This dissertation begins with proposing a novel street Connectivity Indicator (C.I.) to predict transit performance by identifying the role that street network connectivity plays in influencing the service quality of demand responsive feeder transit services. This new C.I. definition is dependent upon the expected shortest path between any two nodes in the network, includes spatial features with transit demand distribution information and is easy to calculate for any given service area. Subsequently, a methodology to identify and locate critical links within a grid street system for operating feeder transit services is also developed. A 'critical' street link causes the largest change in transit performance due to the link's removal or addition to an existing network. The most important contribution of this section on link criticality is to present a simple closed-form analytical formula in locating the critical link(s) for a grid street network system of 'any' size. Easily computable formulas have been provided and validated by simulation analyses. Another related model is proposed to compute the optimal grid street spacing that would enhance performance of a demand responsive feeder transit system. The model is tested using simulation. Lastly, an analytical model is also developed for estimating optimal service cycle length or headway of a demand responsive feeder transit service designed to serve passengers, especially during peak periods of demand. Simulation analyses over a range of networks have been conducted to validate the new C.I. definition. Results show a desirable monotonic relationship between transit performance and the proposed C.I., whose values are directly proportional and therefore good predictors of the transit performance, outperforming other available indicators, typically used by planners. Further, useful insights indicate a monotonic decrease in link criticality as we depart from the centrally located links to those located at boundaries. Using a real case example from Denver of the Call-n-Ride system operating similar to a demand responsive feeder transit, optimal cycle lengths differed very modestly from those computed using the model. Extensive simulations performed for different sets of feeder service areas and demand densities, further validated the optimal cycle length model.