Modelling distributed decision-making in Command and Control using stochastic network synchronisation

Abstract

We advance a mathematical representation of Command and Control as distributed decision makers using the Kuramoto model of networked phase oscillators. The phase represents a continuous Perception-Action cycle of agents at each network node; the network the formal and informal communications of human agents and information artefacts; coupling the strength of relationship between agents; native frequencies the individual decision speeds of agents when isolated; and stochasticity temporal noisiness in intrinsic agent behaviour. Skewed heavy-tailed noise captures that agents may randomly ‘jump’ forward (rather than backwards) in their decision state under time stress; there is considerable evidence from organisational science that experienced decision-makers behave in this way in critical situations. We present a use-case for the model using data for military headquarters staff tasked to drive a twenty-four hour ‘battle-rhythm’. This serves to illustrate how such a mathematical model may be used realistically. We draw on a previous case-study where headquarters’ networks were mapped for routine business and crisis scenarios to provide advice to a military sponsor. We tune the model using the first data set to match observations that staff performed synchronously under such conditions. Testing the impact of the crisis scenario using the corresponding network and heavy-tailed stochasticity, we find increased probability of decision incoherence due to the high information demand of some agents in this case. This demonstrates the utility of the model to identify risks in headquarters design, and potential means of identifying points to change. We compare to qualitative organisational theories to initially validate the model.