A good understanding of the luminosity performance in a collider, as well as reliable tools to analyse, predict, and optimise the performance, are of great importance for the successful planning and execution of future runs. In this article, we present two different models for the evolution of the beam parameters and the luminosity in heavy-ion colliders. The first, Collider Time Evolution (CTE) is a particle tracking code, while the second, the Multi-Bunch Simulation (MBS), is based on the numerical solution of ordinary differential equations for beam parameters. As a benchmark, we compare simulations and data for a large number of physics fills in the 2018 Pb-Pb run at the CERN Large Hadron Collider (LHC), finding excellent agreement for most parameters, both between the simulations and with the measured data. Both codes are then used independently to predict the performance in future heavy-ion operation, with both Pb-Pb and p-Pb collisions, at the LHC and its upgrade, the High-Luminosity LHC. The use of two independent codes based on different principles gives increased confidence in the results.
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