Abstract
A Functional Strong-Law-of-Large-Numbers (known as fluid limit or fluid approximation) and a Functional Central Limit Theorem (known as diffusion approximation) are proved for both open and closed networks of multi-server queues in heavy traffic. The fluid limit is a reflected piecewise linear deterministic process, and the diffusion limit is a reflected Brownian motion; both limiting processes are on the nonnegative orthant for open networks and on the nonnegative unit simplex for closed networks. The results generalize the existing ones for networks of single-server queues.
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Chen, H., Shanthikumar, J.G. Fluid limits and diffusion approximations for networks of multi-server queues in heavy traffic. Discrete Event Dyn Syst 4, 269–291 (1994). https://doi.org/10.1007/BF01438710
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DOI: https://doi.org/10.1007/BF01438710