Open Access

ARTICLE

# Computing Resource Allocation for Blockchain-Based Mobile Edge Computing

1 School of Computer Science and Information Engineering, Intelligent Interconnected Systems Laboratory of Anhui Province, Hefei University of Technology, Hefei, 230601, China

2 Anhui Province Key Lab of Aerospace Structural Parts Forming Technology and Equipment, Hefei University of Technology, Hefei, 230009, China

3 College of Future Industry, Gachon University, Seongnam, 13120, South Korea

* Corresponding Authors: Xu Ding. Email: ; Jung Yoon Kim. Email:

(This article belongs to the Special Issue: Machine Learning Empowered Distributed Computing: Advance in Architecture, Theory and Practice)

*Computer Modeling in Engineering & Sciences* **2024**, *140*(1), 863-885. https://doi.org/10.32604/cmes.2024.047295

**Received** 01 November 2023; **Accepted** 17 January 2024; **Issue published** 16 April 2024

## Abstract

Users and edge servers are not fully mutually trusted in mobile edge computing (MEC), and hence blockchain can be introduced to provide trustable MEC. In blockchain-based MEC, each edge server functions as a node in both MEC and blockchain, processing users’ tasks and then uploading the task related information to the blockchain. That is, each edge server runs both users’ offloaded tasks and blockchain tasks simultaneously. Note that there is a trade-off between the resource allocation for MEC and blockchain tasks. Therefore, the allocation of the resources of edge servers to the blockchain and the MEC is crucial for the processing delay of blockchain-based MEC. Most of the existing research tackles the problem of resource allocation in either blockchain or MEC, which leads to unfavorable performance of the blockchain-based MEC system. In this paper, we study how to allocate the computing resources of edge servers to the MEC and blockchain tasks with the aim to minimize the total system processing delay. For the problem, we propose a computing resource Allocation algorithm for Blockchain-based MEC (ABM) which utilizes the Slater’s condition, Karush-Kuhn-Tucker (KKT) conditions, partial derivatives of the Lagrangian function and subgradient projection method to obtain the solution. Simulation results show that ABM converges and effectively reduces the processing delay of blockchain-based MEC.## Keywords

Numerous mobile devices have become the indispensable instruments in people’s work, study, and living due to the fast development of mobile networks [1]. Intelligent bracelets, smart garbage disposals, smart signal light controls, smart home appliances, and other intelligent applications have quickly garnered popularity and public attention. It is widely acknowledged that these intelligent applications have significantly improved social efficiency, raised human productivity, and improved people’s quality of life [2,3]. Innumerable innovative applications call for considerable computing power, which imposes a significant barrier for the IoT devices with limited resources and energy [4,5]. Cloud computing offers the users on-demand services through a pool of computing resources. However, cloud data centers are typically located far from mobile devices (users), and hence mobile cloud computing faces the issues of high latency, slow channel transmission, etc. [6,7].

Mobile Edge Computing (MEC) [8–10] has been developing to address the issues mentioned above by offloading computing tasks to edge servers. Therefore, the quality of service for task processing, including lower energy consumption and reduced execution delay, can be considerably enhanced by offloading computing workloads from users to edge servers [11,12]. However, the users and edge servers are not fully mutually trusted [13]. Blockchain is considered as a viable strategy to solve the problem of trust [14,15]. Blockchain uses community verification to synchronize a decentralized ledger replicated over several nodes, unlike conventional digital ledger systems that depend on a reliable central authority [16–18]. Accordingly, both academia and business are paying attention to building MEC based on blockchain [19].

In the blockchain-based MEC system shown in Fig. 1, each edge server functions as a node in both MEC and blockchain. As an MEC node, each edge server processes users’ tasks and uploads the information about each task, e.g., user, time, task workload, results, etc., to the blockchain. As a blockchain node, the edge server treats the information of each task as a transaction and generates the blocks, each containing several transactions. Each transaction contains the encrypted file and the hash of the data and the result related to the task execution. The sources of the transactions in a block are all the users served by the edge server. That is, the transactions in a block may come from several users. After creating a block, the edge server propagates it to other edge servers which will verify the blocks. In this way, blockchain can provide trust between users and edge servers by transparent task-related information sharing. The transactions recording the information of the tasks are stored in blockchain, such that they cannot be modified. The anti-tampering characteristics of blockchain guarantee the authenticity and legitimacy of each transaction, thus allowing the users to check and track the details of the task related information. Each user can also evaluate the trustworthiness of other users based on their transaction history on the blockchain. If there is a dispute or controversy over a transaction, the transactions recorded in the blockchain can be used as a reliable evidence, which is used to resolve the dispute [20].

