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The Internet of Things (IoT) is transforming almost every industry, including agriculture, food processing, health care, oil and gas, environmental protection, transportation and logistics, manufacturing, home automation, and safety. Cost-effective, small-sized batteries are often used to power IoT devices being deployed with limited energy capacity. The limited energy capacity of IoT devices makes them vulnerable to battery depletion attacks designed to exhaust the energy stored in the battery rapidly and eventually shut down the device. In designing and deploying IoT devices, the battery and device specifications should be chosen in such a way as to ensure a long lifetime of the device. This paper proposes diffusion approximation as a mathematical framework for modelling the energy depletion process in IoT batteries. We applied diffusion or Brownian motion processes to model the energy depletion of a battery of an IoT device. We used this model to obtain the probability density function, mean, variance, and probability of the lifetime of an IoT device. Furthermore, we studied the influence of active power consumption, sleep time, and battery capacity on the probability density function, mean, and probability of the lifetime of an IoT device. We modelled ghost energy depletion attacks and their impact on the lifetime of IoT devices. We used numerical examples to study the influence of battery depletion attacks on the distribution of the lifetime of an IoT device. We also introduced an energy threshold after which the device's battery should be replaced in order to ensure that the battery is not completely drained before it is replaced. [ABSTRACT FROM AUTHOR]

It has been recently observed that Software Defined Networks (SDN) can change the paths of different connections in the network at a relatively frequent pace to improve the overall network performance, including delay and packet loss, or to respond to other needs such as security. These changes mean that a network that SDN controls will seldom operate in steady state; rather, the network may often be in transient mode, especially when the network is heavily loaded and path changes are critically important. Hence, we propose a transient analysis of such networks to better understand how frequent changes in paths and the switches' workloads may affect multi-hop networks' performance. Since conventional queueing models are difficult to solve for transient behaviour and simulations take excessive computation time due to the need for statistical accuracy, we use a diffusion approximation to study a multi-hop network controlled by SDN. The results show that network optimization should consider the transient effects of SDN and that transients need to be included in the design of algorithms for SDN controllers that optimize network performance. [ABSTRACT FROM AUTHOR]