Multifaceted characteristics of urban travel have an impact on the passengers' overall satisfaction with the transport system. In this study, we investigate the interrelationships among traveler satisfaction, travel and traveler characteristics, and service performance in a multimodal network that comprises of a trunk line and its feeder lines. We analyze the factors influencing the choices of access to rail transit stations and the satisfaction of transit travelers with the rapid rail transit systems. We quantitatively study these relationships and demonstrate the complexity of evaluating transit service performance. Since the interrelationships among variables affecting this system are mainly stochastic, we analyze the satisfaction with transit system problem using a Bayesian Belief Network (BBN), which helps capture the causality among variables with inherent uncertainty. Using the case of Istanbul, we employ the BBN as a decision support tool for policy-makers to analyze the rapid rail transit services and determine policies for improving the quality and the level of service to increase the satisfaction with transit system. In the case study, satisfaction with accessibility and access mode variables are found to be more effective variables than total travel time for travel time satisfaction, confirming the significant role of access in multimodal travels.