Multi-core Real-time Systems (MRS) powered by a battery have been adopted for a wide range of high performance applications, such as mobile communication and automotive systems. A system is composed of N dependent and periodic Operating System (OS) tasks to be assigned to p heterogeneous cores linked by a network-on-chip (NoC). This paper deals with the problem of task allocation in MRS in such a way that the cost of communication between cores is minimized by trying to place the dependent tasks as close as possible to each other. The main objective is to develop a new strategy for allocating N tasks to p cores of a given distributed system using task clustering by considering both the cost of inter task communication and that of communication between cores. The proposed strategy guarantees that, when a task is mapped into the system and accepted, then it is correctly executed prior to the task deadline. A novel periodic task model based on elastic coefficients is proposed to compute useful temporal parameters allowing to assign all tasks to p cores, by minimizing the traffic between cores. Experimental results reveal the effectiveness of the proposed strategy by comparing the derived solutions with the optimal ones, obtained by solving an Integer Linear Program (ILP).