This paper introduces a statistical model for the arrival times of connection events in a computer network. Edges between nodes in a network can be interpreted and modelled as point processes where events in the process indicate information being sent along that edge. A model of normal behaviour can be constructed for each edge in the network by identifying key network user features such as seasonality and self-exciting behaviour, where events typically arise in bursts at particular times of day. When monitoring the network in real time, unusual patterns of activity could indicate the presence of a malicious actor. Four different models for self-exciting behaviour are introduced and compared using data collected from the Imperial College and Los Alamos National Laboratory computer networks.
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