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This dissertation develops a Dynamic Rideshare Optimized Matching (DROM) model and solution that is aimed at identifying suitable matches between passengers requesting rideshare services with appropriate drivers available to carpool for credits and HOV lane privileges. DROM receives passengers and drivers' information and preferences continuously over time and maximizes the overall system performance subject to ride availability, capacity, rider and driver time window constraints, and detour and relocation distances while considering users' preferences. The research develops a spatial, temporal, and hierarchical decomposition solution strategy that leads to the heuristic solution procedure. Three-Spherical Heuristic Decomposition Model (TSHDM). Quality and validity tests for the TSHDM algorithm are done by comparison of results between the exact and implemented algorithm solutions and major sensitivity analyses using the technique of Regression Analysis on all of the related parameters in the model are conducted to thoroughly investigate the properties of the proposed model and solution algorithm. A case study is constructed to analyze the model and TSHDM behaviors on a road network of northwest metropolitan area of Baltimore city. The study shows that however DROM is a very complicated and challenging problem from both mathematical formulation and solution algorithm perspectives, it is possible to implement a dynamic rideshare system using appropriate technical tools and social networking media. Major sensitivity analysis conducted on several parameters and variables affecting the model shows that most influencing factors for the rate of success in the rideshare system are, in order of importance: number of participating drivers, number of stops, area size, and number of participating riders. The study also shows rate of success for the rideshare system is highly dependent to the matched routes connecting directly points of origin and destination for participating riders and also increasing the number of connections from one to two which requires two consecutive change of rides for a rider has the least impact on the rate of success.