The physics pertaining to the asymptotic giant branch (AGB) phase of stellar evolution has been studied for many years. However, the mechanics behind many characteristics displayed at this stage are still not fully understood. As a member of the Long Period Variable class of stars, AGB stars are invaluable in creating three-dimensional maps of the Milky Way, the Magellanic System and other galaxies with resolved stellar populations. Variable stars can be used to determine radial distances from Earth using their periodic luminosity variations. As this type of star has unknown qualities, models of AGB populations need to be calibrated with observed data. Previous research has derived a best-fitting model using the TRILEGAL code (a TRIdimensional modeL of thE GALaxy). This model was calibrated against single-epoch luminosity functions (LFs) calculated from resolved stellar populations in the Small Magellanic Cloud (SMC). With multi-epoch data now available from the VISTA survey of the Magellanic Clouds (VMC), this best-fitting model can now be compared with the LFs as they vary with time. Firstly, statistical tests are completed to measure the extent of the LF variation between epochs and from the mean LF for both the full VMC AGB catalogue and for the oxygen-rich, carbon-rich and extreme AGB classes. Statistical tests are then performed to measure the similarity between the LFs from different epochs and the simulated LFs, again for the entire sample and the three classes. This investigation shows that, while the current best-fitting model is a good approximation of many individual epochs’ AGB LFs in the SMC to within 3σ, inclusion of multi-epoch data would make for a more robust analysis. In order to do this, it would be desirable to have more epochs with deeper and regular observations that could cover full lightcurves of some of the sources. There also seems to be a statistical difference between the inner and outer areas of the SMC, perhaps due to tidal disruptions. It would be interesting to see the results of a similar study using the LMC, which is less affected by the gravitational influence of its smaller companion. / <p>This thesis was written under the supervision of Maria-Rosa Cioni at the Leibniz Institute for Astrophysics in Potsdam. The presentation was held online due to the COVID-19 pandemic.</p>