A Dynamic Resource Allocation Framework for Synchronizing Metaverse with IoT Service and Data

I. Introduction

• Continuous synchronization requires fresh physical-world data to keep digital twins updated in real time.The paper illustrates this with virtual driver training that uses real road, driver, traffic, and weather data.Source: §I · p. 1
• The framework allocates IoT devices to VSP data-collection tasks so virtual services can synchronize with the physical world.The platform engages devices near a VSP’s target region; the paper’s illustrative system uses UAVs.Source: §I · pp. 1–2, Figure 1 · p. 2
• Self-interested device owners choose among VSP tasks, and the paper proposes evolutionary game dynamics for gradual adaptation toward equilibrium.The approach addresses settings where owners are numerous and full equilibrium knowledge is hard to achieve.Source: §I · p. 2
• The sensing model and reward-allocation scheme are designed to extend to specific tasks supporting synchronization between the Metaverse and the real world.The paper motivates synchronization with digital twins that can support monitoring and testing interventions without affecting physical-world operations.Source: §I · pp. 1–2

A. Metaverse General Architecture

• The proposed architecture has infrastructure, interface, cross-world ecosystem, and in-world ecosystem components.Infrastructure supports operations across both worlds; the interface and cross-world ecosystem provide different forms of connection between them.Source: A. Metaverse General Architecture · p. 2
• This paper focuses on IoT-device resource allocation for virtual-service synchronization in the cross-world ecosystem.The architecture distinguishes this from in-world business and economics, such as NFT trading, which does not require frequent data traversal between worlds.Source: A. Metaverse General Architecture · p. 2

B. Related Works

• Prior Metaverse work largely surveyed technologies, architectures, and challenges or studied human-machine interaction, while IoT-assisted synchronization resource allocation had received little attention.The authors position their work in the cross-world component rather than the interface component.Source: C. Research Gap: Resource Allocation… · p. 2, B. Related Works · p. 2

III. System Model and Problem Formulation

• VSPs request data collection for target regions, and the Metaverse platform employs nearby IoT devices to collect data for their virtual services.A VSP or the platform designs a route covering the target region, which can be segmented across devices.Source: §III · pp. 2–3
• The model assumes sensing points are allocated uniformly among selected UAVs and that tasks last relatively long, with repeated data collection.Each UAV travels from its base to a collection point and back; traversal distance is approximated by the distance from its base to the region center.Source: §III · p. 3
• Independent device owners choose among VSP tasks and can improve decisions over multiple rounds by observing payoffs earned by nearby devices.The model groups nearby devices with similar types into populations whose members are treated as anonymous equals.Source: §III · p. 3
• The model combines pairwise and centralized payoff communication in hybrid evolutionary dynamics to find an evolutionary stable strategy.Centralized checks are costly and prone to delay but provide complete payoff information; pairwise communication is fast and cheap but limited.Source: §III · p. 3

A. Population Formulation

• Nearby UAVs with similar sensing capacity, traversal costs, and communication frequency are treated as one population.Devices within a population are regarded as anonymous and similar.Source: A. Population Formulation · p. 3
• Each population’s pure strategies are its available VSP sync tasks, and S denotes the total number of pure strategies across populations.Source: A. Population Formulation · p. 3
• For population p, x_p^m is the percentage choosing region m; the population state is its vector of strategy shares.Source: A. Population Formulation · p. 3
• A social state represents the joint behaviors of all populations, and the society is the set of N UAV owners.Population sizes sum to N.Source: A. Population Formulation · p. 3

B. UAV Sensing Model

• A region’s sensing route is evenly divided among UAVs selecting it, determining each UAV’s segmented sensing distance.The route-sharing map yields the sensing-route length for a UAV in population p.Source: B. UAV Sensing Model · pp. 3–4
• The energy model focuses on propulsion and hover costs, ignoring acceleration and deceleration and assuming constant propulsion power at fixed flying speed.The model distinguishes average traversal speed from sensing or hovering speed.Source: B. UAV Sensing Model · p. 4

C. UAV Utility Model

• A VSP’s reward is evenly allocated to UAVs working in the region, adjusted by a sensor-data-quality weighting factor.The passage associates higher sampling rates with higher-quality sensor data.Source: C. UAV Utility Model · p. 4
• The model defines a utility for each population-p UAV choosing VSP m and treats ζp as the cost per Joule of energy.Source: C. UAV Utility Model · p. 4