In blockchain-based MEC, each edge server runs both blockchain tasks and users’ offloaded tasks simultaneously. Note that there is a trade-off between the resource allocation for MEC and blockchain tasks. Therefore, the resource allocation for the blockchain and the MEC is crucial for the processing delay of blockchain-based MEC. Most of the existing research tackles the problem of resource allocation in either MEC [21–23] or blockchain [24–26], which leads to the unfavorable performance of blockchain-based MEC. In this paper, we tackle the problem of how to allocate the computing resources of edge servers to the MEC and blockchain tasks with the objective of minimizing the total system processing delay. The contributions of this paper are as follows:

(1) We study the problem of resource allocation for both MEC and blockchain tasks to reduce the total processing delay of blockchain-based MEC, different from the existing research that focuses on only one of MEC and blockchain.

(2) We propose a computing resource Allocation algorithm for Blockchain-based MEC (ABM), which consists of four steps. First, we prove that the problem is convex. Second, we prove that the problem satisfies the Slater’s condition, and hence the problem and its dual satisfy strong duality. Third, we use the Karush-Kuhn-Tucker (KKT) conditions and the partial derivatives of the Lagrangian function to obtain the solution with the dual variables. Finally, we decide the values of the dual variables via the subgradient projection method, which obtains the solution to the problem.

(3) Simulation results demonstrate that ABM converges and effectively reduces the processing delay of blockchain-based MEC.

The rest of the paper is organized as follows. The related work is introduced in Section 2. The problem is defined in Section 3. Section 4 proposes the algorithm. In Section 5, the experimental results are presented. The paper is summarized in Section 6.

In blockchain-based MEC, each edge server executes both MEC and blockchain tasks. Both of these two kinds of tasks consume computational resources, and there is a trade-off between the resource allocation for MEC and blockchain tasks. Therefore, the resource allocation for the blockchain and the MEC is crucial for the processing delay of blockchain-based MEC. Nevertheless, most of the existing research tackles the problem of resource allocation in either blockchain or MEC.

Some research studied the problem of computing resource allocation for MEC. Ren et al. [21] proposed a hybrid communication and computing resource allocation approach for delay minimization in a multi-user time-division multiple-access MEC offloading system. Nosrati et al. [27] proposed a community-based solution for the management of data replication based on the model of communication latency between computing and storage nodes. Feng et al. [28] proposed a method to maximize the user utility while reducing the operator’s energy usage in a MEC system with multi-user radios, by jointly optimizing the radio power allocation at the base station and the power allocation for processing users’ offloaded data. Hong et al. [29] proposed an optimal resource allocation strategy that primarily addresses the issue of assigning MEC computing resources to a group of cars within a time window, so as to reduce the overall task processing delay. Liu et al. [30] proposed an edge framework that contains four groups under different locations between mobile edge nodes and users for the resource allocation problem to reduce the total cost of users and edge servers. Gao et al. [31] built a task offloading and resource allocation model which uses the overall computational cost as the objective function. Spallina et al. [22] proposed a deep Q-learning network for the resource allocation problem to reduce the task offloading energy usage while maintaining users’ quality of service. Guo et al. [32] developed an online greedy heuristic algorithm for the resource optimization problem with the aim to maximize the long-term overall performability. Zhang et al. [33] investigated the user association and offloading decision problems for satelliteaerial integrated computing networks, where users can offload their tasks to high-altitude platforms (HAPs) and the satellite with edge computing servers. Zhang et al. [34] proposed a blockchain based containerized edge computing platform for Internet of Vehicles. The platform was integrated with blockchain to improve the security of the network. A heuristic container scheduling algorithm was developed to schedule computing tasks to appropriate edge servers to reduce the computing latency. Gao et al. [35] proposed the resource control algorithm to improve the system performance under the unstable workload in vehicular networks. The proposed resource control algorithm adjusts the priority and proportion of the resource utilization according to the system status obtained from the resource monitor, such as transaction workload or CPU utilization status. Fan et al. [23] proposed a joint task offloading and resource allocation scheme for MEC. Aghapour et al. [36] proposed a deep reinforcement learning-based technique that divides the task offloading and resource allocation problem into two sub-problems, to reduce the delay and power consumption related to work offloading. Xiao et al. [37] proposed an algorithm to reduce users’ task-offloading overhead, by optimizing the computational offloading choice, the wireless resource allocation policy and the computational resource allocation strategy.

