Considering the sprawl of the cities, the conventional public transport (CPT) with fixed route and fixed schedule becomes less efficient and desirable every day. However, the emerging technologies in computation and communication are facilitating more adaptive types of public transport, such as Demand Responsive Transport (DRT) systems, which operate according to the demand. It is crucial to study the feasibility and advantages of these systems before implementation to prevent failure and financial loss. In this work, a realistic model is provided by incorporating a dynamic routing algorithm into an agent-based traffic simulation to compare DRT and CPT. This model provides a high spatial and temporal granularity, which makes it possible to analyze the results on an individual level. The results showed that replacing CPT with DRT will improve the mobility by decreasing the perceived travel time by passengers and without any extra cost under certain circumstances.