Fluid and heavy traffic diffusion limits for a generalized processor sharing model

DOI10.1214/aoap/1042765664zbMath1016.60083OpenAlexW2101049248MaRDI QIDQ1872348

Martin I. Reiman, Kavita Ramanan

Publication date: 6 May 2003

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

Full work available at URL: https://semanticscholar.org/paper/24f02be62a496f4f55e2c0d0105b0ab37c975553

zbMATH Keywords

sojourn timequeue lengthsingle server queueing systemcustomer classesunfinished workgeneralized processor sharing disciplinewaiting time processes

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22)

Related Items (22)

A Fair Policy for the G/GI/N Queue with Multiple Server Pools ⋮ The Skorohod oblique reflection problem in time-dependent domains ⋮ Large deviations and exit-times for reflected McKean-Vlasov equations with self-stabilising terms and superlinear drifts ⋮ Fluid limits of many-server queues with reneging ⋮ Asymptotic behaviors of small perturbation for multivalued Mckean-Vlasov stochastic differential equations ⋮ Limit theorems of invariant measures for multivalued McKean-Vlasov stochastic differential equations ⋮ Law of large numbers limits for many-server queues ⋮ On Viscosity Solution of HJB Equations with State Constraints and Reflection Control ⋮ A Monte Carlo Method for Estimating Sensitivities of Reflected Diffusions in Convex Polyhedral Domains ⋮ Reflected Brownian motion with drift in a wedge ⋮ An ergodic control problem for many-server multiclass queueing systems with cross-trained servers ⋮ The heavy traffic limit of an unbalanced generalized processor sharing model ⋮ Heavy traffic analysis for EDF queues with reneging ⋮ Interacting queues in heavy traffic ⋮ A Dirichlet process characterization of a class of reflected diffusions ⋮ Characterization of stationary distributions of reflected diffusions ⋮ The Skorokhod problem in a time-dependent interval ⋮ AnRG-Factorization Approach for a BMAP/M/1 Generalized Processor-Sharing Queue ⋮ A stochastic analysis of resource sharing with logarithmic weights ⋮ Diffusion Limit of Fair Resource Control—Stationarity and Interchange of Limits ⋮ Pathwise differentiability of reflected diffusions in convex polyhedral domains ⋮ On the roughness of the paths of RBM in a wedge

Cites Work

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