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. 模擬過程和設(shè)置
由于全局信譽(yù)是標(biāo)準(zhǔn)化的，節(jié)點(diǎn)可以使用多種信譽(yù)機(jī)制。在我們的模擬中，所有節(jié)點(diǎn)都使用簡單的個(gè)人聲譽(yù)機(jī)制。我們從誠實(shí)節(jié)點(diǎn) i 評估節(jié)點(diǎn) j 的個(gè)人聲譽(yù) pij 的角度來描述該機(jī)制。

• 節(jié)點(diǎn) i 記錄良好評價(jià)的數(shù)量 goodij 和節(jié)點(diǎn) totij 的總評價(jià)。如果節(jié)點(diǎn) i 從節(jié)點(diǎn) j 接收到一條數(shù)據(jù)，則 totij = totij + 1。如果數(shù)據(jù)完整，goodij = goodij + 1。

• 如果節(jié)點(diǎn) i 給 j 一條數(shù)據(jù)，totij = totij + 1。如果節(jié)點(diǎn) j 收到 i 的數(shù)據(jù)后增加 pij，則 goodij = goodij + 1。

• pij = goodij/totij。

我們生成一個(gè)操作列表，表示按時(shí)間順序排列的網(wǎng)絡(luò)中節(jié)點(diǎn)的操作。從節(jié)點(diǎn) i 的角度，我們介紹以下兩個(gè)操作。

• 節(jié)點(diǎn) i 生成一條新數(shù)據(jù)。節(jié)點(diǎn) i 提供數(shù)據(jù)大小，查詢最新的塊生成器的存儲(chǔ)位置，并將數(shù)據(jù)存儲(chǔ)在相應(yīng)的位置。
• 節(jié)點(diǎn) i 訪問一條現(xiàn)有數(shù)據(jù)。節(jié)點(diǎn) i 從擁有數(shù)據(jù)的節(jié)點(diǎn) j 訪問數(shù)據(jù)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.

每次訪問后，與訪問相關(guān)的節(jié)點(diǎn)都會(huì)更新彼此的個(gè)人聲譽(yù)。當(dāng)操作次數(shù)達(dá)到閾值時(shí)，全局聲譽(yù)最高的節(jié)點(diǎn)成為新的區(qū)塊生成器。它生成一個(gè)新塊并更新全局聲譽(yù)。

我們通過正態(tài)分布 N(1000000, 100000) KB 為每個(gè)節(jié)點(diǎn) i 生成總存儲(chǔ)資源 Wtol(i)。我們生成每條數(shù)據(jù)的大小 N(100, 30) KB。每條數(shù)據(jù)將被一個(gè)均勻隨機(jī)的節(jié)點(diǎn)多次訪問(次數(shù))，由 N(10, 2) 生成。我們生成一個(gè)操作列表，模擬根據(jù)該列表運(yùn)行。生成操作數(shù)除以訪問操作數(shù)約為 0.1，它們均勻地出現(xiàn)在列表中。當(dāng)不在區(qū)塊鏈上的操作達(dá)到 110 次時(shí)，滿足條件 (13) 的節(jié)點(diǎn)會(huì)生成一個(gè)記錄這些操作的新區(qū)塊。當(dāng)塊數(shù)達(dá)到 1000 時(shí)，我們終止模擬。我們通過 Watts- Strogatz 模型[29]生成測試網(wǎng)絡(luò) G = (V，E) 。該模型生成的網(wǎng)絡(luò)揭示了一些真實(shí)通信網(wǎng)絡(luò)的屬性。

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.

我們讓誠實(shí)的節(jié)點(diǎn)不斷地給出事實(shí)性的評價(jià)并提供完整的數(shù)據(jù)。 為了測試我們設(shè)計(jì)的安全性，我們使一些節(jié)點(diǎn)具有惡意。 惡意節(jié)點(diǎn)通過在操作后進(jìn)行惡意評估來進(jìn)行惡意攻擊。 此外，惡意節(jié)點(diǎn)可能會(huì)拒絕提供數(shù)據(jù)。 攻擊概率為0.5，即惡意節(jié)點(diǎn)做出錯(cuò)誤評估的概率為50%，惡意節(jié)點(diǎn)拒絕提供數(shù)據(jù)的概率為50%。 考慮到最壞的情況，我們假設(shè)所有惡意節(jié)點(diǎn)總是相互做出良好的評估。 我們在包含不同比例惡意節(jié)點(diǎn)的環(huán)境下運(yùn)行模擬。 我們只顯示誠實(shí)節(jié)點(diǎn)的測量值，因?yàn)槲覀兊南到y(tǒng)是為誠實(shí)節(jié)點(diǎn)設(shè)計(jì)的。

我們使用[19]中的算法作為基準(zhǔn)。 在下面的模擬中，我們比較了算法和基準(zhǔn)的結(jié)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. 去中心化測試

