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Multi-Time Scale Service Caching and Pricing in MEC Systems with Dynamic Program Popularity

Yiming Chen, Xingyuan Hu, Bo Gu, Shimin Gong, Zhou Su

TL;DR

Addresses dynamic popularity in MEC with a two-time-scale architecture over frames $j$ and slots $t$, coupling large-time-scale caching with small-time-scale pricing and offloading. Proposes GNDRL to learn popularity-aware caching and a two-stage Stackelberg game with incomplete information to obtain pricing and offloading strategies. Provides two pricing algorithms, CPTO and SCAO, and proves equilibrium existence; validates with real-world data. Results show GNDRL improves BS profit and reduces user delay and cost, demonstrating scalability to dynamic program popularity.

Abstract

In mobile edge computing systems, base stations (BSs) equipped with edge servers can provide computing services to users to reduce their task execution time. However, there is always a conflict of interest between the BS and users. The BS prices the service programs based on user demand to maximize its own profit, while the users determine their offloading strategies based on the prices to minimize their costs. Moreover, service programs need to be pre-cached to meet immediate computing needs. Due to the limited caching capacity and variations in service program popularity, the BS must dynamically select which service programs to cache. Since service caching and pricing have different needs for adjustment time granularities, we propose a two-time scale framework to jointly optimize service caching, pricing and task offloading. For the large time scale, we propose a game-nested deep reinforcement learning algorithm to dynamically adjust service caching according to the estimated popularity information. For the small time scale, by modeling the interaction between the BS and users as a two-stage game, we prove the existence of the equilibrium under incomplete information and then derive the optimal pricing and offloading strategies. Extensive simulations based on a real-world dataset demonstrate the efficiency of the proposed approach.

Multi-Time Scale Service Caching and Pricing in MEC Systems with Dynamic Program Popularity

TL;DR

Addresses dynamic popularity in MEC with a two-time-scale architecture over frames and slots , coupling large-time-scale caching with small-time-scale pricing and offloading. Proposes GNDRL to learn popularity-aware caching and a two-stage Stackelberg game with incomplete information to obtain pricing and offloading strategies. Provides two pricing algorithms, CPTO and SCAO, and proves equilibrium existence; validates with real-world data. Results show GNDRL improves BS profit and reduces user delay and cost, demonstrating scalability to dynamic program popularity.

Abstract

In mobile edge computing systems, base stations (BSs) equipped with edge servers can provide computing services to users to reduce their task execution time. However, there is always a conflict of interest between the BS and users. The BS prices the service programs based on user demand to maximize its own profit, while the users determine their offloading strategies based on the prices to minimize their costs. Moreover, service programs need to be pre-cached to meet immediate computing needs. Due to the limited caching capacity and variations in service program popularity, the BS must dynamically select which service programs to cache. Since service caching and pricing have different needs for adjustment time granularities, we propose a two-time scale framework to jointly optimize service caching, pricing and task offloading. For the large time scale, we propose a game-nested deep reinforcement learning algorithm to dynamically adjust service caching according to the estimated popularity information. For the small time scale, by modeling the interaction between the BS and users as a two-stage game, we prove the existence of the equilibrium under incomplete information and then derive the optimal pricing and offloading strategies. Extensive simulations based on a real-world dataset demonstrate the efficiency of the proposed approach.
Paper Structure (42 sections, 3 theorems, 38 equations, 13 figures, 1 table, 4 algorithms)

This paper contains 42 sections, 3 theorems, 38 equations, 13 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Cooperative Task Offloading
  4. Competitive Task Offloading
  5. Service Caching
  6. System Model
  7. Task Model
  8. Service Caching Model
  9. Communication Model
  10. Computation Model
  11. Local Computation
  12. Offloading Computation
  13. Problem Formulation
  14. Utility Function of the BS
  15. Large Time Scale
  16. ...and 27 more sections

Key Result

Lemma 6.1

Each user can estimate the same number of offloading participants $\hat{M}^{t,j}$ under incomplete information:

Figures (13)

  • Figure 1: System model.
  • Figure 2: Two-time scale framework for service caching, pricing and task offloading.
  • Figure 3: The framework of GNDRL.
  • Figure 4: Two-stage Stackelberg game.
  • Figure 5: The average cost of users vs. the number of users $M$ under complete and incomplete information.
  • ...and 8 more figures

Theorems & Definitions (6)

  • Lemma 6.1
  • Lemma 6.2
  • Definition 1: Nash Equilibrium of Game 2
  • Definition 2: Stackelberg Equilibrium of Game 1
  • Theorem 1
  • Definition 3: Exact Potential Game