Some scholars conducted research on resource allocation for blockchain. Xia et al. [38] presented a three-phase auction method to allocate resources for mobile blockchain, which introduces a group buying mechanism to encourage edge servers to join the blockchain network. Kang et al. [13] proposed a reputation-based data-sharing scheme that uses contract technology and federation chains to accomplish secure data storage and avoid inappropriate data sharing. Toulouse et al. [39] investigated the problem of balancing workload of account-based blockchains such as Ethereum and proposed the method to predict transaction processing times. Jiao et al. [40] built an auction-based market model to determine the computing offloading strategy for miners and the allocation of computing resources to edge servers. Alfakeeh et al. [41] proposed the algorithms for the resource allocation of mining nodes, which utilizes the backpack algorithm to allocate the caching space of the mining nodes to resolve the problem of how to efficiently allocate resources so that data can be placed equitably in these fog mining nodes while maintaining the prioritization and sensitivity of patient data. Chang et al. [42] proposed an edge computing based blockchain incentive mechanism for miners to purchase edge server computing resources, and established a two-stage Stackelberg game between miners and edge servers. Fan et al. [43] constructed a computation offloading model composed of multiple miners, multiple ESPs, and a CSP for mobile blockchain and proposed a three-stage Stackelberg game for optimal pricing-based edge computing resource management. Zhang et al. [24] proposed a group-agent strategy with trust computing to ensure the reliability of edge devices during interactions and improve transmission efficiency. Wang et al. [25] proposed an incentive mechanism, in which the client chooses the amount of computational power allocated to each task via a two-stage Stackelberg game based on the rewards. Zhou et al. [44] proposed a blockchain-enabled spectrum trading system to maximize user benefits and designed a spectrum trading matching method. A Dynamic Credit Aggregate Signature Byzantine Fault Tolerant (DCABFT) algorithm based on Boneh-Lynn-Shacham (BLS) aggregated signatures was proposed, which aims to reduce the transaction latency and increase the user quality of service while addressing the latency and energy consumption of blockchain consensus algorithms. Zhang et al. [26] proposed two auction mechanisms for the blockchain network to maximize societal welfare and offer an efficient resource allocation method for edge computing service providers. Baranwal et al. [45] proposed a distributed auction-based resource allocation system in the context of edge computing-enabled industrial IoT. The technique eliminates the need of a trustworthy third party (the auctioneer) using consortium blockchain and smart contracts. Gao et al. [8] proposed a hierarchical resource scheduling scheme for the Vehicular Internetworking System (VINS) to allocate the computational resources, in order to increase the flexibility and efficiency of the system’s resource utilization and to boost the performance of the blockchain-based VINS.

Both MEC and blockchain tasks require computational resources for execution in blockchain-based MEC. Due to the limited computational capability of each edge server, an imbalance in the allocation of computational resources to blockchain and MEC will result in a large system processing delay. However, most of the current research tackles the problem of resource allocation for either blockchain or MEC, and little research has been conducted on the optimization of resource allocation for both blockchain and MEC simultaneously. Feng et al. [46] proposed a joint optimization framework for blockchain-enabled MEC by jointly optimizing user offloading decisions and computational resource allocation to achieve the trade-off between the energy consumption of the MEC system and the latency of the blockchain system. In the framework, some of the users’ tasks cannot be offloaded to the edge servers when they are making the choices of what tasks to be processed. However, this kind of offloading decisions are not reasonable, when the users have to but are unable to process some computation intensive tasks, e.g., real-time video stream processing, etc. As for the energy consumption, it is often difficult for the edge to obtain the factors of power, usage time, etc., of the large amount of heterogeneous users in the applications, which makes it hard to optimize the system energy consumption [47]. Furthermore, the energy consumption of users has no impact on the edge’s utility. Therefore, in this paper, we study the problem of how to allocate the computing resources of edge servers for the MEC and the blockchain tasks with the objective of minimizing the total system processing delay.

