  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.

Accelerator Physics