In this paper we propose that formal modelling techniques are necessary in establishing the trustworthiness of e-voting systems and the software within. We illustrate how a distributed e-voting system architecture can be analysed against quality of service requirements, through simulation of formal models. A concrete example of a novel e-voting system prototype (for use in French elections) is used to justify the utility of our approach. The quality of service that we consider is the total time it takes for a voter to record their vote (including waiting time). The innovative aspects of the e-voting system that required further research were new requirements for voting anywhere and re-voting; and the potential for undesirable interactions between them