In a Distributed Computing Systems (DCS) tasks submitted to it, are usually partitioned into different modules and these modules may be allocated to different processing nodes so as to achieve minimum turn around time of the tasks utilizing the maximum resources of the existing system such as CPU speed, memory capacities etc. The problem lies on how to obtain the optimal allocation of these multiple tasks by keeping in mind that no processing node is overloaded due to this allocation. This paper proposes an algorithm A*RS, using well-known A*, which aims to reduce the search space and time for task allocation. It aims at minimization of turn around time of tasks in the way so that processing nodes do not become overloaded due to this allocation. Our experimental results justify the claims with necessary supports by comparing it with the earlier algorithm for multiple tasks allocation.