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Cost optimization in persistent virtual world design

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Abstract

Virtual world has the potential to become a future global electronic market, integrating many isolated markets in many areas. To achieve this goal, future virtual world is required to be persistent, which means that a virtual world together with its accumulated content shall exist forever regardless of the dynamic changes of its virtual world users and virtual world owners. This paper addresses the content-level persistence issue by proposing a persistence framework which consists of three elements: existence, availability, and sufficiency. Following the framework, a decentralized redundancy model is then proposed, which is immune from the possible collapse of virtual world. The key problem in the model is the selection of a redundancy level, which is based on cost optimization. Furthermore, the replica failure timeout mechanism is introduced to improve the model. The simulation results show that the redundancy model helps improve content availability and minimizes cost.

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Acknowledgements

This research is partially supported by the University of Macau Research Grant No. MYRG2015-00043-FST.

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Authors and Affiliations

  1. University of Macau, Macau Av. Padre Tomás Pereira Taipa, Macau, China

    Bingqing Shen & Jingzhi Guo

  2. Old Dominion University, Norfolk, VA, 23529, USA

    Ling Xia Li

Authors
  1. Bingqing Shen
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  2. Jingzhi Guo
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Corresponding author

Correspondence to Jingzhi Guo.

Appendices

Appendix 1: Derivation of replica failure cycle and replica failure rate

Assume TTF is uniformly distributed with mean equal to MTTF. Let t 1 be the TTF of replica 1, t 2 be the TTF of 2, …, and t N be the TTF of replica N. On average, t 1 = T f , t 2 = 2·T f , …, t N  = N·T f , and

$$\begin{aligned} MTTF & = \sum\limits_{i = 1}^{N} {T_{i} } \cdot \frac{1}{N} \\ & = \frac{{T_{f} + 2T_{f} + \cdots + NT_{f} }}{N} \\ & = \frac{N + 1}{2}T_{f} \\ \end{aligned}$$

Therefore, T f and R f can then be estimated by

$$T_{f} = \frac{1}{{R_{f} }} = \frac{2 \cdot MTTF}{n + e + 1}$$

Appendix 2: Derivation of the revised mean time-to-rejoin

Given replica group size N, the average replica join rate R r is:

$$R_{r} = \frac{1}{{T_{r} }} = \frac{N + 1}{2 \cdot MTTR}.$$

Let P d be the probability that a replica failure is a permanent failure. Then, the equivalent replica rejoin rate \(R_{r}^{{\prime }}\) is \(R_{r}^{\prime } = \left( {1 - P} \right) \cdot R_{r}\). Let MTTR’ be the equivalent mean time-to-rejoin. Then, it can be derived from:

$$\begin{aligned} R_{r}^{{\prime }} & = (1 - P_{d} )R_{r} \\ & \Leftrightarrow \frac{N + 1}{{2 \cdot MTTR^{{\prime }} }} = (1 - P_{d} ) \cdot \frac{N + 1}{2 \cdot MTTR} \\ & \Leftrightarrow MTTR^{{\prime }} = \frac{MTTR}{{1 - P_{d} }}. \\ \end{aligned}$$

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Shen, B., Guo, J. & Li, L.X. Cost optimization in persistent virtual world design. Inf Technol Manag 19, 155–169 (2018). https://doi.org/10.1007/s10799-017-0283-y

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