Source-linked AI summary
Price-Based Distributed Offloading for Mobile-Edge Computing with Computation Capacity Constraints
Mengyu Liu, Yuan Liu
TL;DR
IoT devices face intensive computation demands despite limited resources, motivating MEC’s low-latency edge execution. The paper models finite edge capacity with a Stackelberg pricing game and proposes distributed uniform and differentiated pricing. Simulations report better latency and revenue as capacity increases, with differentiated pricing outperforming uniform pricing at a complexity trade-off.
Problem
Prior MEC offloading work largely assumed infinite edge-cloud computation capacity, although practical edge servers have finite capacity under intensive workloads.
Method
The paper models finite edge computation as a divisible resource and uses a Stackelberg game with uniform and differentiated pricing to coordinate distributed offloading.
Results
Differentiated pricing has better latency and revenue performance than uniform pricing in simulations, while increasing computation capacity improves both measures.
Takeaways & Limitations
Pricing provides a distributed way to manage users’ access to finite MEC computation resources, with differentiated allocation offering greater accuracy at higher complexity.
Abstract
from arXiv · showhide
Mobile-edge computing (MEC) is a promising technology to enable real-time information transmission and computing by offloading computation tasks from wireless devices to network edge.
I. INTRODUCTION
MEC addresses IoT devices’ computation and latency constraints by moving intensive tasks to the network edge. This paper focuses on finite edge-cloud capacity and proposes pricing-based distributed offloading through a Stackelberg game.
- Motivation: IoT devices have limited physical size and battery capacity, yet must support intensive computation for real-time information processing.
- Motivation: MEC moves intensive computation from IoT devices to a physically proximal edge, providing low-latency and flexible computing and communication services.
- Research Gap: Prior game-theoretic MEC mechanisms generally assumed infinite edge-cloud computation capacity, although practical edge servers have finite capacity under intensive workloads.
- Approach: The paper models finite edge-cloud computation as a divisible resource sold among users through a Stackelberg game.
- Contributions: It proposes optimal uniform and differentiated pricing algorithms that users can implement in a distributed manner.
A. System Model
The system supports partial offloading in a multiuser MEC network, where local and edge execution times, transmission, and finite cloud computation capacity determine task completion.
- System Model: The system contains K single-antenna users and one base station integrated with a MEC server, with each user’s data divisible between local computing and offloading.
- Local and Edge Computing: User k offloads ℓ_k bits from total input R_k, while R_k − ℓ_k bits are processed by its local CPU.
- Timing Model: Offloading time comprises uplink transmission, cloud execution, and downlink feedback, with cloud execution time t_c,k = ℓ_kC_k/f_c,k.
- Timing Model: Local computing and offloading run concurrently, so total execution time is t_k = max{t_loc,k, t_off,k}.
- Capacity Constraint: The model allocates equal cloud computation speed f_c,k = f_C/K to users and imposes an upper bound on CPU cycles used for total offloaded data.
B. Stackelberg Game Formulation
The Stackelberg formulation treats the edge cloud as a pricing leader and users as followers who independently choose offloading quantities to minimize latency plus payment.
- Game Structure: The edge cloud prices users’ offloaded CPU cycles, then users divide their input data between local computing and offloading according to announced prices.
- Leader Problem: The cloud maximizes revenue from selling finite computation resources, with user offloading decisions depending on the assigned prices.
- Follower Problem: Each user minimizes a cost defined as latency plus payment by choosing its offloaded data size subject to 0 ≤ ℓ_k ≤ R_k.
- Game Coupling: The pricing and offloading problems are coupled because prices influence offloaded data sizes, which in turn affect cloud revenue.
III. OPTIMAL ALGORITHM
The algorithm section solves users’ offloading decisions by backward induction: users respond to prices, and the edge cloud then selects an optimal pricing strategy.
- Backward Induction: Each user independently determines its optimal offloading strategy for a given price.
- Backward Induction: After observing users’ optimal responses, the edge cloud solves for its optimal price.
- Pricing Strategies: The paper investigates uniform pricing and differentiated pricing as two optimal pricing strategies.
A. Uniform Pricing
Uniform pricing lets the edge cloud broadcast one price while users independently choose offloading amounts. The optimal price is selected from threshold candidates, yielding an O(log K) distributed search under the finite-capacity constraint.
- A. Uniform Pricing: Uniform pricing broadcasts one common CPU-cycle price to all users, after which each user independently optimizes its offloaded data size.The cloud uses users’ CPU frequencies and cycle requirements, while users report their decisions for price updates.
