Due to the multi-technology advancements, internet of things (IoT) applications are in high demand to create smarter environments. Smart objects communicate by exchanging many messages, and this creates interference on receivers. Collection tree algorithms are applied to only reduce the nodes/paths’ interference but cannot fully handle the interference across the underlying IoT. This paper models and analyzes the interference spread in the IoT setting, where the collection tree routing algorithm is adopted. Node interference is treated as a real-life contamination of a disease, where individuals can migrate across compartments such as susceptible, attacked and replaced. The assumed typical collection tree routing model is the least interference beaconing algorithm (LIBA), and the dynamics of the interference spread is studied. The underlying network’s nodes are partitioned into groups of nodes which can affect each other and based on the partition property, the susceptible–attacked–replaced (SAR) model is proposed. To analyze the model, the system stability is studied, and the compartmental based trends are experimented in static, stochastic and predictive systems. The results shows that the dynamics of the system are dependent groups and all have points of convergence for static, stochastic and predictive systems.

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Estimation of the extreme-value index of a heavy-tailed distribution is investigated when some functional random covariate (i.e. valued in some infinite dimensional space) information is available and the scalar response variable is right-censored. A weighted kernel version of Hill’s estimator of the extreme-value index is proposed and its asymptotic normality is established under mild assumptions.A simulation study is conducted to assess the finite-sample behavior of the proposed estimator. An application to ambulatory blood pressure trajectories and clinical outcome in stroke patients is also provided.