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Mobile ad-hoc networks are used in a wide array of applications. Service discovery architecture has become one of the most important research areas in mobile ad-hoc networks. In our paper, a totally distributed service directory-based model is introduced. We consider the number of service directory nodes to be one of the most important system parameters, and we mathematically analyze how the number of service directory nodes affects path availability time between a random node and its nearest service directory node, a relationship that has been overlooked by other proposed service discovery models.