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A Paradigm For Collaborative Pervasive Fog Computing Ecosystems at the Network Edge

Abderrahmen Mtibaa

TL;DR

The paper addresses reducing blocking and cloud offload in multi-provider fog networks by enabling fog-to-fog cooperation. It develops a Continuous-Time Markov Chain model for $N$ cooperating fog nodes with cooperation probabilities $\mathbf{p}$ and blocking vector $\mathbf{b}$, and formulates the optimization problem $\mathcal{P}$ to enforce fair load distribution while minimizing blocking. A closed-form solution is derived for $N=2$ ($p_1^*=1$, $p_2^*=(\lambda_2/\lambda_1)^2$ for $\lambda_1\ge\lambda_2$), and a numerical fixed-point approach is described for $N>2$, yielding Pareto-efficient cooperative strategies that reduce local blocking relative to non-cooperation. The framework demonstrates a scalable, decentralized edge-resource sharing paradigm with potential QoE improvements, while recognizing future work on security/privacy and coalition selection in more complex networks.

Abstract

While the success of edge and fog computing increased with the proliferation of the Internet of Things (IoT) solutions, such novel computing paradigm, that moves compute resources closer to the source of data and services, must address many challenges such as reducing communication overhead to/from datacenters, the latency to compute and receive results, as well as energy consumption at the mobile and IoT devices. fog-to-fog (f2f) cooperation has recently been proposed to increase the computation capacity at the network edge through cooperation across multiple stakeholders. In this paper we adopt an analytical approach to studying f2f cooperation paradigm. We highlight the benefits of using such new paradigm in comparison with traditional three-tier fog computing paradigms. We use a Continuous Time Markov Chain (CTMC) model for the N f2f cooperating nodes and cast cooperation as an optimization problem, which we solve using the proposed model.

A Paradigm For Collaborative Pervasive Fog Computing Ecosystems at the Network Edge

TL;DR

The paper addresses reducing blocking and cloud offload in multi-provider fog networks by enabling fog-to-fog cooperation. It develops a Continuous-Time Markov Chain model for cooperating fog nodes with cooperation probabilities and blocking vector , and formulates the optimization problem to enforce fair load distribution while minimizing blocking. A closed-form solution is derived for (, for ), and a numerical fixed-point approach is described for , yielding Pareto-efficient cooperative strategies that reduce local blocking relative to non-cooperation. The framework demonstrates a scalable, decentralized edge-resource sharing paradigm with potential QoE improvements, while recognizing future work on security/privacy and coalition selection in more complex networks.

Abstract

While the success of edge and fog computing increased with the proliferation of the Internet of Things (IoT) solutions, such novel computing paradigm, that moves compute resources closer to the source of data and services, must address many challenges such as reducing communication overhead to/from datacenters, the latency to compute and receive results, as well as energy consumption at the mobile and IoT devices. fog-to-fog (f2f) cooperation has recently been proposed to increase the computation capacity at the network edge through cooperation across multiple stakeholders. In this paper we adopt an analytical approach to studying f2f cooperation paradigm. We highlight the benefits of using such new paradigm in comparison with traditional three-tier fog computing paradigms. We use a Continuous Time Markov Chain (CTMC) model for the N f2f cooperating nodes and cast cooperation as an optimization problem, which we solve using the proposed model.
Paper Structure (10 sections, 1 theorem, 41 equations, 4 figures)

This paper contains 10 sections, 1 theorem, 41 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Fog-to-Fog Cooperation
  4. Motivation
  5. Cooperative Model for N = 2 Nodes
  6. Closed form solution of ${\mathcal{P}}$ for $N=2$ Nodes
  7. Cooperative Model for N > 2 Nodes
  8. Numerical solution of ${\mathcal{P}}$ for $N>2$ Nodes
  9. Numerical evidence of the optimal solution
  10. Discussions & Conclusion

Key Result

Theorem 1

The pair where $\lambda_1 \ge \lambda_2$, is the solution of ${\mathcal{P}}$ under the $MC$ model of Fig. fig:MC.

Figures (4)

  • Figure 1: Cooperation among two fog nodes receiving tasks from their corresponding clients; fog node $n_1$ accepts tasks from neighboring nodes with a cooperation probability $p_1$ and sends tasks to the cloud with a blocking probability $b_1$.
  • Figure 2: The state transition diagram of the CTMC used to model a two node cooperating network.
  • Figure 3: A sketch of a Pareto improvement; Segments are contour lines of $b_i$ and semicircles represent regions where the value of blocking probability decreases. Vectors in the intersection of the two semicircles, as $\delta \mathbf{p}$, is a Pareto improvement.
  • Figure 4: Partition of the cooperation probability domain for $\lambda_1=0.9,\lambda_2=0.8$.

Theorems & Definitions (5)

  • Definition 1: Pareto improvement
  • Definition 2: Efficiency
  • proof
  • Theorem 1: Solution of the Minimization Problem ${\mathcal{P}}$
  • proof