Source-linked AI summary
Social Welfare Maximization Auction in Edge Computing Resource Allocation for Mobile Blockchain
Yutao Jiao, Ping Wang, Dusit Niyato, Zehui Xiong
TL;DR
Mobile proof-of-work mining is difficult on handheld devices because it requires substantial computing power and energy. The paper proposes an edge-computing auction that models competition and network effects while maximizing social welfare; theory and simulations support its stated mechanism properties and optimization objective.
Problem
Proof-of-work mining requires computing power and energy that mobile devices cannot satisfy, restricting blockchain applications in mobile environments.
Method
The paper proposes an auction-based edge-computing resource market that maximizes social welfare while accounting for miner competition and blockchain network effects.
Results
The auction is globally optimal for social welfare and is truthful, individually rational, and computationally efficient.
Takeaways & Limitations
The proposed edge-computing resource market solves the social welfare maximization problem for the edge computing service provider.
Abstract
from arXiv · showhide
Blockchain, an emerging decentralized security system, has been applied in many applications, such as bitcoin, smart grid, and Internet-of-Things. However, running the mining process may cost too much energy consumption and computing resource usage on handheld devices, which restricts the use of blockchain in mobile environments. In this paper, we consider deploying edge computing service to support the mobile blockchain. We propose an auction-based edge computing resource market of the edge computing service provider. Since there is competition among miners, the allocative externalities (positive and negative) are taken into account in the model. In our auction mechanism, we maximize the social welfare while guaranteeing the truthfulness, individual rationality and computational efficiency. Based on blockchain mining experiment results, we define a hash power function that characterizes the probability of successfully mining a block. Through extensive simulations, we evaluate the performance of our auction mechanism which shows that our edge computing resources market model can efficiently solve the social welfare maximization problem for the edge computing service provider.
I. INTRODUCTION
The paper addresses the difficulty of running proof-of-work mining on mobile devices by introducing an edge-computing resource market. Its auction model connects mobile users, miners, and the edge service provider to support mobile blockchain applications.
- Mobile blockchain adoption is constrained because proof-of-work mining requires computing power and energy unavailable to many mobile devices.
- The auction accounts for miner competition and blockchain network effects through allocative externalities.
- The paper evaluates mobile blockchain mining experimentally and analyzes the probability of successfully mining a block.
- The paper develops a social-welfare-maximizing auction mechanism for edge-computing resource allocation.
- The proposed market lets mobile users buy edge-computing resources from an edge computing service provider and use them as miners.
B. Edge Computing Resources Trading
The trading model describes an ESP auction in which mobile users seek resources to become miners. After receiving demands and bids, the ESP allocates resources, determines prices, and grants service to winners.
- The scenario contains one ESP, one blockchain owner, and a community of mobile users who want to become miners.
- Mobile users offload proof-of-work tasks to nearby edge servers because their devices have limited computing capacity.
- The ESP announces its service, receives user demands and bids, selects winners, and determines resource allocations and service prices.
- An allocation x_i of 1 indicates that user i wins and receives the resources demanded, while x_i = 0 indicates no allocation.
- Winners pay the ESP and access its edge-computing service, while users receiving no resources pay zero.
C. Blockchain Mining with Edge Computing Service
The mining model combines relative hash power, Poisson block generation, and propagation delay to characterize each miner’s chance of receiving the blockchain reward. Larger transaction blocks require more propagation time and face greater orphaning risk.
- Miner i’s relative hash power is calculated from its demand and allocation compared with the allocated resources of all miners.
- The hash-power function is a fraction function whose curve-fitting parameter α was verified through a real-world experiment.
- New blocks arrive according to a Poisson process with network-wide rate 1/λ, while miners compete to solve proof-of-work first.
- A miner’s probability of mining a new block equals its hash power γ_i, but receiving the reward also requires immediate propagation and consensus.
- Propagation time is modeled as τ_i = ξs_i, so larger transaction blocks require more time and have a higher chance of becoming orphaned.
D. Blockchain Management
The blockchain owner controls mining incentives and difficulty while modeling the value of participation as a positive network effect. This effect increases with allocated computing resources but eventually saturates.
- The blockchain owner sets the fixed mining bonus T and transaction fee rate r in the mining protocol.
- The owner adjusts mining difficulty to maintain the average block-generation time λ at a reasonable constant value.
- More mining power creates a positive network effect because a more stable and secure blockchain increases the value of miner rewards.
- The network-effect utility grows slowly, then accelerates, then decelerates and converges asymptotically to 1 as allocated resources increase.
