Diffusion approximation for open state-dependent queueing networks in the heavy traffic situation

DOI10.1214/aoap/1177004602zbMath0870.60025OpenAlexW2044770455WikidataQ56084150 ScholiaQ56084150MaRDI QIDQ1916479

Keigo Yamada

Publication date: 8 September 1997

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

Full work available at URL: https://doi.org/10.1214/aoap/1177004602

zbMATH Keywords

diffusion approximationqueueing systemsopen queueing networkheavy traffic conditionmultidimensional birth and death processesmultidimensional diffusion with oblique reflection

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Applications of stochastic analysis (to PDEs, etc.) (60H30) Functional limit theorems; invariance principles (60F17)

Related Items (16)

Approximations and Optimal Control for State-Dependent Limited Processor Sharing Queues ⋮ Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic ⋮ A note on transition density for the reflected Ornstein-Uhlenbeck process ⋮ On moment stability properties for a class of state-dependent stochastic networks ⋮ A note on stability in distribution of Markov-modulated stochastic differential equations with reflection ⋮ On the default probability in a regime-switching regulated market ⋮ Diffusion approximation for signaling stochastic networks ⋮ Exit time and invariant measure asymptotics for small noise constrained diffusions ⋮ \(V\)-uniform ergodicity for state-dependent single class queueing networks ⋮ Multiscale diffusion approximations for stochastic networks in heavy traffic ⋮ Monotonicity properties of multi-dimensional reflected diffusions in random environment and applications ⋮ A nonzero-sum stochastic differential game in the orthant ⋮ Convergence of a queueing system in heavy traffic with general patience-time distributions ⋮ A stochastic differential game in the orthrant ⋮ Non-Markovian State-Dependent Networks in Critical Loading ⋮ Optimal service rate perturbations of many server queues in heavy traffic

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