PERFORMANCE EVALUATION
A. Simulation Process and Settings Since global reputation is standardized, nodes can use a variety of reputation mechanisms. In our simulations, all nodes use a simple personal reputation mechanism. We describe the mechanism in the perspective of an honest node i evaluates personal reputation pij of a node j.
- Node i records the number of good evaluations goodij and total evaluations of node totij . If node i receives a piece of data from node j, then totij = totij 1. If the data is complete, goodij = goodij 1.
- If node i gives a piece of data to j, totij = totij 1. If node j increases pij after receives the data from i, then goodij = goodij 1.
- pij = goodij/totij .
We generate an operation list, representing the operations of the nodes in the network arranged in chronological order. From the perspective of node i, we introduce the following two operations.
- Node i generates a new piece of data. Node i provides the data size, queries the latest block generator for storage locations, and stores the data in the corresponding locations.
- Node i accesses a piece of existing data. Node i accesses the data from node j that owns the data to minimize rij/pij .
A. 模拟过程和设置 由于全局信誉是标准化的，节点可以使用多种信誉机制。在我们的模拟中，所有节点都使用简单的个人声誉机制。我们从诚实节点 i 评估节点 j 的个人声誉 pij 的角度来描述该机制。
- 节点 i 记录良好评价的数量 goodij 和节点 totij 的总评价。如果节点 i 从节点 j 接收到一条数据，则 totij = totij 1。如果数据完整，goodij = goodij 1。
- 如果节点 i 给 j 一条数据，totij = totij 1。如果节点 j 收到 i 的数据后增加 pij，则 goodij = goodij 1。
- pij = goodij/totij。
我们生成一个操作列表，表示按时间顺序排列的网络中节点的操作。从节点 i 的角度，我们介绍以下两个操作。
- 节点 i 生成一条新数据。节点 i 提供数据大小，查询最新的块生成器的存储位置，并将数据存储在相应的位置。
- 节点 i 访问一条现有数据。节点 i 从拥有数据的节点 j 访问数据以最小化 rij/pij 。
After each access, nodes related to the access update the personal reputation of each other. When the number of operations reaches a threshold, the node with the highest global reputation becomes a new block generator. It generates a new block and updates the global reputation. We generate the total storage resource Wtol(i) for each node i by a normal distribution, N(1000000; 100000) KB. We generate the size of each piece of data by N(100; 30) KB. Each piece of data will be accessed by a uniformly random node multiple times, which are generated by N(10; 2). We generate an operation list, and the simulation runs according to that list. The number of generating operations divided by the number of access operations is approximately 0.1, and they appear evenly in the list. When the number of operations not on the blockchain reaches 110, the node that satisfies condition (13) generates a new block that records these operations. We terminate simulations when the number of blocks reaches 1000. We generate the test network G = (V， E) by the Watts- Strogatz model [29]. This model generates networks that reveal properties of some real communication networks.
每次访问后，与访问相关的节点都会更新彼此的个人声誉。当操作次数达到阈值时，全局声誉最高的节点成为新的区块生成器。它生成一个新块并更新全局声誉。
我们通过正态分布 N(1000000, 100000) KB 为每个节点 i 生成总存储资源 Wtol(i)。我们生成每条数据的大小 N(100, 30) KB。每条数据将被一个均匀随机的节点多次访问(次数)，由 N(10, 2) 生成。我们生成一个操作列表，模拟根据该列表运行。生成操作数除以访问操作数约为 0.1，它们均匀地出现在列表中。当不在区块链上的操作达到 110 次时，满足条件 (13) 的节点会生成一个记录这些操作的新区块。当块数达到 1000 时，我们终止模拟。我们通过 Watts- Strogatz 模型[29]生成测试网络 G = (V，E) 。该模型生成的网络揭示了一些真实通信网络的属性。
We let honest nodes constantly give factual evaluations and provide complete data. To test the security of our design, we make some nodes malicious. Malicious nodes perform badmouthing attacks by conducting malicious evaluations after operations. In addition, malicious nodes may refuse to provide data. The attack probability is 0.5, that is, there is a probability of 50% that malicious nodes make wrong evaluations, and malicious nodes refuse to provide data with a probability of 50%. Considering the worst case, we assume that all malicious nodes always make good evaluations with each other. We run simulations under environments that include the different proportions of malicious nodes. We only show measurements of honest nodes, since our system is designed for honest nodes. We use the algorithm in [19] as the benchmark. In the following simulation, we compare the results of the algorithm and the benchmark.
