Pervasive computing applications deal with the intelligence surrounding users that can facilitate their activities. This intelligence is provided in the form of software components incorporated in embedded systems or devices in close distance with end users. One example of infrastructure that can host intelligent pervasive services is the Edge Computing (EC) ecosystem. EC nodes can execute a number of tasks for data collected by devices present in the Internet of Things (IoT). In this paper, we propose an intelligent, proactive tasks management model based on demand. Demand depicts the number of users or applications interested in using the available tasks in EC nodes, thus characterizing their popularity. We rely on a Deep Machine Learning (DML) model and more specifically on a Long Short Term Memory (LSTM) network to learn the distribution of demand indicators for each task and estimate the future interest in them. This information is combined with historical observations of and support for a decision making scheme to conclude which tasks that are offloaded due to limited interest in them. We have to recognise that, in our decision making, we also take into consideration the load that every task may add to the processing node where it will be allocated. The description of our model is accompanied by a large set of experimental simulations for evaluating the proposed mechanism. We provide numerical results and reveal that the proposed scheme is capable of deciding on the fly, while concluding the most efficient decisions.