A mathematical approach for mission planning and rehearsal Erol Gelenbe * and Yu Wang ** Imperial College London, London, SW7 2BT, UK ABSTRACT 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. Keywords: mathematical modeling, military strategy & planning 1. INTRODUCTION As a society evolves, its structure and content transform accordingly to reflect and address its needs. As a result, more and more large scale systems occur in various forms in the surrounding world, from diverse areas of study such as biology, ecology, finance or transportation. Large scale systems have been traditionally characterized by a large number of variables, nonlinearities and uncertainties. As an example taken from biology, a human body, where organs, containing billions of cells, perform different functions that contribute towards the operating of the body can be seen as a large scale system. Inspired by the desire to better understand and utilize the environment, we study such systems and hope to gain insights, predict the future and control them partially if not fully. There have been many attempts to model large scale systems, such as building differential equations or with simulations [1-5]. However the sheer complexity and diversity of large scale systems make them difficult to be described and modelled, and it is even more difficult to provide numerical predictions of the underlying processes of such systems. To tackle these problems, we propose to use a stochastic approach, in particular G-networks [6-10], to model the individuals of the same nature collectively. In doing so, the computational complexity is greatly reduced. Another innovative aspect of our approach is that it is able to model systems with multiple geographical locations at different levels of abstraction. With our approach, we aim to provide insights into systems in terms of their performance and behaviours, to identify the parameters which strongly influence them, and to evaluate how well an individual’s task can be achieved and, therefore compare the effects of alternative strategies. * e.gelenbe@imperial.ac.uk ; phone: +44 207 5946342; fax + 44 207 5946274; http://www.ee.ic.ac.uk/gelenbe/ ** yu.wang3@imperial.ac.uk ; phone: + 44 207 5946323