Multilayer networks have been the subject of intense research in the recent years in different applications. However, in urban mobility, the multi-layer nature of transportation systems has been generally ignored, even though most large cities are spanned by more than one transportation system. These different modes of transport have usually been studied separately. It is however important to understand the interplay between different transport modes. In this study, we consider the multimodal transportation system, represented as a multiplex network, and we address the problem of urban mobility in the transportation system, in addition to its robustness and resilience under random and targeted failures. Multiplex networks are formed by a set of nodes connected by links having different relationships forming the different layers of the multiplex. We study, in particular, how random and targeted failures to the transportation multiplex network affect the way people travel in the city. More specifically, we are interested in assessing the portion of the city covered by a random walker under various scenarios. We consider the public transport of London as an application to illustrate the proposed capacity analysis method of multi-modal transportation, and we report on the robustness and the resilience of the system. This study is part of a project to develop a computational framework to better understand and predict mobility patterns in the city of Doha once its ambitious metro system is deployed in 2019. The computational framework will help the city to efficiently manage the flow of people and intelligently handle capacity through different transportation modes, in particular during mega events such as Soccer Wold cup FIFA 2022. The proposed method is based on the study in , but with an efficient computational approach resulting in tremendous savings in computational time. It is scalable and lends itself to efficient implementation on parallel computers.