Functional central limit theorems for a large network in which customers join the shortest of several queues

DOI10.1007/s00440-004-0372-9zbMath1058.60077arXivmath/0403538OpenAlexW2045453593MaRDI QIDQ1765118

Carl Graham

Publication date: 22 February 2005

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403538

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of dynamical systems (37N99) Functional limit theorems; invariance principles (60F17) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (16)

Nonlinear Markov processes in big networks ⋮ On a doubly dynamically controlled supermarket model with impatient customers ⋮ Scalable Load Balancing in Networked Systems: A Survey of Recent Advances ⋮ Stability of Parallel Server Systems ⋮ Universality of Power-of-d Load Balancing in Many-Server Systems ⋮ Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory ⋮ The mean-field computation in a supermarket model with server multiple vacations ⋮ Block-structured supermarket models ⋮ A functional central limit theorem for the Becker-Döring model ⋮ The supermarket model with bounded queue lengths in equilibrium ⋮ On the maximum queue length in the supermarket model ⋮ Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues ⋮ Insensitivity of the mean field limit of loss systems under SQ(d) routeing ⋮ Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime ⋮ Sensitivity of mean-field fluctuations in Erlang loss models with randomized routing ⋮ Strong approximation for the supermarket model

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