我们让诚实的节点不断地给出事实性的评价并提供完整的数据。 为了测试我们设计的安全性，我们使一些节点具有恶意。 恶意节点通过在操作后进行恶意评估来进行恶意攻击。 此外，恶意节点可能会拒绝提供数据。 攻击概率为0.5，即恶意节点做出错误评估的概率为50%，恶意节点拒绝提供数据的概率为50%。 考虑到最坏的情况，我们假设所有恶意节点总是相互做出良好的评估。 我们在包含不同比例恶意节点的环境下运行模拟。 我们只显示诚实节点的测量值，因为我们的系统是为诚实节点设计的。
我们使用[19]中的算法作为基准。 在下面的模拟中，我们比较了算法和基准的结果。
B. Decentralization Test We count the number of blocks generated by each node, and use a histogram in Fig. 2 to show the distribution of the number under different proportions of malicious nodes. The reason for the distribution of a certain number of nodes in the range of 0 to 19 is that all malicious nodes are distributed in this range. It is worth mentioning that in all simulations, malicious nodes can generate up to 2 blocks out of 1000. Very few honest nodes generate more than 100 blocks or less than 20 blocks, and no node generates more than 120 blocks. Most honest nodes can generate 40 to 100 blocks. These phenomena show that in the PoR blockchain, most honest nodes can generate close to the average number of blocks, and very few nodes generate a small or large number of blocks. Thus, we can conclude that our PoR blockchain is decentralized, and it can ensure that the block generators are honest with a high probability.
B. 去中心化测试
我们统计每个节点产生的区块数量，并使用图 2 中的直方图来展示不同比例的恶意节点下数量的分布情况。 之所以会在 0 到 19 范围内分布一定数量的节点，是因为所有的恶意节点都分布在这个范围内。 值得一提的是，在所有的模拟中，恶意节点最多可以产生1000个区块中的2个。很少有诚实节点产生超过100个区块或少于20个区块，并且没有节点产生超过120个区块。 大多数诚实节点可以生成 40 到 100 个块。 这些现象表明，在 PoR 区块链中，大多数诚实节点可以产生接近平均数量的区块，而极少数节点产生少量或大量区块。 因此，我们可以得出结论，我们的 PoR 区块链是去中心化的，它可以确保区块生成者是诚实的，并且概率很高。
C. Fairness Test
We use the Gini coefficient1 of the used storage ratio to show the fairness of our system. Once a new block is generated, we compute the Gini coefficient of the used storage ratio for all honest nodes. In Fig. 3(b), in different proportions of malicious nodes, the Gini coefficients of all tests decrease with blocks increase. Although the Gini coefficients are unstable at the beginning, it decreases as the block is generated, and finally converges to less than 0.2. The reason for this phenomenon is similar to the reason for the phenomenon Fig. 3(a), reputation gaps in the initial stages also affect the balance of storage allocation results. As blocks increase, the used storage ratio balances. Therefore, we can conclude that our algorithm is fair in the long term.
C. 公平测试
我们使用已用存储比率的基尼系数1 来显示我们系统的公平性。 一旦生成了一个新块，我们就会计算所有诚实节点的已用存储比率的基尼系数。 在图 3（b）中，在不同比例的恶意节点中，所有测试的 Gini 系数随着块的增加而减小。 虽然一开始基尼系数不稳定，但随着块的产生而降低，最终收敛到小于0.2。 这种现象的原因与图3（a）现象的原因相似，初始阶段的声誉差距也会影响存储分配结果的平衡。 随着块的增加，使用的存储比率平衡。 因此，我们可以得出结论，我们的算法从长远来看是公平的。
D. Efficiency Test To show the efficiency of our algorithm, we count the average hop-count distance to access data. Since the benchmark is an efficient algorithm, we can conclude that our algorithm is efficient if the average hop-count distance of data request computed by these two algorithms is close. In Fig. 4(a), the average hop-count distance computed by our algorithm rapidly reaches 2, then increases slowly and stabilizes at 2.2. Fig.4(b) shows that the growth rate of the average hop-count distance computed by the benchmark algorithm is relatively slow, and the average eventually tended to around 2.2. The average access distance of our algorithm is unstable at the beginning, and after rapid stabilization, it is close to the result obtained by the benchmark.
