The Boyden chamber assay provides a convenient method of assessing cell migration and measuring cell motility coefficients at the population level. Previous models of this assay completely ignore cell sedimentation in the suspension, assuming that all cells have already settled on the filter surface before commencing migration within the filter. However, ignoring cell sedimentation could lead to poor data interpretation because the time required for cells to settle through the suspension is close to the incubation period of only a few hours. This study models the Boyden chamber assay by incorporating the cell settling process to account for the cells remaining in the upper well when other cells migrate in the filter. The simulations in this study elucidate the experiments in the literature that test the haptotactic and chemotactic responses of rabbit chondrocytes to type II collagen. This study determines the cell population random motility, as well as the haptotaxis and chemotaxis coefficients, by fitting the experimental data. Results show that the chemotactic motility coefficient is 100 times greater than the haptotactic coefficient, and the equilibrium collagen-receptor dissociation constant is about 10-fold the haptotactic counterpart. Diffusion causes the soluble collagen gradients in the chemotactic case to decline over time, while the coated collagen gradients in the haptotactic assay are likely to remain fixed. As a result, the chemotactic case exhibits a lower number of migrated cells than the haptotactic assay. This study also demonstrates the influences of the dimensionless parameters that control cell behavior in the Boyden assay, providing a reference for future experiment designs.