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Model-Based Performability and Dependability Evaluation of a System with VM Migration as Rejuvenation in the Presence of Bursty Workloads

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Abstract

Software aging accumulation leads to increased resource consumption. In this context, the memory leak is one of the well-known problems related to software aging. A bursty workload can accelerate software aging bug activation as it requires instantaneous resource allocation. Then, the rapid resource allocation and deallocation may lead to software aging through memory leaks. Moreover, a bursty workload may cause a resource exhaustion failure in a system already overloaded by software aging accumulation. Virtual Machine (VM) migration schedules can be used to mitigate software aging moving services away from a compromised physical host. Despite the considerable progress made in this area, the state-of-the-art still lacks a modeling framework for performability and dependability evaluation of VM migration as rejuvenation in a system under bursty workloads. This paper proposes a set of Stochastic Reward Net (SRN), aiming at filling this research gap. We consider five scenarios covering different bursty workload conditions, and present a specific model to cover the uncertainties related to bursty workloads. Our results present the specific rejuvenation schedule to maximize system performability and dependability for each scenario. The proposed modeling framework may be useful to support virtualized environment management decisions.

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Notes

  1. Bursty workload occurrence usually causes a system utilization peak.

  2. https://cloud.google.com/.

  3. https://aws.amazon.com/.

  4. https://simpy.readthedocs.io/en/latest/.

  5. Arcs terminating in a circle instead of an arrowhead.

  6. Receiving and returning.

  7. We consider a year with 365 days.

  8. Considering a month with 30 days. \(30 \cdot 24 \cdot 60 = 43,200\).

  9. Note that, in this case, the performance is degradable due to software aging accumulation issues, then the computed metrics are related to system performability [37].

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Acknowledgements

This work has been partially supported by Portuguese Foundation for Science and Technology (FCT), through the PhD Grant SFRH/BD/146181/2019, within the scope of the project CISUC - UID/CEC/00326/2020. This work is also funded by the European Social Fund, through the Regional Operational Program Centro 2020. This work also received support from AIDA: (Adaptive, Intelligent and Distributed Assurance Platform) project, funded by Operational Program for Competitiveness and Internationalization (COMPETE 2020) and FCT (under CMU Portugal Program) through Grant POCI-01-0247-FEDER-045907. And, from project TalkConnect funded by COMPETE 2020 trough Grant POCI-01-0247-FEDER-039676.

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  1. CISUC, DEI, University of Coimbra, Coimbra, Portugal

    Matheus Torquato & Marco Vieira

  2. Federal Institute of Alagoas, Campus Arapiraca, Arapiraca, Brazil

    Matheus Torquato

  3. Centro de Informática, Universidade Federal de Pernambuco (CIn-UFPE), Recife, Brazil

    Paulo Maciel

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Appendix: Stochastic Reward Nets

Appendix: Stochastic Reward Nets

Stochastic Reward Nets (SRN) are a sub-type of Petri Nets (PN). A PN is a 5-tuple, \(PN = (P, T, F, W, M_0)\) where: \(P = \{p_1, p_2, \ldots , p_n\}\) is a finite set of places, \(T = \{t_1, t_2, \ldots , t_n\}\) is a finite set of transitions, \(F \subseteq (P \times T) \cup (T \times P)\) is a set of arcs, \(W: F \rightarrow \{0, 1, 2, 3, \ldots \}\) is a weight function, and \(M_0: P \rightarrow \{0, 1, 2, 3, \ldots \} \) is the initial marking [39].

The graphical representation of PN has four main components, as presented in Fig. 14. The places keep the tokens, the arcs indicate the relation between places and transitions, and the PN state is altered upon a transition firing, which moves tokens from one transition to other. In SRNs, it is possible to assign time delays to the transitions.

Fig. 14
figure 14

Petri net components

Full size image

Let us consider the flow of a simple SRN availability model in the Fig. 15. In the initial state, the system is running, presented by the token in the UP place. The transition MTTF represents the system mean time to failure (MTTF). MTTF firing represents a system failure occurrence. The same transition moves the token from UP place to the DW place. The system repair is represented by the MTTR transition (mean time to repair (MTTR)). MTTR transition firing brings the model back to its initial state.

Fig. 15
figure 15

Flow of a SRN simple availability model

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We can compute the system availability using the following reward measure \(Availability = P\{UP > 0\}\), which captures the probability of tokens presence in the UP place.

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Torquato, M., Maciel, P. & Vieira, M. Model-Based Performability and Dependability Evaluation of a System with VM Migration as Rejuvenation in the Presence of Bursty Workloads. J Netw Syst Manage 30, 3 (2022). https://doi.org/10.1007/s10922-021-09619-3

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