No Arabic abstract
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.
In order to maintain consistent quality of service, computer network engineers face the task of monitoring the traffic fluctuations on the individual links making up the network. However, due to resource constraints and limited access, it is not possible to directly measure all the links. Starting with a physically interpretable probabilistic model of network-wide traffic, we demonstrate how an expensively obtained set of measurements may be used to develop a network-specific model of the traffic across the network. This model may then be used in conjunction with easily obtainable measurements to provide more accurate prediction than is possible with only the inexpensive measurements. We show that the model, once learned may be used for the same network for many different periods of traffic. Finally, we show an application of the prediction technique to create relevant control charts for detection and isolation of shifts in network traffic.
Point process models have been used to analyze interaction event times on a social network, in the hope to provides valuable insights for social science research. However, the diagnostics and visualization of the modeling results from such an analysis have received limited discussion in the literature. In this paper, we develop a systematic set of diagnostic tools and visualizations for point process models fitted to data from a network setting. We analyze the residual process and Pearson residual on the network by inspecting their structure and clustering structure. Equipped with these tools, we can validate whether a model adequately captures the temporal and/or network structures in the observed data. The utility of our approach is demonstrated using simulation studies and point process models applied to a study of animal social interactions.
We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It arises from a limit approximation of the traffic fluctuations as the time--scale and the number of users sharing the network grow. The resulting probability model is comprised of a Gaussian and/or a stable, infinite variance components. They can be succinctly described and handled by certain space-time random fields. The model is validated against simulated and real data. It is then applied to predict traffic fluctuations over unobserved links from a limited set of observed links. Further, applications to anomaly detection and network management are briefly discussed.
We present a model to describe the inbound air traffic over a congested hub. We show that this model gives a very accurate description of the traffic by the comparison of our theoretical distribution of the queue with the actual distribution observed over Heathrow airport. We discuss also the robustness of our model.
This paper describes several applications in astronomy and cosmology that are addressed using probabilistic modelling and statistical inference.