Customer journey maps (CJMs) are used to understand customers' behavior, and ultimately to better serve them. This new approach is used in numerous disciplines for different purposes. As a response, several software applications have emerged. Although they provide interfaces to understand CJMs, they lack measures to assist in decision making. We contribute by proposing a CJM model. We show its potential by using it with process mining, a data analytics technique that we leverage to assess the impact of the journey's duration on the customer experience. The model brings data scientists and customer journey planners closer together, the first step in gaining a better understanding of customer behavior. This study also highlights the prospective value of process mining for CJM analysis.