This paper aims to quantify the responsiveness of two on-orbit servicing infrastructures providing services to multiple serviceable platforms in medium Earth orbit (MEO) and geostationary orbit (GEO). The platforms to be serviced are assumed to be made of elementary units (EUs). EUs are small standardized structural units capable of aggregating with each other and gathering the key functions of a typical satellite within the size of a 6U cubesat. The first servicing infrastructure considered in this paper, called “Without Depot” (WoD), includes a launch vehicle and a robotic servicer. The second servicing infrastructure, called “With Depot” (WD) includes a launch vehicle, a robotic servicer and an orbital depot of EUs. The responsiveness of these infrastructures is quantified using a queueing theory-based stochastic simulation in Simulink taking into account the launch and platform random failures. The metrics used to quantify the responsiveness are the service completion rate and the average waiting time before a failed EU on the client platform is replaced over a 10-year period of operation. With respect to those metrics, it is demonstrated that WD is more responsive than WoD. However, WD is also shown to be likely to cost more than WoD. Finally, the sensitivity of the responsiveness of WD to the capacity of the orbital depot is analyzed to find the capacity level of the orbital depot, beyond which the responsiveness of WD is not significantly improved. This last result could be of interest for space designers dealing with the sizing of on-orbit servicing infrastructures. We believe that the project introduced in this paper will be a critical milestone in the design of a responsive integrated space infrastructure dedicated to the development and prosperity of a new GEO/MEO economy.