pVarband: Efficient and Performance Guaranteed Scheduling With Variable Bandwidth in IRS-Assisted FSO Systems in DCNs

Intelligent reflective surface (IRS)-assisted free-space optics (FSO) systems allow allocation of different number of IRS elements between communication end-points. It thus can provide connectivity with variable bandwidth in data centers, where the traffic between top-of-rack switches is often unevenly distributed in space and time. In this paper, we propose a novel traffic scheduling technique that allows variable bandwidth in the context of IRS-assisted FSO systems in data center networks (DCNs). We formalize the problem of scheduling with variable bandwidth, explore the performance space for designing scheduling algorithms, and provide insights on how to use heuristics in practice. Then, we propose a low-complexity and performance-guaranteed parallel scheduling algorithm, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pVarband</i>, that takes advantage of variable bandwidth to avoid the time-consuming maximum weight matching and can run at a complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(N\log N)$</tex-math> </inline-formula> in a DCN with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> racks. We theoretically demonstrate that scheduling with variable bandwidth requires at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(\log (1/\epsilon))$</tex-math> </inline-formula> reconfigurations to obtain an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $</tex-math> </inline-formula>-approximate decomposition for an arbitrary traffic matrix. Also, we provide insights for design and deployment of an IRS-assisted FSO system to achieve performance saturation. Our results show that scheduling allowing variable bandwidth can achieve almost optimal performance for unevenly distributed traffic, and also outperforms its fixed bandwidth counterpart in terms of running time and decomposition error. Our work also provides useful insights for scheduling with variable bandwidth in contexts other than IRS-assisted FSO systems.