A distributed processing system (DPS) contains many autonomous nodes, which contribute their own computing power. DPS is considered a unified logical structure, operating in a distributed manner; the processing tasks are divided into fragments and assigned to various nodes for processing. That type of operation requires and involves a great deal of communication. We propose to use the decentralized approach, based on a distributed hash table, to reduce the communication overhead and remove the server unit, thus avoiding having a single point of failure in the system. This paper proposes a mathematical model and algorithms that are implemented in a dedicated experimental system. Using the decentralized approach, this study demonstrates the efficient operation of a decentralized system which results in a reduced energy emission.