Abstract

A complex model based on Continuous-Time Markov Chains is proposed, which combines an extended aging and rejuvenation model taking into account different aging levels and a model of mobile device usage activity. A graph of states and transitions is constructed, which describes the proposed model without taking into account mobile device usage activity, and taking it into account. A system of Kolmogorov – Chapman differential equations is written on the basis of the states graph. A set of test simulations for conducting experimental calculations of the model and analysis of results is described. A system of differential equations for each simulation is calculated using the 4th order Runge-Kutta method. The analysis of simulations with recovery after aging-related failure and without recovery allowed to formulate the main objectives of the rejuvenation procedure in the proposed model to improve the user experience. Analysis of different rejuvenation planning strategies indicates that the most effective approach is to perform rejuvenation in the “Aging” state, when the device is already aging, but it is not yet a state with a high probability of aging-related failure. Analysis of simulations with warm and cold rejuvenation shows that this factor affects the results of the model calculation, and the application of one or another approach depends on the aging conditions and the mobile device usage activity. The developed model based on the Markov chain can be used to predict the optimal time of the rejuvenation procedure. In addition, the model considers both cold and warm rejuvenation. Further studies which take into account the real data and aging conditions are needed for proposed aging and rejuvenation model.

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