A Distributed Computing System (DCS) contributes in proper partitioning of the tasks into modules and allocating them to various nodes so as to enable parallel execution of their modules by individual different processing nodes of the system. The scheduling of various modules on particular processing nodes may be preceded by appropriate allocation of modules of the different tasks to various processing nodes and then only the appropriate execution characteristic can be obtained. A number of algorithms have been proposed for allocation of tasks in a DCS. Most of the solutions proposed had simplifying assumptions. The very first assumption has been: consideration of a single task with their corresponding modules only; second, no consideration of the status of processing nodes in terms of the previously allocated modules of various tasks and third, the capacity and capability of the processing nodes. This work proposes algorithms for a realistic situation wherein multiple tasks with their modules compete for execution on a DCS dynamically considering their architectural capability. In this work, we propose two algorithms based on the two well-known A* and GA for the task allocation models. The paper explains the algorithms elaborately by illustrated examples and presents a comparative performance study among our algorithms and the algorithms for task allocation proposed in the various literatures. The results demonstrate that our GA based task allocation algorithm achieves better performance compared with the other algorithms.