A multiclass closed queueing network with unconventional heavy traffic behavior

DOI10.1214/aoap/1034968064zbMath0865.60078OpenAlexW2059463621MaRDI QIDQ1921430

J. Michael Harrison, Ruth J. Williams

Publication date: 7 July 1997

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

Full work available at URL: http://purl.umn.edu/2780

zbMATH Keywords

Brownian motionmulticlass queueing networksheavy traffic theory

Mathematics Subject Classification ID

Stochastic network models in operations research (90B15) Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (11)

Heavy traffic limits for some queueing networks ⋮ Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline ⋮ Diffusion limits for shortest remaining processing time queues under nonstandard spatial scaling ⋮ An Analysis of a Large-Scale Machine Repair Model ⋮ Special issue: 1st international workshop on retrial queues, WRQ '98. Complutense University of Madrid, Spain, September 22--24, 1998 ⋮ Switching stochastic models and applications in retrial queues ⋮ Serve the shortest queue and Walsh Brownian motion ⋮ Induced idleness leads to deterministic heavy traffic limits for queue-based random-access algorithms ⋮ On Singular Control Problems, the Time-Stretching Method, and the Weak-M1 Topology ⋮ Diffusion approximations for Kumar-Seidman network under a priority service discipline ⋮ Averaging methods for transient regimes in overloading retrial queueing systems.

Cites Work

• Point processes and queues. Martingale dynamics
• Random time changes and convergence in distribution under the Meyer-Zheng conditions
• Weak limit theorems for stochastic integrals and stochastic differential equations
• Stochastic discrete flow networks: Diffusion approximations and bottlenecks
• Brownian models of multiclass queueing networks: Current status and open problems
• Ergodicity of stochastic processes describing the operation of open queueing networks
• Brownian models of closed queueing networks with homogeneous customer populations
• Some Useful Functions for Functional Limit Theorems
• Stability and Instability of Fluid Models for Reentrant Lines
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