This paper describes the results from an industry-oriented research project conducted by the authors at the University of Melbourne. The project was aimed at working out event- based models and 'business process'-oriented simulations of sequential arrivals and departures at airports which we refer to as air-to-air business processes. This paper initially describes the problems to be solved that are related to increasingly frequent bottleneck situations at airports. Following, the paper presents a vision for achieving global optimization of air-to-air business processes that would integrate business processes and software systems of different stakeholders. As the first step towards achieving the vision, the paper proposes agent-oriented modelling and simulation of the problem domain. The paper then describes in more detail how event-based models of integrated business processes involving several stakeholders can be created. After that, the paper presents and explains the business process model of arrivals at airports. Finally, the paper proposes an avenue for transforming business process models into the constructs of a simulation environment enabling experimentation with global optimization.