Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks

DOI10.1007/BF01206549zbMath0879.60087OpenAlexW2026976591MaRDI QIDQ1362298

Maury Bramson

Publication date: 28 January 1998

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

Full work available at URL: https://doi.org/10.1007/bf01206549

zbMATH Keywords

entropyfluid modelsqueueing networksequilibria

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Queues and service in operations research (90B22) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (27)

Heavy traffic limits for some queueing networks ⋮ Invariant states and rates of convergence for a critical fluid model of a processor sharing queue. ⋮ Fluid model for a network operating under a fair bandwidth-sharing policy. ⋮ Justifying diffusion approximations for multiclass queueing networks under a moment condition ⋮ FLUID LIMIT OF A PS-QUEUE WITH MULTISTAGE SERVICE ⋮ Instability of SRPT, SERPT and SJF multiclass queueing networks ⋮ Queueing Network Controls via Deep Reinforcement Learning ⋮ Instability of LAS multiclass queueing networks ⋮ State space collapse and stability of queueing networks ⋮ The fluid limit of the multiclass processor sharing queue ⋮ Instability of LRTF multiclass queueing networks ⋮ Continuity and monotonicity of solutions to a greedy maximization problem ⋮ Stability of Kumar-Seidman networks under longest queue first policy ⋮ Stability of HLPPS and modified HLPPS policies for the re-entrant line ⋮ Lyapunov method for the stability of fluid networks ⋮ Spatial homogenization in a stochastic network with mobility ⋮ A Lyapunov view on positive harris recurrence of multiclass queueing networks ⋮ Bounds on the Mean Delay in Multiclass Queueing Networks under Shortfall-Based Priority Rules ⋮ State-space collapse in stationarity and its application to a multiclass single-server queue in heavy traffic ⋮ Stability of preemptive EDF queueing networks ⋮ Concave switching in single-hop and multihop networks ⋮ A stochastic analysis of resource sharing with logarithmic weights ⋮ STABILITY OF THE MULTI-TYPE REENTRANT LINES WITH TYPE PRIORITY SERVICE DISCIPLINE ⋮ Instability of LIFO queueing networks ⋮ A simple proof for the stability of global FIFO queueing networks ⋮ Minimal and Locally Edge Minimal Fluid Models for Resource-Sharing Networks ⋮ Measurement and optimization of robust stability of multiclass queueing networks: applications in dynamic supply chains

Cites Work

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