D. 效率测试
为了展示我们算法的效率，我们计算访问数据的平均跳数距离。 由于基准是一种有效的算法，如果这两种算法计算的数据请求的平均跳数距离接近，我们可以得出结论，我们的算法是有效的。 在图 4(a) 中，我们的算法计算的平均跳数距离迅速达到 2，然后缓慢增加并稳定在 2.2。 图 4(b) 表明，基准算法计算的平均跳数距离的增长速度相对较慢，平均值最终趋于 2.2 左右。 我们算法的平均访问距离一开始是不稳定的，经过快速稳定后，接近基准得到的结果。
E. Successful Access Rate Test The successful access rate test reveals the reliability of our algorithm. The reliability requires the algorithm to store data to honest nodes, and it is supposed to improve the successful access rate. Once a new block is generated, we compute the successful rate of accessing data. In Fig. 5(a), the successful access rate is above 99.9% in all simulations. In Fig. 5(b), the successful access rate decreases significantly with the increase in the proportion of malicious nodes. When the network includes 40% malicious nodes, compared with the benchmark, our algorithm improves the successful access rate by 14.6%. Therefore, our algorithm greatly improves the successful access rate compared with the benchmark and meets the reliability requirements.
E. 成功的访问速率测试
成功的访问率测试揭示了我们算法的可靠性。 可靠性要求算法将数据存储到诚实节点，并且应该提高访问成功率。 生成新块后，我们计算访问数据的成功率。 在图 5(a) 中，所有模拟的成功访问率都在 99.9% 以上。 在图 5（b）中，成功访问率随着恶意节点比例的增加而显着下降。 当网络中包含 40% 的恶意节点时，与基准相比，我们的算法提高了 14.6% 的成功访问率。 因此，与基准相比，我们的算法大大提高了访问成功率，满足了可靠性要求。
CONCLUSION AND FUTURE WORK
In this paper, we have proposed a reputation mechanism that consists of personal reputation and global reputation. All nodes evaluate others by personal reputations, and they obtain global reputations by aggregating the same personal reputations of all nodes. We have designed a storage allocation mechanism that satisfies fairness, efficiency, and reliability. We have constructed a PoS blockchain based on our reputation mechanism, which costs low computing power and avoids centralization. Our simulations show that our system meets our expectations from multiple measurements. The storage allocation algorithm improves the access success rate while maintaining fairness and efficiency. In the case of malicious nodes that may not provide data, our system can achieve a 99.9% success rate of accessing data. The simulations also show that the PoR blockchain prevents centralization and ensures that the block generators are honest with a high probability. In edge networks, new devices and servers will replace old devices and servers. It requires us to manage the joining and leaving of nodes. In addition, we use a permissioned blockchain to manage access to the blockchain to prevent attacks. Based on the above two concerns, we will further improve the permissioned blockchain network protocol to manage nodes joining and leaving the network, and eliminate nodes with lower reputations.
在本文中，我们提出了一种由个人声誉和全局声誉组成的声誉机制。所有节点通过个人声誉评价他人，通过聚合所有节点相同的个人声誉获得全局声誉。我们设计了一种满足公平、高效、可靠的存储分配机制。我们基于我们的信誉机制构建了一个 PoS 区块链，计算能力成本低，避免了中心化。我们的模拟表明，我们的系统符合我们对多次测量的期望。存储分配算法在保持公平和效率的同时提高了访问成功率。在可能不提供数据的恶意节点的情况下，我们的系统可以达到99.9%的数据访问成功率。模拟还表明，PoR 区块链可以防止中心化，并确保块生成器很可能是诚实的。
在边缘网络中，新设备和服务器将取代旧设备和服务器。它需要我们管理节点的加入和离开。此外，我们使用许可的区块链来管理对区块链的访问以防止攻击。基于以上两个考虑，我们将进一步完善许可区块链网络协议，管理节点加入和离开网络，淘汰信誉度较低的节点。
ACKNOWLEDGMENT
The work in this paper was supported in part by the grant from US National Science Foundation under grant numbers 1513719 and 1730291.
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- The Gini coefficient is widely used to measure the statistical disparities, and previous work [30], [31] used it to measure the fairness properties in edge environments.基尼系数被广泛用于衡量统计差异，之前的工作[30]、[31]用它来衡量边缘环境中的公平性。 ↩︎ ↩︎