- A. Uniform Pricing: The optimal offloading policy is threshold-based: users offload all eligible bits when Fk ≤ 1/µ and otherwise compute locally.The threshold is 1/µ, so users with smaller computational speed are the ones who prefer offloading.
- A. Uniform Pricing: The cloud searches candidate prices in decreasing order and stops when the computation-capacity constraint becomes active.Because total offloaded CPU cycles decrease with price, remaining candidates need not be bargained after the constraint is active.
- A. Uniform Pricing: Algorithm 1 finds the optimal uniform price with total complexity O(log K) using limited network information and iterative price–decision exchanges.The cloud broadcasts prices, and users return their independently selected offloading decisions.
B. Differentiated Pricing
Differentiated pricing assigns user-specific prices and reduces the cloud’s optimization to a binary knapsack problem. It remains distributed but requires more information and higher complexity than uniform pricing.
- B. Differentiated Pricing: Differentiated pricing lets the edge cloud charge different users different CPU-cycle prices while retaining the threshold-based user decision structure.For each user, the uniform-price solution applies with µ replaced by the individual price µk.
- B. Differentiated Pricing: Each participating user receives optimal price µk = 1/Fk, while a nonparticipating user is assigned an infinite price and earns no revenue.The price is chosen at the largest value consistent with the user’s offloading decision.
- B. Differentiated Pricing: The resulting optimization is a binary knapsack problem with weight mkCk and value mkCk/Fk for user k.Dynamic programming solves this formulation in pseudopolynomial time.
- B. Differentiated Pricing: Differentiated pricing requires each user to report mk, Ck, and Fk, eliminating iteration between the cloud and users.Users then determine their strategies from the resulting prices.
- B. Differentiated Pricing: Compared with uniform pricing, the differentiated scheme is distributed but needs more information and higher complexity.The tradeoff follows from solving the binary allocation problem rather than using the lower-complexity uniform-price search.
IV. NUMERICAL RESULTS
Simulations compare uniform pricing, differentiated pricing, and local-only computing across computation capacities and user populations. Differentiated pricing performs best in latency and revenue, while increasing users raises latency and revenue.
- IV. NUMERICAL RESULTS: The simulation uses B = 1 MHz, N0 = −174 dBm/Hz, Fk from 0.1 to 1 GHz, Ck ∈[500, 1500] cycles/bit, and Rk ∈[100, 500] KB.Average latency and revenue are the evaluation metrics.
- IV. NUMERICAL RESULTS: Differentiated pricing has better average latency and revenue performance than uniform pricing and local-only computing.The results attribute this to more accurate resource allocation, while also identifying a performance–complexity tradeoff.
- IV. NUMERICAL RESULTS: As computation capacity increases, both latency and revenue improve for the pricing schemes, whereas local-only computing has the worst latency and is capacity-independent.The local-only baseline does not use edge-cloud computation capacity.
- IV. NUMERICAL RESULTS: Increasing the number of users decreases each user’s allocated spectrum, lowers transmission rates, and increases latency.The passage also reports that more users force up edge-cloud prices and revenue through competition.
V. CONCLUSION
The paper studies price-based offloading with finite edge-cloud computation capacity and models cloud–user interaction as a Stackelberg game. It proposes uniform and differentiated pricing schemes that can both be implemented distributively.
- V. CONCLUSION: The system models the interaction between the edge cloud and users as a Stackelberg game with finite edge-cloud computation capacity.The capacity manages the offloaded tasks from multiple users.
- V. CONCLUSION: The paper proposes uniform and differentiated pricing schemes based on the edge cloud’s network information.Both schemes are described as implementable in distributed manners.
APPENDIX B THE PROOF OF PROPOSITION 2
The proof shows that an optimal price cannot lie strictly between consecutive reciprocal thresholds. At each such interval, an endpoint yields the same offloading pattern and higher revenue.
- An assumed optimum inside (1/F_i, 1/F_{i+1}) produces the same binary offloading decisions as the endpoint 1/F_{i+1}.Both prices yield x_k = 0 for k = 1, ..., i and x_k = 1 for k = i + 1, ..., K.
- The two prices therefore induce equivalent total CPU-cycle usage from the offloaded data.The proof compares the corresponding sum of offloaded data and CPU cycles.
- Because revenue is increasing and linear in price for this unchanged offloading pattern, the endpoint achieves higher revenue than the interior price.
- Thus, the optimal price belongs to the finite set {1/F_1, ..., 1/F_K}.