Due to their highly dynamic nature, vehicular ad hoc networks (VANETs) are occasionally found difficult for their parameter optimization. Some attempts have been made to challenge the difficulty by modeling VANETs mathematically to predict parameter values successfully such as average cluster size and the lifetime of a path. Nevertheless, there have been no systematic approaches to analyze both node mobility and communication performances over a VANET by investigating its microscopic conditions. In this paper, we create a model for VANETs with basic natural assumptions. It mainly considers sparsely arranged vehicular nodes on a one-directional straight road, and assumes four hypotheses on the i) initial distribution of node density, ii) mobility, and iii) communication between nodes. Based on them, we will be able to find expressions for the exact delay time and delivery ratio, when a car sends a packet to k - 1 cars ahead. We will especially obtain a closed formula for the delivery ratio. We also compute the actual delay time and delivery ratio from available field data. Through the analysis, we observe that small values of the maximum wait time create sufficiently good performance even in a very sparse VANET.