With the widespread availability of smartphones and advancement in communication technologies, Dew Computing paradigm(DCp) has emerged as a state-of-the-art computing paradigm. DCp provides an ecosystem to execute computationally intensive tasks which comprise of several subtasks. Each subtask is allocated for execution to an available and capable mobile device by taking into consideration its features like mobility, processing power, remaining battery, etc. This kind of “on-the-spot” paradigm comprises of mobile devices only which are part of mobile grid and it doesn’t use the fixed infrastructure based computing systems for computational purposes. Being resource constrained, such a paradigm needs an efficient scheme for allocation of resources. Here we propose a scheme called MGRA for allocation of computing nodes which takes into account challenging issues like mobility of users, inefficient resource allocation and handling of failure situations. Experimentation was carried out using a DCp testbed comprising Android devices connected with Wi-Fi Direct protocol. MGRA exhibited significant improvement in terms of time for application completion, amount of battery usage and time required for recovering from failure as compared to present-day approaches.