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Computing Resource Allocation in Three-Tier IoT Fog Networks: a Joint Optimization Approach Combining Stackelberg Game and Matching
Huaqing Zhang, Yong Xiao, Shengrong Bu, Dusit Niyato, Richard Yu, Zhu Han
TL;DR
The paper addresses limited resource allocation in multi-FN, multi-DSO, and multi-DSS IoT fog networks, where remote data centers can impose high transmission cost and latency. It combines Stackelberg games for pricing and resource purchasing with two many-to-many matching stages, and simulations report higher utility with fog nodes than without them.
Problem
Limited computing-resource allocation among fog nodes, DSOs, and DSSs remains an open problem when DSSs can select operators and corresponding fog nodes.
Method
The framework uses Stackelberg games for DSO pricing and DSS resource purchasing, followed by many-to-many matching for DSO-FN and FN-DSS pairing.
Results
Simulation results show higher DSS utility with fog nodes than with massive data centers alone, while utilities increase with additional DSSs or FNs in reported settings.
Takeaways & Limitations
The framework produces equilibrium or stable outcomes at each stage and achieves high reported performance for FNs, DSOs, and DSSs compared with services without fog nodes.
Abstract
from arXiv · showhide
Fog computing is a promising architecture to provide economic and low latency data services for future Internet of things (IoT)-based network systems. It relies on a set of low-power fog nodes that are close to the end users to offload the services originally targeting at cloud data centers. In this paper, we consider a specific fog computing network consisting of a set of data service operators (DSOs) each of which controls a set of fog nodes to provide the required data service to a set of data service subscribers (DSSs). How to allocate the limited computing resources of fog nodes (FNs) to all the DSSs to achieve an optimal and stable performance is an important problem. In this paper, we propose a joint optimization framework for all FNs, DSOs and DSSs to achieve the optimal resource allocation schemes in a distributed fashion. In the framework, we first formulate a Stackelberg game to analyze the pricing problem for the DSOs as well as the resource allocation problem for the DSSs. Under the scenarios that the DSOs can know the expected amount of resource purchased by the DSSs, a many-to-many matching game is applied to investigate the pairing problem between DSOs and FNs. Finally, within the same DSO, we apply another layer of many-to-many matching between each of the paired FNs and serving DSSs to solve the FN-DSS pairing problem. Simulation results show that our proposed framework can significantly improve the performance of the IoT-based network systems.
I. INTRODUCTION
The paper motivates fog computing as a lower-latency alternative to remote clouds and frames limited fog-node resource allocation among DSOs, DSSs, and FNs as an open problem. It introduces a joint framework combining Stackelberg pricing and resource purchasing with matching-based pairing.
- Motivation: Remote clouds incur high transmission cost and service latency, motivating fog nodes deployed closer to DSSs for low-latency services.Fog nodes are described as small-scale, lower-cost, and mobility-supporting devices near the network edge.
- Research problem: Limited computing-resource allocation among fog nodes, DSOs, and DSSs remains an open problem when DSSs can choose both operators and corresponding fog nodes.The paper focuses on resource selection and allocation in a multi-DSO, multi-FN setting.
- Approach: The proposed framework combines Stackelberg pricing and DSS resource purchasing with matching-based DSO-FN and FN-DSS pairing.The architecture coordinates virtualized services from DSOs with physical CRBs supplied by FNs.
- System model: Each DSS subscribes to at most one DSO and must purchase enough CRBs to keep service delay within its acceptable threshold.The model uses qth_j as the lower bound of CRBs required to satisfy the delay boundary.
- Utility model: DSO utility accounts for payments from DSSs, payments to physical-CRB providers, and additional energy cost when services remain on massive data centers.FNs charge prices determined by their costs and current traffic, while FN utility includes payment from DSOs minus transmission cost.
III. PROBLEM FORMULATION
The formulation models sequential decisions among DSOs, DSSs, and FNs under resource, demand, and delay constraints. It separates DSS purchasing, DSO pricing, DSO-FN pairing, and FN-DSS pairing problems.
