Intracellular transport is the process by which cargoes, such as organelles, travel to their needed locations within the cell in a timely manner via cytoskeletal filaments. This process involves the cargo that needs to be transported, motor proteins such as kinesin, and a filament, such as the microtubule. The process is broken down into several sub-processes, two of which are the focus in this study: the binding process (in which the cargo-motor protein ensemble binds to the microtubule) and processivity (where the cargo-motor ensemble walks on the microtubule). It is known which structures in the cell are used in intracellular transport, such as motor proteins, microtubules, and tubulin C terminal tails (CTTs); however, it is unclear how their properties affect the entire process. In this study, we use mathematical modeling and computational simulations to explain perplexing details of experimental data. Specifically, we show that motor diffusion alone cannot explain binding times measured from optical trap studies. Through computational analysis, we suggest that ADP release from the motor head may be an integral component of the binding process. We also propose the contribution CTTs provide to motor proteins processivity, where we believe CTTs help motor heads that are searching for microtubule binding sites by holding them near the microtubule, thus allowing for quicker steps. By combining modeling and simulations with experimental data, we can tune physical parameters that have the most potential of explaining the data, which in turns allow us a deeper understanding of intracellular transport.