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• W2022941684 abstract "Let $Z = { Z(t),t > 0} $ be a reflected Brownian motion on the K-dimensional nonnegative orthant, with the direction of reflection constant over each boundary surface. Such processes arise in heavy traffic theory for K-station networks of queues. This paper continues our study of the diffusion process Z,with attention restricted to the case $k = 2$ for simplicity. (Most of the results extend directly to higher dimensions; our notation and style of argument are designed to suggest appropriate generalizations for arbitrary K wherever possible.) The backward equation for the transition density function (with boundary and initial conditions), the corresponding forward equation and the equation for the steady-state distribution are all derived informally. Also presented are various calculations relating to steady-state distributions, including a moment formula and the derivation of a condition (involving the drifts and directions of reflection), that we conjecture to be necessary and sufficient for existence of a steady-state. Finally, the relevance of reflected Brownian motion for approximate analysis of queuing networks is reviewed, and some further references on the associated differential equations are given." @default.
• W2022941684 created "2016-06-24" @default.
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• W2022941684 date "1981-10-01" @default.
• W2022941684 modified "2023-10-18" @default.
• W2022941684 title "On the Distribution of Multidimensional Reflected Brownian Motion" @default.
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• W2022941684 doi "https://doi.org/10.1137/0141030" @default.
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