Abstract: Intracellular transport is conducted largely by molecular motor proteins such as kinesin and dynein, which walk along microtubules or actin filaments, from which they can attach or detach.The progress of cargo carried by these molecular motors is therefore determined by the effective transport of these motors over several cycles of attachment an detachment.We employ a framework of switched stochastic differential equations to model this process, with switching rates influenced by the spatial configuration of the motors and the cargo.Mean first passage time calculations are also developed to provide a model for how attachment rates depend on the geometry of the cargo and the microtubule network.