# A Markov regenerative model of software rejuvenation beyond the enabling restriction

## L. Carnevali, M. Paolieri, R. Reali, L. Scommegna, E. Vicario

**Abstract:** Software rejuvenation is a proactive maintenance technique that
counteracts software aging by restarting a system or some of its
components. We present a non-Markovian model of software rejuvenation
where the underlying stochastic process is a Markov Regenerative
Process (MRGP) beyond the enabling restriction, i.e., beyond the
restriction of having at most one general (GEN, i.e., non-exponential)
timer enabled in each state. The use of multiple concurrent GEN timers
allows more accurate fitting of duration distributions from observed
statistics (e.g., mean and variance), as well as better model
expressiveness, enabling the formulation of mixed rejuvenation
strategies that combine time-triggered and event-triggered
rejuvenation. We leverage the functions for regenerative analysis
based on stochastic state classes of the ORIS tool (through its SIRIO
library) to evaluate this class of models and to select the
rejuvenation period achieving an optimal tradeoff between two
steady-state metrics, availability and undetected failure probability.
We also show that, when GEN timers are replaced by exponential timers
with the same mean (to satisfy enabling restriction), transient and
steady-state are affected, resulting in inaccurate rejuvenation
policies.

Stochastic ProcessesReliability ModelsSoftware RejuvenationApplications

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