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Performance evaluation of snapshot isolation in distributed database system under failure-prone environment

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Abstract

Database systems are widely used in many fields. As the scale of database systems increases, more firms decide to deploy the database system in a distributed environment for the sake of data integrity fault tolerance. For guaranteeing the consistency of data, database management systems adopt isolation policies. This paper discusses probabilistic models for snapshot isolation of database management system. Snapshot isolation is an effective method to enhance the consistency of database system, although it degrades the system performance where the system has large network latency such as distributed database system. Also, under the failure-prone environment, a restart scheme is considered as one countermeasure. This paper proposes probabilistic models for the dynamics of snapshot isolation of database system and exhibits the optimization of system performance with respect to updating interval of snapshot isolation within the failure-prone environment from the analytical point of view. Numerical experiments are conducted to validate the effectiveness of analytical results by using real traffic data.

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Acknowledgments

This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), Grant Nos. 23510171 (2011–2013) and 23500047 (2011–2013). This paper is an extension of work originally reported in IEEE 9th International Conference on Autonomic Trusted Computing (ATC) 2012, Sept. [9].

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Appendix: Numerical inverse Laplace transform

Appendix: Numerical inverse Laplace transform

Generally, since the LS transform \(F^*(s)\) can be reduced to the Laplace transform by multiplying the LS transform by \(1/s\), we can apply numerical inverse Laplace transform techniques to obtain the inverse LS transfrom. In this paper, we use Gaver’s method [5] to obtain the inverse LS transform of \(G^*(s)\).

Gaver’s method is based on the following formulas:

$$\begin{aligned}&\lim _{n \rightarrow \infty } p_n(t) = \delta (t - \tau ), \end{aligned}$$
(41)
$$\begin{aligned}&\lim _{n \rightarrow \infty } \int \limits _0^\infty p_n(t) f(t) \mathrm{d}t = f(\tau ), \end{aligned}$$
(42)

where \(\delta (t)\) is the Dirac delta function. By taking appropriate sequence \(p_n(t)\), the left-hand side of Eq. (42) corresponds to the Laplace transform. Concretely, Gaver proposed the following sequence:

$$\begin{aligned} p_{n,m}^a(t) = \frac{(n+m)!}{n!(m-1)!} (1-\mathrm{e}^{-at})^n a \mathrm{e}^{-mat}, \quad a > 0, \quad m=1,2,\ldots , \quad n=0,1,\ldots , \end{aligned}$$
(43)

where \(n/m=c\) and \(a=\log (1+c)/\tau \). Letting

$$\begin{aligned} \phi ^a_{n,m} = \int \limits _0^\infty p_{n,m}^a(t) f(t) \mathrm{d}t, \end{aligned}$$
(44)

we have the following recurrence formula:

$$\begin{aligned} \phi _{0,m}^a = m a f^*(ma), \quad \phi _{n,m}^a = \left( 1+\frac{1}{c}\right) \phi _{n-1,m}^a - \frac{1}{c} \phi _{n-1,m+1}^a, \end{aligned}$$
(45)

where \(f^*(s)\) is the Laplace transform. In our numerical experiment, we use an improved Gaver’s method that is accelerated by Wynn’s rho algorithm [16].

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Luo, C., Okamura, H. & Dohi, T. Performance evaluation of snapshot isolation in distributed database system under failure-prone environment. J Supercomput 70, 1156–1179 (2014). https://doi.org/10.1007/s11227-014-1162-5

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