- Decision process: DSOs predict aggregate DSS demand and set service prices first, after which DSSs choose CRB purchases to maximize utility.The sequential process reflects the Stackelberg relationship between operators and subscribers.
- Constraints: Resource allocations are bounded by each FN’s available CRBs and each DSO’s or DSS’s demand limits.The formulation imposes upper bounds on total distributed and purchased CRBs.
- DSS resource purchasing: DSS purchasing balances delay tolerance and DSO prices because higher delay tolerance can reduce the CRBs needed for satisfactory service.The formulation requires purchased CRBs to satisfy service-delay requirements.
- DSO pricing: DSO pricing seeks profitable service prices while accounting for DSS reactions and the rent announced by fog nodes.Prices that are too high can reduce DSS demand, so DSOs must anticipate purchasing behavior.
- DSO-FN pairing: The DSO-FN pairing problem allocates accessible fog nodes among competing DSOs using preferences and low-latency service considerations.FNs are accessible to DSOs rather than directly to DSSs in the multi-DSO setting.
IV. SYSTEM ANALYSIS
The analysis solves the interactions in stages: first DSOs and DSSs determine service quantities, then FNs and DSOs pair according to preferences, and finally paired FNs and DSSs are matched within each DSO.
- DSO-DSS interaction: The framework first analyzes DSO-DSS interactions to determine how many CRBs DSSs require during service.This stage addresses the resource-purchasing behavior induced by DSO pricing.
- FN-DSO interaction: Given optimized DSO and DSS behavior, the framework analyzes FN-DSO interactions using different participant preferences.This stage determines which fog nodes are paired with operators.
- FN-DSS interaction: The final stage matches FNs and DSSs within the same DSO to improve service outcomes.The matching follows the previously obtained operator-node pairings.
A. The Interaction between DSOs and DSSs
The DSO–DSS interaction is modeled as a Stackelberg game: DSOs set service prices, and DSSs respond by selecting CRB purchases that maximize their utility. The resulting optimization characterizes DSS purchasing and DSO pricing decisions.
- DSOs act as leaders by announcing service prices, while DSSs act as followers that determine their optimal CRB purchases.
- Lemma 1 states that each DSS’s optimal CRB purchase is determined after observing the DSO’s announced service price.
- The DSS utility is optimized by exploiting its quasi-concavity with respect to the purchased CRBs.
- The optimal CRB amount is obtained by setting the first derivative of the DSS utility to zero.
- Considering DSS reactions, the DSO’s optimization is adjusted to determine its service price, including the maximum optimal price characterized in the model.
- Because service delay cannot exceed its threshold, the purchased CRBs have a lower bound, and the DSS utility increases monotonically with the purchase amount.
B. The Interaction between FNs and DSOs
The DSO–FN pairing problem is solved through many-to-many matching based on preference lists over service prices and resource allocations. The iterative proposal process converges to a stable matching.
- The framework constructs preference lists for DSOs over FNs and for FNs over DSOs before performing many-to-many matching.
- FNs iteratively propose available CRBs to DSOs, which retain their most preferred offers until their required CRB amounts are met.
- Rejected CRBs can trigger a flag and cause the FN’s pointer to remain or advance according to the matching round.
- The matching repeats until all FN preference-list pointers have been exhausted.
- An FN’s pointer moves only forward, so after rejection by a DSO it cannot improve utility by returning to that DSO.
- Lemma 3 concludes that the DSO–FN pairing algorithm converges and achieves a stable matching result.
C. The Interaction between FNs and DSSs
After FNs rent CRBs to DSOs, a second many-to-many matching layer allocates those resources between FNs and DSSs within each DSO. Preferences reflect FN rent, transmission distance, and utility.
- The remaining problem is to allocate FNs’ rented CRBs among DSSs within each DSO.
- DSS preference lists over neighboring FNs are based on the rent charged by the FNs.