3.1 System Model of Blockchain-Based MEC

There are multiple users (IoT devices, sensors, wearables, etc.) and edge servers in the blockchain-based MEC system. Each edge server with constrained computing resources serves an area, and the users in the area can offload the tasks to the edge server. At the same time, the edge servers comprise the blockchain. After running the users’ tasks, each edge server uploads the information related to the task execution, e.g., user, time, task workload, result, etc., to the blockchain. Each edge server, as a blockchain node, treats the task related information as a transaction and generates blocks, each containing several transactions. Each transaction contains the encrypted file and the hash of the data and the result related to the task execution. The sources of the transactions in a block are all the users served by the edge server. That is, the transactions in a block may come from several users. The blocks are broadcast to all blockchain nodes which verify the blocks. The block generation and verification are referred to as blockchain tasks. Accordingly, as shown in Fig. 1, each edge server runs two kinds of tasks: those offloaded by users and those in blockchain. Table 1 lists the symbols and notations used in this paper.

3.1.1 Latency of Task Execution in MEC

Denote the sets of users and edge servers as

where

where

where

where

3.1.2 Latency of Blockchain Task Execution

The total latency

where

where

where

The block transmission delay

where

Each edge server executes the tasks in both MEC and blockchain. In this paper, we study how to allocate the computing resources of each edge server to MEC and blockchain, with the aim to minimize the total system processing latency. That is, our objective is to

Constraint C1 stipulates that the computational resources assigned by each edge server must be within the processing capacity of the edge server. Constraint C2 states that the edge server should allocate the computing resources to both MEC and blockchain.

The variables in the computing resource allocation problem in this paper are

In this section, we propose a computing resource Allocation algorithm for Blockchain-based MEC (ABM), which consists of four steps as shown in Fig. 2. First, we prove that the problem is convex. Second, we prove that the problem satisfies the Slater’s condition, and hence the problem and its dual satisfy strong duality. Third, we use the KKT conditions and the partial derivatives of the Lagrangian function to obtain the solution with the dual variables. Finally, we decide the values of the dual variables via the subgradient projection method, which obtains the solution to the problem.

We denote

where

The following equations can be obtained by calculating the first-order derivative of objective function O:

The second-order derivative of objective function O can be calculated as follows:

The principal subequations of the Hessian matrix for each order have values greater than 0, and hence we can derive that the Hessian matrix is positive definite. Consequently, according to Theorem 4.1, objective function O is convex. Furthermore, the function in constraint C1 exhibits convexity, and hence the original problem is also convex.

Theorem 4.1. For a function

Proof. The Hessian matrix

where

Consider any two points, denoted as

where

Lemma 4.1. The resource allocation problem in this paper satisfies the Slater’s condition.

Proof. The Slater’s condition holds for the definition domain of

According to Lemma 4.1, we can derive that the original problem and its dual problem meet strong duality, since they both satisfy the Slater’s condition and are mutually adequate to satisfy strong duality. The optimal solution using the KKT conditions can be found, if the original problem is convex and fulfills strong duality. We find the optimal solution by calculating the partial derivative of the Lagrangian dual function via the KKT conditions, using dual variables. The original problem’s Lagrangian function can be written as follows:

where

where

Following the definition of KKT conditions, we can derive

We can further obtain

where

According to Theorem 4.2, we can obtain the dual variables via the subgradient projection method, since the objective function and constraints in the original problem are convex.

Theorem 4.2.

Proof. From

After substitution, we have the following inequality:

Subgradient means that points

where

Therefore, we can use the subgradient projection method to decide the values of the dual variables. That is

and

where

The users in the service area of edge server

In the simulations, there are 60 users and 6 edge servers in the blockchain-based MEC system. The parameters of the system are listed in Table 2. The performance of ABM is evaluated by utilizing three benchmark algorithms, namely IADA [46], JCCR [33] and DSRC [24].

(1) IADA [46]: The algorithm first adopts binary search to obtain the resource allocation for processing MEC tasks, and then solves the stationing point to obtain the resource allocation for processing blockchain tasks.

