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A comprehensive evaluation of availability and operational cost for a virtualized server system using stochastic reward nets

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A Correction to this article was published on 18 May 2018

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Abstract

Virtualized server systems, as a major underlying element in high-performance computing systems, require further studies on many aspects of dependability. Among the significant factors, the availability measures are crucial to deliver high-quality services. Previous studies presented various modeling and analysis results on system availability of a virtualized system with two servers using a continuous-time Markov chain. In this study, we propose a cluster model of m virtualized servers using stochastic reward nets (SRNs). We focused on the overall configuration of the entire system, and in the modeling, we considered the detailed interactions between the servers. The model incorporates specific techniques for high availability of the system: standby techniques, virtual machine (VM) live migration and VM failover techniques. Simplified failures and recovery behaviors of physical servers and VMs are taken into consideration. Various SRN models are developed based on different case studies in which the techniques to improve the system’s overall availability are incorporated one after another. We conducted comprehensive analyses on the models with significant metrics of interest including: steady-state availability (SSA), sensitivity analysis of the SSA, downtime cost and operational cost analyses. We propose to use reward functions featured in SRN as a solution to help ease the computation of operational costs. The study provides an analytical basis for system adjustment and configuration of virtualized systems in data centers, cloud computing in practice.

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  • 18 May 2018

    The section “Acknowledgement” was incorrect in the original article. The correct section “Acknowledgement” is given below.

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Acknowledgements

We appreciate and thank a number of peer reviewers and colleagues who are devoted to give valuable and constructive comments and suggestions. This research was supported by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2017-2016-0-00465) supervised by the IITP (Institute for Information & communications Technology Promotion).

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Authors and Affiliations

  1. Office of Research, University-Industry Cooperation Foundation, Konkuk University, Seoul, South Korea

    Tuan Anh Nguyen

  2. Department of Computer Engineering, Konkuk University, Seoul, South Korea

    Tuan Anh Nguyen & Dugki Min

  3. School of Management Information Systems, Kookmin University, Seoul, South Korea

    Eunmi Choi

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  1. Tuan Anh Nguyen
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  2. Dugki Min
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  3. Eunmi Choi
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Correspondence to Tuan Anh Nguyen or Dugki Min.

Appendices

Appendix 1: Stochastic reward nets

Stochastic reward net (SRN) is used in sufficiently modeling many hardware and software structures of real-time computing systems [78, 79]. To build SRN model, we use three main components: places, transitions and arcs. Arcs only connect place(s) to transition(s) and transition(s) to places. There is an integer number of entities named token denoted by dot sign or integer number in the places. Transition can be enabled to transport tokens from and to places called firing. The state or condition of the system is decided by location of tokens [22, 64]. That means, a set of current location of tokens in SRN models reflects the state or condition of the system, called marking. Guard is a Boolean condition attached to each transition to perform marking dependence. To succinctly describe many complex behaviors, marking-dependent firing rates of transitions are applied as a function of the current marking. This dependency is denoted by \( \# \) sign next to the transition. More general dependencies are often needed and hence allowed in the SRN formalism [64]. There are other features such as input arcs, inhibit arcs, multiplicities, so that SRN models can be simplified. In the following sections, we present very detailed description of the SRN models for small-scale VSS.

Appendix 2: Definition of guard functions in SRN models

See Table 7.

Table 7 Definition of guard functions and entities used in the SRN models
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Nguyen, T.A., Min, D. & Choi, E. A comprehensive evaluation of availability and operational cost for a virtualized server system using stochastic reward nets. J Supercomput 74, 222–276 (2018). https://doi.org/10.1007/s11227-017-2127-2

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