- FN preferences over DSSs account for the distance between each FN and its serving DSS because longer distances increase data-transmission costs.
- The framework applies many-to-many matching between FNs and DSSs within each DSO using the two sides’ preference lists.
- DSSs propose to FNs, which reject less-preferred DSSs when requests exceed available CRBs; rejected DSS pointers then advance to the next FN.
V. SIMULATION RESULTS AND DISCUSSIONS
Simulations evaluate the proposed framework under a configured IoT fog scenario and examine utilities as network size, workload, and system parameters vary. Results show distinct utility trends for FNs, DSSs, and DSOs under these conditions.
- Simulation setup: The MATLAB simulation uses 120 DSSs, 4 DSOs, and 20 randomly placed FNs in a 10-kilometer-diameter district.It also sets a 0.1 (ms)−1 service rate per CRB, average DSS workload of 0.5 (ms)−1, 50km/ms transmission speed, and 60 ms delay tolerance.
- FN utility versus DSS population: As DSS numbers increase, FN utility generally rises, then its growth slows to zero when nearby FN CRBs are exhausted.Additional FNs allow convergence to a higher utility bound, although competition makes gains smaller when the DSS population is small.
- DSS utility: With more DSSs, DSS utility generally increases and exceeds the utility achieved when services rely only on massive data centers.At fixed DSS numbers, increasing average workload also increases DSS utility because subscribers receive more service revenue.
- FN utility versus workload: As average workload λ increases, FN utility first rises and then converges to a fixed value; more FNs produce a higher converged value.The convergence occurs after all available FN CRBs are allocated to DSSs.
- DSO utility: As µ increases, DSO utility rises because DSSs require fewer CRBs, allowing higher prices; serving more DSSs further increases total DSO utility.The reported relationship is evaluated for the utility of all DSOs against µ.
- Utility versus delay tolerance: As delay tolerance tth increases, FN utility generally decreases, DSO utility generally increases, and DSS utility generally decreases.The paper attributes these trends to lower CRB demand, higher DSO prices, and greater DSS delay burden at higher tth.
VI. RELATED WORKS
Related work covers fog and edge architectures for bringing cloud capabilities closer to users, IoT-oriented resource management, and game-theoretic network optimization.
- Fog and edge computing: Fog-related studies examine mist computing, edge-cloud deployment, and fog architectures for distributing cloud benefits closer to network users.These works address cloud proximity, edge deployment, and fog-computing features.
- Fog computing for IoT: IoT-focused research investigates fog opportunities and challenges, resource estimation for QoS, and utility-based pairing between fog nodes and IoT devices.The cited approaches connect resource estimation and pairing mechanisms to fog-enabled IoT service management.
- Game-theoretic optimization: Game-theoretic studies use Stackelberg models for distributed resource allocation, including bandwidth allocation, smart-city data forwarding, and cloud data-center power allocation.These examples apply Stackelberg games to interactions among infrastructure and service participants.
VII. CONCLUSIONS
The paper proposes a joint optimization framework for multi-FN, multi-DSO, and multi-DSS IoT fog networks. It combines Stackelberg games with two many-to-many matching stages, yielding equilibrium or stable outcomes and improved performance over services without fog nodes.
- VII. CONCLUSIONS: The framework jointly optimizes resource allocation in multi-FN, multi-DSO, and multi-DSS IoT fog networks.It addresses the three-participant fog-network setting considered in the paper.
- VII. CONCLUSIONS: Stackelberg games solve DSO pricing and DSS resource purchasing, followed by many-to-many matching for DSO-FN and FN-DSS pairings.The second matching stage operates between paired fog nodes and serving DSSs within the same DSO.
- VII. CONCLUSIONS: Each stage reaches equilibrium or stable results where participants cannot unilaterally change behavior for higher utility.The conclusion describes stability across the sequential optimization stages.
- VII. CONCLUSIONS: Simulation results report optimal utilities for FNs, DSOs, and DCOs, with higher performance than data services without fog nodes.The comparison is made against services operating without fog nodes.