A mathematical approach for mission planning and rehearsal

The world that we live in is filled with large scale agent systems, from diverse fields such as biology, ecology or finance. Inspired by the desire to better understand and make the best out of these systems, we propose an approach which builds stochastic mathematical models, in particular G-networks models, that allow the efficient representation of systems of agents and offer the possibility to analyze their behavior using mathematics. This work complements our previous results on the discrete event simulation of adversarial tactical scenarios. We aim to provide insights into systems in terms of their performance and behavior, to identify the parameters which strongly influence them, and to evaluate how well individual goals can be achieved. With our approach, one can compare the effects of alternatives and chose the best one available. We model routine activities as well as situations such as: changing plans (e.g. destination or target), splitting forces to carry out alternative plans, or even changing on adversary group. Behaviors such as competition and collaboration are included. We demonstrate our approach with some urban military planning scenarios and analyze the results. This work can be used to model the system at different abstraction levels, in terms of the number of agents and the size of the geographical location. In doing so, we greatly reduce computational complexity and save time and resources. We conclude the paper with potential extensions of the model, for example the arrival of reinforcements, the impact of released chemicals and so on.