IV. Heterogeneous Evolutionary Game

• The population game specifies players, populations, strategies, and a continuous payoff map assigning each social state strategy payoffs.The payoff map is also subject to stronger regularity requirements such as Lipschitz continuity or continuous differentiability.Source: §IV · p. 4
• A revision protocol specifies conditional switch rates between strategies given a population’s payoff vector and state.Source: §IV · p. 4
• Owners receive stochastic, Poisson-distributed opportunities to revise their strategies.Source: §IV · p. 4
• Mean dynamics track changes in strategy shares through switches into a strategy from others and out of it to other strategies.Source: §IV · p. 4
• Imitative replicator dynamics requires payoff information from one random opponent, whereas direct Smith dynamics requires payoff information for all S_p strategies.Source: §IV · p. 4

1) Imitative Protocols and Dynamics [23]:

• The chance of meeting an opponent playing strategy i is represented by x_i.Source: 1) Imitative Protocols and Dynamics [23] · p. 4
• Pairwise Proportional Imitation switches toward an opponent’s strategy only when that opponent’s payoff is higher, with probability proportional to the payoff difference.The conditional switch rate is denoted ρp,m,i(πp, x).Source: 1) Imitative Protocols and Dynamics [23] · p. 4
• The mean dynamics using this revision protocol are identified as replicator dynamics, and πp_m denotes population p’s average payoff at state x.Source: 1) Imitative Protocols and Dynamics [23] · pp. 4–5
• In the pairwise-comparison scheme, owners can obtain the population’s payoff information centrally, and switching depends on excess payoffs between strategies.The text gives requesting payoff information from the base station or checking the Metaverse bulletin board as examples.Source: 2) Direct Protocol and Dynamics [18] · p. 5

2) Direct Protocol and Dynamics [18]:

• Smith dynamics lets an owner choose a higher-payoff alternative with probability proportional to the payoff difference.Source: 2) Direct Protocol and Dynamics [18] · p. 5
• A hybrid revision protocol assigns each population p a probability αp,k of using protocol k and combines the protocols’ conditional switch rates.The protocol probabilities sum to one, and the mean dynamics are linear in the conditional switch rates.Source: 3) Hybrid Protocol for Heterogeneous… · p. 5
• By default, the hybrid combines Smith dynamics with probability αp,1 and replicator dynamics with probability 1 − αp,1.Smith corresponds to centralized payoff information; replicator corresponds to observing one opponent’s payoff.Source: 3) Hybrid Protocol for Heterogeneous… · p. 5

b) Stability of the Equilibrium Strategies

• Fig. 4(b) reports mixed equilibrium (0.1, 0.19) and another equilibrium (0.38, 0.62) where strategy 3 is extinct.Source: §V · p. 5
• Fig. 4(c) reports equilibrium states, including one where strategy 3 is extinct, as population 2 states vary.Source: §V · p. 5

a) Existence of the Equilibrium Strategies

• Fig. 3 shows stationary strategy distributions at equilibrium, where the payoffs for selecting any VSP are equal.Population 3 receives a higher average payoff, attributed to its higher data quality.Source: §V · p. 5, Figure 3 · p. 6

c) Impact of Smith Protocol on the Convergence Time

• Convergence time decreases as α3,1 increases from 0 to 1; the experiment defines convergence using threshold τ = 0.05.Fig. 5 varies α3,1 in increments of 0.1 while fixing the Smith-protocol adoption probabilities in populations 1 and 2.Source: §V · pp. 5–6, Figure 5 · p. 6

b) Stability of the Equilibrium Strategies

• Fig. 4's direction field traces population states along arrows toward equilibrium states in the reduced visualization.Population 3 is removed from the default setting and the probability of selecting region 3 is fixed.Source: §V · p. 5, Figure 4 · p. 6

• The studied problem has UAV populations autonomously selecting VSPs for an IoT-assisted Metaverse synchronization task.Source: §VI · p. 6
• Hybrid evolutionary dynamics are proposed for a heterogeneous multi-population game with potentially different in-population communication protocols.Source: §VI · p. 6
• Experiments demonstrate the existence and stability of equilibrium strategies; future work will incorporate spatial correlation of sensing data into utility models.Source: §VI · p. 6