This paper develops a model based on the Markov Chain technique to evaluate performance of a public transport route. The model addresses a special situation where a passenger left behind by a bus leaves the system without any further waiting to make an alternative travel arrangement. Such reneging behavior is indicative of an infinite penalty associated with further waiting from a passenger viewpoint. Apart from the theoretical derivations for the various attributes of interest, numerical examples to analyze the system performance (such as expected number of passengers served, expected number of abandoned passengers, and expected amount of unused space on the transit system) are presented. This provides insights for optimum selection of fleet size and size of vehicles