Platooning of cars or trucks is one of the most relevant applications of autonomous driving, since it has the potential to greatly improve efficiency in road utilization and fuel consumption. Traditional proposals of vehicle platoon- ing were based on distributed architectures with computation on board platoon vehicles and direct vehicle-to-vehicle (V2V) communications (or Dedicated Short Range Communication - DSRC), possibly with the support of roadside units. However, with the introduction of the 5G technology and of computing elements at the edge of the network, according to the multi-access edge com- puting (MEC) paradigm, the possibility emerges of placing control of platoons on MEC, with several significant advantages with respect to the V2V approach. For this reason, in this article we investigate the feasibility of vehicle platooning in an edge-based scenario where the control of vehicle speed and acceleration is managed by the network through its MEC facilities, possibly with a platooning- as-a-service (PaaS) paradigm. Using a detailed simulator, we show that, with realistic values of latency and packet loss probability, as well as of engines and inertia of vehicles, large platoons can be effectively controlled by MEC hosts. On the one hand, we unveil that platooning on the edge is a viable and robust solution. On the other hand, we also shed light on the necessity to consider realistic characteristics of vehicles and speed profiles, since they can yield severe, yet not critical, performance degradation with respect to simple models. Ramon y Cajal grant RYC-2014-16285 from the Spanish Ministry of Economy and Competitiveness The work was supported by the Spanish Ministry of Science and Innovation grant PID2019-109805RB-I00 (ECID). TRUE pub