# Research on SWIM Services Dynamic Migration Method +
## 5 Experimental Results and Analysis
### Services Invulnerability Analysis  
The invulnerability is proposed in [13] to describe the system's ability to resist destructive attacks. It means that in the system, the number of servers in migration clusters is \(n\), the probability that the server will migrate to the \(i\)-th server is \(P_{i}\). Drawing on the concept of information entropy, the invulnerability is expressed as:  
\[R_{d}=-\sum_{i=1}^{n}P_{i}\log(P_{i}),n\geq 2 \tag{16}\]  
The higher the services invulnerability is, the higher the randomness of services migration is, and the more difficult for malicious attackers to detect system vulnerabilities is, the more secure the system is. First, the time interval length is \(L\): refers to the number of bits of the pseudo-random sequence contained in the time interval [_Tl, Thl_]. From the definition of services invulnerability, only when the output of pseudo-random sequence is '1' within the time interval will it trigger, and in the time interval, the probability that each bit of the pseudo-random sequence outputs '0' or '1' is equal, then only when all of the output sequence in the time interval is '0', the migration mechanism will not be trigged by the pseudo-random sequence. Therefore, the services invulnerability of the proposed model is defined as follows:  
\[R_{d}=-\bigg{[}(\frac{1}{2}^{L})\times\log(\frac{1}{2}^{L})+(n-1)(1-\frac{1}{ 2}^{L})\frac{1}{(n-1)}\times\log((1-\frac{1}{2}^{L})\frac{1}{(n-1)})\bigg{]}. \tag{17}\]  
In the SASS model [11], services migration is trigged by a pseudo-random sequence. The probability of '0' or '1' in the pseudo-random sequence is equal. due to the SASS model target node selection strategy is the Brownian movement model. Then, the probability that each service be selected is equal. From the definition of the invulnerability, the SASS model's services invulnerability is as follows:  
\[R_{d}=-\bigg{[}\frac{1}{2}\log(\frac{1}{2})+(n-1)\frac{1}{2(n-1)}\log(\frac{1 }{2(n-1)})\bigg{]}. \tag{18}\]  
The TOKEN model is trigged according to the time slice and random sequence [12]. The probability of triggering is as same as the SASS model. However, the TOKEN model selects the destination node based on the minimum load. Assume that in the migration cluster, the number of minimum load  
Figure 10: The sequence in time of migration node. servers is \(n_{0}\), and \(1\leq n_{0}\leq n-1\). The probability that minimum load servers is selected is the same, so the TOKEN model's services invulnerability is as follows:  
\[R_{d}=-\left[\frac{1}{2}\log(\frac{1}{2})+n_{0}\times\frac{1}{2n_{0}}\log( \frac{1}{2n_{0}})\right],1\leq n_{0}\leq n-1. \tag{19}\]  
The SWIM service dynamic migration method is compared the services invulnerability with the SASS model and TOKEN model. The comparison results are shown in Figure 11. First, as the size of the migration cluster continues to expand, the number of the alternative servers are increases, so the probability of each server being selected become smaller, the randomness of this system are increases. Therefore, the invulnerability of the three models is increasing. When \(L=1\), the SWIM service dynamic migration method has the same degree of invulnerability as the SASS model and TOKEN model at \(n_{0}=n-1\). This is because at that time, the SWIM service dynamic migration method triggers the migration mechanism is only determined by a bit pseudo-random sequence, and the probability of the output sequence outputs '0' or '1' is the same. At the same time, the Brownian movement model is used to randomly select the destination node. Therefore, when the SSM model is \(L=1\), the invulnerability is the same as the SASS model. In the TOKEN model, \(n_{0}=n-1\) means that the load of the other nodes is the same, which is the optimal situation. We can randomly select the destination node; therefore, the three models have the same degree of invulnerability. With the same size of the migration cluster, the randomness of the services migration is smaller with the decrease of the services cluster size.