(2) JCCR [33]: Each edge server allocates a fixed amount of computing resources to process MEC tasks.

(3) DSRC [24]: Each edge server allocates a fixed amount of computing resources to process blockchain tasks.

Fig. 3 shows the total latency performance of ABM with different step sizes. ABM converges after 4 iterations, when step size

The convergence performance of the proposed algorithm is illustrated in Fig. 4. It is noteworthy that the latency of the algorithm exhibits a decreasing trend as the number of iterations increases and the algorithm converges to a stable value. For example, the total latency decreases by 40.78

It can be observed from Fig. 5 that the total latency of IADA, JCCR, and DSRC is higher than that of ABM with a given number of users. The total latency of ABM is 4.85

Fig. 6 illustrates the impact of the number of servers on the overall delay, when the number of edge servers increases from 6 to 10. The total latency of all algorithms reduces with more edge servers. As the number of edge servers increases, the number of users served by each edge server decreases, which reduces the total size of the tasks to be processed by each edge server. Therefore, the overall latency is reduced. ABM achieves up to 8.15

Fig. 7 demonstrates the impact of the user’s task size on the total delay. We can observe that the total delay of the four algorithms exhibits an increasing trend with the increase in the user’s task size. The increase in the user’s task size requires more computing resources and time for processing and more time for data and block transmission. Consequently, the overall delay experiences an increase. Fig. 7 illustrates that ABM consistently outperforms IADA, JCCR and DSRC in terms of the total latency. When the user’s task sizes are 1, 2, and 3 MB, the total latency of ABM is respectively lower than that of IADA by 13.63

Fig. 8 shows the total latency of the four algorithms with various block sizes. It can be observed that the total delay increases with the increasing block size. The block with a large size contains more transactions, which means that the edge server needs more time to aggregate enough MEC task related information for block generation. A large block size also means that the blockchain needs more time to transmit and validate the block. ABM jointly optimize the resource allocation for MEC and blockchain tasks, such that the resource allocation can adapt to various block sizes to achieve a favorable total latency performance. Our algorithm outperforms IADA, JCCR and DSRC. Specifically, when the block sizes are 4, 6, and 8 MB, the total latency of ABM is 8.18

Fig. 9 shows the total latency with different clock cycles required for the edge server to process 1 bit data. The total latency increases with the increase of the number of clock cycles

Fig. 10 depicts the total system delay with different processing capacities of the edge server. The total latency declines with the increasing processing capacity of the edge server. A higher processing capacity leads to short processing time of MEC and blockchain tasks. Accordingly, the total delay of each algorithm reduces, as the processing capacity of the edge server increases. Fig. 10 illustrates that ABM achieves better total latency performance than IADA, JCCR and DSRC. Specifically, the total latency of ABM is up to 7.04

Fig. 11 illustrates the total latency vs. the transaction size. The total latency rises, as the transaction size increases. The edge server requires more time to generate the blocks with a large transaction size. ABM always incurs less total latency than IADA, JCCR and DSRC, due to the joint optimization of resource allocation for MEC and blockchain tasks. The total latency of ABM is less than that of IADA by 8.33

In this paper, we studied how to allocate the computing resources of edge servers to the MEC and blockchain tasks with the aim to minimize the total processing delay of blockchain-based MEC. For the problem, we proposed a computing resource Allocation algorithm for the Blockchain-based MEC system (ABM), which consists of four steps. First, we prove that the problem is convex. Second, we prove that the problem satisfies the Slater’s condition, and hence the problem and its dual satisfy strong duality. Third, we use the KKT conditions and the partial derivatives of the Lagrangian function to obtain the solution with the dual variables. Finally, we decide the values of the dual variables via the subgradient projection method, which obtains the solution to the problem. We conducted experiments through simulations. ABM demonstrates superior performance in terms of the total system latency under various parameters, including the number of users, user task sizes, block sizes, number of clock cycles required for edge servers to process 1 bit data, number of edge servers, processing capacity of the edge servers, block sizes and step sizes.

The users’ tasks may have different priorities, which have a significant impact on the resource allocation. In our future work, we will work on how to allocate the computing resources of edge servers, to provide the QoS of different tasks.

