This thesis has two parts. The first focuses on shared e-bike and e-scooter systems, which have become globally popular solutions for urban mobility.However, they introduce new operational challenges around charging and many charging mechanisms have been proposed (e.g. employees swapping batteries, charging stations, crowd-sourced, etc.). We develop a model that allows the direct comparison of different mechanisms and quantifies their impact on platform performance. In order to achieve this, novel ideas for analyzing the underlying stochastic process are introduced. The second part considers an emerging idea in public transit, using on-demand shuttles for first- and last-mile.We develop a modelling framework to help cities assess the feasibility of integrating on-demand shuttles. It consists of two modular components. The first models individual regions serviced by shuttles and the second efficiently optimizes the deployment of shuttles throughout the day. A key feature of this framework is that it can be easily extended to key considerations of transit operators such as latent demand and equity across regions.