Recently, the edge resource provisioning schemes were defined considering the low-latency Mobile Edge Computing (MEC) paradigm. Most of these models only consider battery-powered devices like smart-phones, thus are agnostic to the energy harvesting techniques that achieves a green MEC system. Further, most of the studies on MEC assume unlimited edge resources which is not the case as it is with the conventional data-centers (public clouds). Hence, unrestricted use of edge resources is not ideal. This work mainly considers two problems: (1) the offloading of data traffic from the Internet of Things (IoT) devices that rely on energy harvesting to the MEC entities and (2) assignment of the resources at the MEC. The novelty of this paper lies in the energy scavenging based architecture that is developed over the Contiki OS. Secondly, saving the energy for computations to maximize the lifetime of the sensing nodes by performing the execution of the computationally-intensive tasks at the edge which is a single hop away. The proposed architecture uses the ambient triggers to form the sensor network and establish links with computationally capable resources located at the edge. Further, a mathematical model to manage the resources at the edge is proposed. Finally, we evaluate a threshold-policy for optimizing the resources participating in an edge computation service for an IoT scenario and discuss the improvements achieved.