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# Node performance score

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Note: This chapter is currently under development.
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#### Node latency index

Latency index (the node performance delay):

$$D(i)=1-\left( \dfrac{d\_{ij}}{d\_{max}}\right)^3$$

, where $$d\_{ij}$$ denotes the delay of the $$j$$-th transaction of node $$i$$; $$d\_{max}$$ denotes the maximum performance delay allowed by the system.

#### Transaction completion rate

Transaction completion rate with penalty mechanism, which refers to the percentage of nodes that successfully participate in each transaction after entering the system:

$$T(i)=\dfrac{1}{n}\displaystyle\sum\_{i=1}^m\mu\_i$$

$$\mu\_k=\begin{cases}1\text{, if transaction }k\text{ successful}\\-1 \text{, otherwise}\end{cases}$$

, where $$n$$ is the total number of system transactions, $$m$$ denotes the number of transactions completed by node $$i$$, $$μ$$ is the identifier of whether the transaction is successful or not.

#### Historical performance values

The performance status of the current node is influenced by the historical performance values:

$$C(i)'=zC(i-1)$$

, where $$z$$ is a coefficient indicating historical state influence.

#### Node performance rate calculation 

$$C(i)=xD(i)+yT(i)+C(i)'$$

$$x$$ is the weight of the node's transaction latency, $$y$$ is the weight of the node's own completed transactions,  $$z$$ is historical state coefficient, and:

$$x+y+z=1$$