Acknowledgement: The authors would like to express their gratitude to all who supported this research. We are thankful for the insightful comments from anonymous reviewers, which have greatly improved this manuscript. We also appreciate the Anhui Province Key Laboratory of Industry Safety and Emergency Technology for technical support.

Funding Statement: This work is partially supported by the Key Research and Development Project in Anhui Province of China (Grant No. 202304a05020059), the Fundamental Research Funds for the Central Universities of China (Grant No. PA2023GDSK0055) and the Project of Anhui Province Economic and Information Bureau (Grant No. JB20099).

Author Contributions: The authors confirm contribution to the paper as follows: study conception and design: Yuqi Fan, Wanbo Zhang; algorithm design: Wanbo Zhang, Yuqi Fan; analysis and interpretation of results: Wanbo Zhang, Jun Zhang, Xu Ding, Jung Yoon Kim; draft manuscript preparation: Wanbo Zhang, Yuqi Fan. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: All data is synthesized using MATLAB and the generation method is described in detail in the simulation section.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

## References

1. Cau, E., Corici, M., Edmonds, A. (2016). Efficient exploitation of mobile edge computing for virtualized 5G in EPC architectures. 2016 4th IEEE International Conference on Mobile Cloud Computing, Services, and Engineering (MobileCloud), USA. [Google Scholar]

2. Borgia, E., Bruno, R., Conti, M. (2016). Mobile edge clouds for information-centric IoT services. IEEE Symposium on Computers and Communication, Italy. [Google Scholar]

3. Gao, H., Wang, X., Wei, W. (2023). Com-DDPG: Task offloading based on multiagent reinforcement learning for information-communication-enhanced mobile edge computing in the Internet of Vehicles. IEEE Transactions on Vehicular Technology, 73(1), 348–361. [Google Scholar]

4. Orsini, G., Dirk, B., Winfried, L. (2015). Edge intelligence: The confluence of edge computing and artificial intelligence. 2015 8th IFIP Wireless and Mobile Networking Conference, Canada. [Google Scholar]

5. Khan, W. Z., Ahmed, E., Ejaz, A. (2019). Edge computing: A survey. Future Generation Computer Systems, 97(39), 219–235. [Google Scholar]

6. Gao, H., Fang, D., Xiao, J. (2023). CAMRL: A joint method of channel attention and multidimensional regression loss for 3D object detection in automated vehicles. IEEE Transactions on Intelligent Transportation Systems, 24(8), 8831–8845. [Google Scholar]

7. Jararweh, Y., Doulat, A., AlQudah, O. (2016). The future of mobile cloud computing: Integrating cloudlets and mobile edge computing. 2016 23rd International Conference on Telecommunications, Greece. [Google Scholar]

8. Gao, H., Huang, J., Tao, Y. (2022). Enabling low-latency applications in LTE-A based mixed fog/cloud computing systems. IEEE Transactions on Computational Social Systems, 9(6), 1725–1735. [Google Scholar]

9. Tran, T. X., Hajisami, Pandey, P. (2017). Collaborative mobile edge computing in 5G networks: New paradigms, scenarios, and challenges. IEEE Communications Magazine, 55(4), 54–61. [Google Scholar]

10. Liu, J., Mao, Y., Zhang, J. (2016). Delay-optimal computation task scheduling for mobile-edge computing systems. IEEE International Symposium on Information Theory, USA. [Google Scholar]

11. Mao, Y., Zhang, J., Song, S. (2017). Stochastic joint radio and computational resource management for multi-user mobile-edge computing systems. IEEE Transactions on Wireless Communications, 16(9), 5994–6009. [Google Scholar]

12. You, C., Huang, K., Chae, H. (2016). Energy-efficient resource allocation for mobile-edge computation offloading. IEEE Internet of Things Journal, 16(3), 1397–1411. [Google Scholar]

13. Kang, J., Yu, R., Huang, X. (2018). Blockchain for secure and efficient data sharing in vehicular edge computing and networks. IEEE Transactions on Wireless Communications, 6(3), 4660–4670. [Google Scholar]

14. Xiong, Z., Zhang, Y., Niyato, D. (2018). When mobile blockchain meets edge computing. IEEE Communications Magazine, 56(8), 33–39. [Google Scholar]

15. Dang, T., Duong, T. A. (2021). An effective and elastic blockchain-based provenance preserving solution for the open data. International Journal of Web Information Systems, 17(5), 480–515. [Google Scholar]