我們統(tǒng)計(jì)每個(gè)節(jié)點(diǎn)產(chǎn)生的區(qū)塊數(shù)量，并使用圖 2 中的直方圖來展示不同比例的惡意節(jié)點(diǎn)下數(shù)量的分布情況。 之所以會(huì)在 0 到 19 范圍內(nèi)分布一定數(shù)量的節(jié)點(diǎn)，是因?yàn)樗械膼阂夤?jié)點(diǎn)都分布在這個(gè)范圍內(nèi)。 值得一提的是，在所有的模擬中，惡意節(jié)點(diǎn)最多可以產(chǎn)生1000個(gè)區(qū)塊中的2個(gè)。很少有誠實(shí)節(jié)點(diǎn)產(chǎn)生超過100個(gè)區(qū)塊或少于20個(gè)區(qū)塊，并且沒有節(jié)點(diǎn)產(chǎn)生超過120個(gè)區(qū)塊。 大多數(shù)誠實(shí)節(jié)點(diǎn)可以生成 40 到 100 個(gè)塊。 這些現(xiàn)象表明，在 PoR 區(qū)塊鏈中，大多數(shù)誠實(shí)節(jié)點(diǎn)可以產(chǎn)生接近平均數(shù)量的區(qū)塊，而極少數(shù)節(jié)點(diǎn)產(chǎn)生少量或大量區(qū)塊。 因此，我們可以得出結(jié)論，我們的 PoR 區(qū)塊鏈?zhǔn)侨ブ行幕?，它可以確保區(qū)塊生成者是誠實(shí)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. 公平測試

我們使用已用存儲(chǔ)比率的基尼系數(shù)¹ 來顯示我們系統(tǒng)的公平性。 一旦生成了一個(gè)新塊，我們就會(huì)計(jì)算所有誠實(shí)節(jié)點(diǎn)的已用存儲(chǔ)比率的基尼系數(shù)。 在圖 3（b）中，在不同比例的惡意節(jié)點(diǎn)中，所有測試的 Gini 系數(shù)隨著塊的增加而減小。 雖然一開始基尼系數(shù)不穩(wěn)定，但隨著塊的產(chǎn)生而降低，最終收斂到小于0.2。 這種現(xiàn)象的原因與圖3（a）現(xiàn)象的原因相似，初始階段的聲譽(yù)差距也會(huì)影響存儲(chǔ)分配結(jié)果的平衡。 隨著塊的增加，使用的存儲(chǔ)比率平衡。 因此，我們可以得出結(jié)論，我們的算法從長遠(yuǎn)來看是公平的。

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. 效率測試

為了展示我們算法的效率，我們計(jì)算訪問數(shù)據(jù)的平均跳數(shù)距離。 由于基準(zhǔn)是一種有效的算法，如果這兩種算法計(jì)算的數(shù)據(jù)請求的平均跳數(shù)距離接近，我們可以得出結(jié)論，我們的算法是有效的。 在圖 4(a) 中，我們的算法計(jì)算的平均跳數(shù)距離迅速達(dá)到 2，然后緩慢增加并穩(wěn)定在 2.2。 圖 4(b) 表明，基準(zhǔn)算法計(jì)算的平均跳數(shù)距離的增長速度相對較慢，平均值最終趨于 2.2 左右。 我們算法的平均訪問距離一開始是不穩(wěn)定的，經(jīng)過快速穩(wěn)定后，接近基準(zhǔn)得到的結(jié)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. 成功的訪問速率測試

成功的訪問率測試揭示了我們算法的可靠性。 可靠性要求算法將數(shù)據(jù)存儲(chǔ)到誠實(shí)節(jié)點(diǎn)，并且應(yīng)該提高訪問成功率。 生成新塊后，我們計(jì)算訪問數(shù)據(jù)的成功率。 在圖 5(a) 中，所有模擬的成功訪問率都在 99.9% 以上。 在圖 5（b）中，成功訪問率隨著惡意節(jié)點(diǎn)比例的增加而顯著下降。 當(dāng)網(wǎng)絡(luò)中包含 40% 的惡意節(jié)點(diǎn)時(shí)，與基準(zhǔn)相比，我們的算法提高了 14.6% 的成功訪問率。 因此，與基準(zhǔn)相比，我們的算法大大提高了訪問成功率，滿足了可靠性要求。

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，我們提出了一種由個(gè)人聲譽(yù)和全局聲譽(yù)組成的聲譽(yù)機(jī)制。所有節(jié)點(diǎn)通過個(gè)人聲譽(yù)評價(jià)他人，通過聚合所有節(jié)點(diǎn)相同的個(gè)人聲譽(yù)獲得全局聲譽(yù)。我們設(shè)計(jì)了一種滿足公平、高效、可靠的存儲(chǔ)分配機(jī)制。我們基于我們的信譽(yù)機(jī)制構(gòu)建了一個(gè) PoS 區(qū)塊鏈，計(jì)算能力成本低，避免了中心化。我們的模擬表明，我們的系統(tǒng)符合我們對多次測量的期望。存儲(chǔ)分配算法在保持公平和效率的同時(shí)提高了訪問成功率。在可能不提供數(shù)據(jù)的惡意節(jié)點(diǎn)的情況下，我們的系統(tǒng)可以達(dá)到99.9%的數(shù)據(jù)訪問成功率。模擬還表明，PoR 區(qū)塊鏈可以防止中心化，并確保塊生成器很可能是誠實(shí)的。

在邊緣網(wǎng)絡(luò)中，新設(shè)備和服務(wù)器將取代舊設(shè)備和服務(wù)器。它需要我們管理節(jié)點(diǎn)的加入和離開。此外，我們使用許可的區(qū)塊鏈來管理對區(qū)塊鏈的訪問以防止攻擊?；谝陨蟽蓚€(gè)考慮，我們將進(jìn)一步完善許可區(qū)塊鏈網(wǎng)絡(luò)協(xié)議，管理節(jié)點(diǎn)加入和離開網(wǎng)絡(luò)，淘汰信譽(yù)度較低的節(jié)點(diǎn)。

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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