Regenerative closed queueing networks

DOI10.1080/17442509208833777zbMath0767.60094OpenAlexW2050995572MaRDI QIDQ4018646

Haya Kaspi, Avishai Mandelbaum

Publication date: 16 January 1993

Published in: Stochastics and Stochastic Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442509208833777

zbMATH Keywords

stationary distributionclosed queueing networkpiecewise-deterministic Markov processreflected Brownian motion on a simplex

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Continuous-time Markov processes on general state spaces (60J25) Queueing theory (aspects of probability theory) (60K25) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17) Ergodic theory (37A99) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

Related Items (13)

Ergodicity of Jackson-type queueing networks ⋮ Stability analysis of regenerative queueing systems ⋮ The stability of a non-homogeneous queueing system with regenerative input ⋮ Fluid limits to analyze long-term flow rates of a stochastic network with ingress discarding ⋮ Blocking a transition in a free choice net and what it tells about its throughput. ⋮ Stability of mixed generalized Jackson networks ⋮ Strong consistency of infinitesimal perturbation analysis for tandem queueing networks ⋮ Validity of heavy traffic steady-state approximations in generalized Jackson networks ⋮ State-space collapse in stationarity and its application to a multiclass single-server queue in heavy traffic ⋮ Weak regenerative structure of an open Jackson queueing network ⋮ Diffusion Limit of Fair Resource Control—Stationarity and Interchange of Limits ⋮ State-dependent stochastic networks. I: Approximation and applications with continuous diffusion limits ⋮ Wide sense regenerative processes with applications to multi-channel queues and networks

Cites Work

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• The stability of open queueing networks
• Queues as Harris recurrent Markov chains
• Stochastic discrete flow networks: Diffusion approximations and bottlenecks
• Stability of generalized Jackson networks
• Notes on the stability of closed queueing networks
• Brownian models of closed queueing networks with homogeneous customer populations
• Sojourn times in closed queueing networks
• Continuity of Generalized Semi-Markov Processes
• Regeneration in tandem queues
• On Harris Recurrence in Continuous Time
• Limit Theorems for Queueing Networks. I
• Closed Queuing Systems with Exponential Servers

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