16. Miller, D. (2018). Blockchain and the Internet of Things in the industrial sector. IT Professional, 20(3), 15–18. [Google Scholar]

17. Liang, X., Zhao, J., Shetty, S. (2017). Towards data assurance and resilience in IoT using blockchain. IEEE Military Communications Conference, USA. [Google Scholar]

18. Aitzhan, N., Svetinovic, D. (2018). Security and privacy in decentralized energy trading through multi-signatures, blockchain and anonymous messaging streams. IEEE Transactions on Dependable and Secure Computing, 17(5), 840–852. [Google Scholar]

19. Li, Z., Kang, J., Zhang, Y. (2017). Consortium blockchain for secure energy trading in industrial Internet of Things. IEEE Transactions on Industrial Informatics, 14(8), 3690–3700. [Google Scholar]

20. Lang, P., Tian, D. X., Duan, X. T., Zhou, J. S., Sheng, Z. G. et al. (2022). Cooperative computation offloading in blockchain based vehicular edge computing networks. IEEE Transactions on Intelligent Vehicles, 7(3), 783–798. [Google Scholar]

21. Ren, J., Yu, G., He, Y. (2018). Latency optimization for resource allocation in mobile edge computation offloading. IEEE Transactions on Wireless Communications, 17(8), 5506–5519. [Google Scholar]

22. Spallina, A., Araldo, A., Chahed, T. (2022). Energy-efficient resource allocation in multi-tenant edge computing using Markov decision processes. Computer Networks, 140(24), 1–5. [Google Scholar]

23. Fan, W., Su, Y., Huang, W. (2023). Joint task offloading and resource allocation for vehicular edge computing based on V2I and V2V modes. IEEE Transactions on Intelligent Transportation Systems, 24(4), 4277–4292. [Google Scholar]

24. Zhang, L., Zou, Y., Su, Y. (2021). Resource allocation and trust computing for blockchain-enabled edge computing system. Computers and Security, 105(41), 102249. [Google Scholar]

25. Wang, Z., Hu, Q., Xiong, Z. (2023). Incentive mechanism design for joint resource allocation in blockchain-based federated learning. IEEE Transactions on Parallel and Distributed System, 34(5), 1536–1547. [Google Scholar]

26. Zhang, J., Lou, W., Li, W. (2022). Truthful auction mechanisms for resource allocation in the Internet of Vehicles with public blockchain networks. Future Generation Computer Systems, 132(39), 625–629. [Google Scholar]

27. Nosrati, M., Fazlali, M. (2018). Community-based replica management in distributed systems. International Journal of Web Information Systems, 14(1), 41–61. [Google Scholar]

28. Feng, J., Pei, Q., Yu, F. (2019). Computation offloading and resource allocation for wireless powered mobile edge computing with latency constraint. IEEE Wireless Communications Letters, 8(5), 1320–1323. [Google Scholar]

29. Hong, G., Wen, Q., Wu, P. (2019). An optimal resource allocation mechanism in vehicular MEC systems. International Conference on Networking and Network Applications, South Korea. [Google Scholar]

30. Liu, J. H., Wu, Z. B., Liu, J. J., Zou, Y. (2022). Cost research of internet of things service architecture for random mobile users based on edge computing. International Journal of Web Information Systems, 18(4), 217–235. [Google Scholar]

31. Zhang, Y., Zhang, M., Li, B. (2021). Computing resource allocation scheme of IOV using deep reinforcement learning in edge computing environment. EURASIP Journal on Advances in Signal Processing, 2021, 33. [Google Scholar]

32. Guo, Y., Liu, F., Xiao, N., Li, Z. G., Cai, Z. P. et al. (2022). PARA: Performability-aware resource allocation on the edges for cloud native services. International Journal of Intelligent Systems, 37(11), 8523–8547. [Google Scholar]

33. Zhang, L., Zhang, H. L., Guo, C., Xu, H. T., Song, L. Y. et al. (2020). Satellite aerial integrated computing in disasters: User association and offloading decision. IEEE International Conference on Communications, Ireland. [Google Scholar]

