J. H. McDiarmid

Publication date: 26 July 2006

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

Full work available at URL: https://arxiv.org/abs/math/0605639

zbMATH Keywords

join the shortest queuerandom choices

Mathematics Subject Classification ID

Combinatorics in computer science (68R05) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Combinatorial probability (60C05) Performance evaluation, queueing, and scheduling in the context of computer systems (68M20) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (26)

Nonlinear Markov processes in big networks ⋮ Two Parallel Queues with Infinite Servers andJoin the Shortest QueueDiscipline ⋮ Long-term concentration of measure and cut-off ⋮ Near equilibrium fluctuations for supermarket models with growing choices ⋮ Decay of tails at equilibrium for FIFO join the shortest queue networks ⋮ Asymptotic independence of queues under randomized load balancing ⋮ Scalable Load Balancing in Networked Systems: A Survey of Recent Advances ⋮ Stability of Parallel Server Systems ⋮ Stochastic coordination in heterogeneous load balancing systems ⋮ Universality of Power-of-d Load Balancing in Many-Server Systems ⋮ Introduction to shape stability for a storage model ⋮ Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory ⋮ Stability of join the shortest queue networks ⋮ The mean-field computation in a supermarket model with server multiple vacations ⋮ Choice-driven phase transition in complex networks ⋮ Negatively reinforced balanced urn schemes ⋮ Block-structured supermarket models ⋮ The supermarket model with bounded queue lengths in equilibrium ⋮ Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues ⋮ Linear de-preferential urn models ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime ⋮ The Supermarket Game ⋮ On the power of two choices: balls and bins in continuous time ⋮ Strong approximation for the supermarket model ⋮ Balanced routing of random calls ⋮ Dynamics of the Non-Homogeneous Supermarket Model

Cites Work

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• Queueing system with selection of the shortest of two queues: An asymptotic approach
• Fast Jackson networks
• 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 power of two choices: balls and bins in continuous time
• Strong approximation for the supermarket model
• Chaoticity on path space for a queueing network with selection of the shortest queue among several
• The Effect of Increasing Routing Choice on Resource Pooling

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