IV. SOCIAL WELFARE MAXIMIZATION AUCTION FOR EDGE COMPUTING SERVICE
The paper proposes an auction mechanism for allocating edge computing resources efficiently while pursuing social welfare maximization and guaranteeing truthfulness, individual rationality, and computational efficiency.
- The mechanism allocates edge computing resources through an auction designed for the ESP.
- Its objective is to maximize social welfare.
- The design guarantees truthfulness, individual rationality, and computational efficiency.
A. Valuation of mobile users
Mobile users bid according to expected mining rewards, while their realized valuations account for network effects; the paper defines both ex-ante and ex-post valuation expressions.
- A mobile user’s bid represents its valuation and is based on the expected reward R_i.The expected reward is called the ex-ante valuation.
- The blockchain owner specifies protocol values T, r, and λ but does not control miners’ data storage or mining strategies.
- After the auction, user i has an ex-post valuation for edge computing service that considers network effects.
- The network effect is denoted by w and is used in the ex-post valuation definition.
- The paper derives specific ex-ante and ex-post valuation expressions by substituting the earlier reward and network-effect definitions.
B. Auction Maximizing Social Welfare
The auction selects resource-allocation winners to maximize social welfare, defined from users’ ex-post valuations minus ESP cost, while using a truthful and efficient mechanism design.
- The ESP selects winners and payments from bids to maximize social welfare, with total cost C(d_N) = cd_N.
- Social welfare equals the sum of users’ ex-post valuations minus the ESP’s total cost, subject to resource capacity D.
- The simpler fixed-resource case sets d_i = 1 for every user and formulates winner selection over competing bids.
- Truthfulness is characterized by monotonic winner selection and critical payments.
- Algorithm 1 uses greedy winner selection, adding users while social welfare does not decrease and resource limits are respected.
- Algorithm 1’s allocation is globally optimal for the stated social welfare maximization problem.
- The auction is truthful because its payment calculation uses VCG and its winner selection satisfies monotonicity.
- The auction is computationally efficient and individually rational, with overall time complexity O(N^3).
V. EXPERIMENT RESULTS AND PERFORMANCE ANALYSIS
The paper evaluates the proposed auction through simulations and uses the results to derive decision-making strategies for the ESP and blockchain owner.
- The proposed auction is evaluated using simulation results.
- The simulations support useful decision-making strategies for the ESP and blockchain owner.
A. Verification for Hash Power Function
The paper uses a real-world mobile blockchain mining experiment to estimate the hash power function γ(d), which characterizes mining capability as service demand varies.
- A mobile blockchain client was implemented on three Android devices, with each miner using one CPU core under Go-Ethereum.CPU utilization was managed and measured through Docker.
- The experiment varied one miner’s service demand while fixing the others to verify hash power function (1).
- Figure 2 estimates the hash power function γ(d) used to represent mining performance.
B. Simulation Results
Simulations examine how mobile-user population, mining bonus, transaction fees, and mining time affect social welfare and the number of winners. The results show gains that are moderated by miner competition and changing valuation.
- Simulation settings: The simulations vary N from 100 to 1000, T from 0 to 5, r from 0.001 to 0.009, and λ from 100 to 1800.Each measurement is averaged over 100 instances.
- Impact of the number of mobile users N: As the number of mobile users N increases, social welfare S and the number of winners |W| increase at a diminishing rate.The experiment fixes T = 2.5, r = 0.007, and λ = 600.
- Impact of the number of mobile users N: Competition among more miners slows the growth of both social welfare and the number of winners.
- Impact of the fixed bonus T and transaction fee rate r: Raising the fixed bonus T or transaction fee rate r generates nearly proportional increases in social welfare.The number of winners increases and tends to stabilize as either parameter rises.
- Impact of the average time λ: When the average mining time λ increases, social welfare rises while the number of winners first increases and then declines.The expected reward R grows with increasing λ.
VI. CONCLUSIONS
The paper proposes an auction-based edge-computing market for mobile blockchain and evaluates it as a social-welfare maximization mechanism with formal incentive and efficiency guarantees.
- The proposed auction-based market allocates computing resources for mobile blockchain while maximizing social welfare.
- The auction model accounts for allocative externalities from miner competition and network effects in the blockchain network.
- Theoretical analysis and simulation show that the mechanism is truthful, individually rational, computationally efficient, and solves the social welfare maximization problem.
- Future work will consider variable demands and corresponding bids from mobile users.