34. Cui, L. Z., Chen, Z. T., Yang, S., Ming, Z. X., Li, Q. et al. (2020). A blockchain-based containerized edge computing platform for the Internet of Vehicles. IEEE Internet of Things Journal, 8(4), 2395–2408. [Google Scholar]

35. Gao, L., Wu, C., Du, Z., Yoshinaga, T., Zhong, L. et al. (2022). Toward efficient blockchain for the Internet of Vehicles with hierarchical blockchain resource scheduling. Electronics, 11(5), 832. [Google Scholar]

36. Aghapour, Z., Sharifian, S., Taheri, H. (2023). Task offloading and resource allocation algorithm based on deep reinforcement learning for distributed AI execution tasks in IoT edge computing environments. Computer Networks, 223(24), 213–223. [Google Scholar]

37. Xiao, J., Gao, Q., Wang, H. (2023). Multi-round auction-based resource allocation for edge computing: Maximizing social welfare. Future Generation Computer Systems, 223(39), 365–375. [Google Scholar]

38. Xia, C., Chen, H., Chen, L. (2018). ETRA: Efficient three-stage resource allocation auction for mobile blockchain in edge computing. IEEE International Conference on Parallel and Distributed Systems, China. [Google Scholar]

39. Toulouse, M., Dai, H. K., Le, T. G. (2022). Distributed load-balancing for account-based sharded blockchains. International Journal of Web Information Systems, 18(2), 100–116. [Google Scholar]

40. Jiao, Y., Wang, P., Niyato, D., Suankaewmanee, K. (2019). Auction mechanisms in cloud/fog computing resource allocation for public blockchain networks. IEEE Transactions on Parallel and Distributed Systems, 30(9), 1975–1989. [Google Scholar]

41. Alfakeeh, A. S., Javed, M. A. (2022). Efficient resource allocation in blockchain assisted health care systems. Applied Sciences, 13(17), 9625. [Google Scholar]

42. Chang, Z., Guo, W. L., Guo, X. J., Zhou, Z. Y., Ristaniemi, T. (2020). Incentive mechanism for edge-computing-based blockchain. IEEE Transactions on Industrial Informatics, 16(11), 7105–7114. [Google Scholar]

43. Fan, Y. Q., Jin, Z. F., Shen, G. M., Hu, D. H., Shi, L. et al. (2021). Three-stage stackelberg game based edge computing resource management for mobile blockchain. Peer-to-Peer Networking and Applications, 14, 1431–1445. [Google Scholar]

44. Zhou, Y., Yu, L., Maharjan, S. (2023). An improved spectrum trading design based on dynamic credit aggregate signature blockchain. IEEE Wireless Communications Letters, 12(4), 625–629. [Google Scholar]

45. Baranwal, G., Kumar, D., Vidyarthi, D. (2022). BARA: A blockchain-aided auction-based resource allocation in edge computing enabled Industrial Internet of Things. Future Generation Computer Systems, 135(39), 333–347. [Google Scholar]

46. Feng, J., Yu, F., Pei, Q. (2020). Joint optimization of radio and computational resources allocation in blockchain-enabled mobile edge computing systems. IEEE Transactions on Wireless Communications, 19(6), 4321–4334. [Google Scholar]

47. Li, P., Wang, Z. X., Wang, N., Yang, W. H., Li, M. Z. et al. (2021). Stochastic robust optimal operation of community integrated energy system based on integrated demand response. International Journal of Electrical Power and Energy Systems, 128(14), 106735. [Google Scholar]

48. Yan, S., Hanly, S. I. B. (2021). Optimal transmit power and flying location for UAV covert wireless communications. IEEE Journal on Selected Areas in Communications, 39(11), 3321–3333. [Google Scholar]

49. Zuo, Y. P., Jin, S., Zhang, S. L. (2021). Computation offloading in untrusted MEC-aided mobile blockchain IoT systems. IEEE Transactions on Wireless Communications, 20(12), 8333–8347. [Google Scholar]

## Cite This Article

**APA Style**

*Computer Modeling in Engineering & Sciences*,

*140*

*(1)*, 863-885. https://doi.org/10.32604/cmes.2024.047295

**Vancouver Style**

**IEEE Style**

*Comput. Model. Eng. Sci.*, vol. 140, no. 1, pp. 863-885. 2024. https://doi.org/10.32604/cmes.2024.047295

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.