Evolution of grid has drawn attention from various resource intensive applications addressing domains of bio-informatics, astrology and multimedia, to name a few. Image analysis applications in both biosciences and astrophysics are explicitly built in modular fashion to exploit the potential offered by grid. In this paper we present a framework for resource allocation and task scheduling, MARS, which efficiently allocates resources for such resource intensive applications which can be represented as Task Interaction Graph (TIG), while keeping makespan as minimum as the current state of resources in grid allows. Simulation experiments with MARS show a considerable improvement in job completion time and host utilization over traditional resource management and scheduling algorithms for grid.