Luminosity modeling of the LHC operation and performance projections for HL-LHC

The LHC luminosity model is a powerful tool for studying the evolution of beam and machine parameters during the LHC operation. The model includes important effects that are present in LHC operation such as Intra-Beam Scattering, synchrotron radiation and burn-off. By comparing model predictions with experimental data, the presence of additional emittance blow-up and intensity loss mechanisms can be identified and then further studied. Using this model for comparing different configurations such as optics, filling schemes and beam types, allows identifying the best strategy to be adopted in operation to maximize integrated luminosity. In this contribution, we show the benchmarking of this model with data from the presently ongoing LHC Run 3, and its application to predicting the integrated luminosity for its future High-Luminosity LHC upgrade.