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In this paper, we will introduce a new method to achieve the fair distribution of data among distributed memories in a distributed system. Some processes consume larger amount of heap spaces [1] in its local memory than the others. So, those processes may use the virtual memory and may cause the thrashing problem [2].At the same time, the rest of heap memories in that distributed system remain almost empty without best utilization for heap memories of the whole distributed system. So, a UDP-Based process communication system is defined [3] to make use of remote heap memories. This is done by allocating dynamic data spaces for other processes in other machines. In fact, the increasing use of high-bandwidth and low-latency networks provides the possibility to use the distributed memory as an alternative to disk.