Brownian models of multiclass queueing networks: Current status and open problems

DOI10.1007/BF01158927zbMath0781.60090OpenAlexW1974927663MaRDI QIDQ1801804

J. Michael Harrison, Vien Nguyen

Publication date: 17 February 1994

Published in: Queueing Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01158927

zbMATH Keywords

functional central limit theoremnumerical examplesnetwork processessojourn time distributionsheavy traffic approximationBrownian modelcumulative service capacity processmulticlass customers

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Brownian motion (60J65)

Related Items (42)

Heavy traffic limits for some queueing networks ⋮ Real-time queues in heavy traffic with earliest-deadline-first queue discipline ⋮ Strong approximations for multiclass feedforward queueing networks. ⋮ Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant ⋮ A law of the iterated logarithm for the sojourn time process in queues in series ⋮ Polling systems with periodic server routing in heavy traffic: renewal arrivals ⋮ Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks ⋮ Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline ⋮ Splitting Algorithms for Rare Events of Semimartingale Reflecting Brownian Motions ⋮ Queueing Network Controls via Deep Reinforcement Learning ⋮ Continuum modeling and control of large nonuniform wireless networks via nonlinear partial differential equations ⋮ Convergence to equilibria for fluid models of FIFO queueing networks ⋮ A multiclass closed queueing network with unconventional heavy traffic behavior ⋮ Nonnegativity of solutions to the basic adjoint relationship for some diffusion processes ⋮ Positive recurrence for reflecting Brownian motion in higher dimensions ⋮ Large systems of diffusions interacting through their ranks ⋮ About the sojourn time process in multiphase queueing systems ⋮ Ergodic optimization of stochastic differential systems in wireless networks ⋮ A law of the iterated logarithm for global values of waiting time in multiphase queues. ⋮ Competing particle systems evolving by interacting Lévy processes ⋮ A multi-dimensional SRBM: geometric views of its product form stationary distribution ⋮ State space collapse for asymptotically critical multi-class fluid networks ⋮ A LINEAR PROGRAMMING APPROACH TO THE STEADY-STATE ANALYSIS OF REFLECTED BROWNIAN MOTION ⋮ On the global values of the queue length in open queueing networks ⋮ Positive recurrence of reflecting Brownian motion in three dimensions ⋮ On extreme values in open queueing networks ⋮ A positive recurrent reflecting Brownian motion with divergent fluid path ⋮ Unnamed Item ⋮ Bounds on the Mean Delay in Multiclass Queueing Networks under Shortfall-Based Priority Rules ⋮ Sample path large deviations for multiclass feedforward queueing networks in critical loading ⋮ State-space collapse in stationarity and its application to a multiclass single-server queue in heavy traffic ⋮ Optimal scheduling and power allocation in wireless networks with heavy traffic ⋮ Polling systems with periodic server routeing in heavy traffic: distribution of the delay ⋮ Maximum Values in Queueing Processes ⋮ Nonexistence of Brownian models for certain multiclass queueing networks ⋮ Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling ⋮ On the analysis of the virtual waiting time in open queueing networks ⋮ Beyond Heavy-Traffic Regimes: Universal Bounds and Controls for the Single-Server Queue ⋮ Robust scheduling for flexible processing networks ⋮ Fractional Brownian heavy traffic approximations of multiclass feedforward queueing networks ⋮ Complex transient phenomena in multiphase queuing systems. II ⋮ Towards better multi-class parametric-decomposition approximations for open queueing networks

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