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Thanks to the important and increasing growth of the carpooling phenomenon throughout the world, many researchers have particularly focused their efforts on this concept. Researches led to many systems affording carpooling service not usually effective. In fact, most of them present multiple drawbacks regarding automation, functionalities, accessibility, etc. Besides, only few researchers focused on real time carpooling concept without producing promising results. To address these gaps, we introduce a novel approach called DARTiC: a Distributed dijkstra for the implementation of a Real Time Carpooling system based on the multi-agent concept, we particularly focus on the distributed and dynamic aspect within dijkstra's implementation. A new modeling of the served network highlights the distributed architecture, helping to perform decentralized parallel process. This helped to take into consideration different aspects we should be involved in, especially optimization issue. Users' requests must be performed in a reasonable time and responses should be as efficient as possible with regards to the fixed optimization criteria.