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Balancing Costs and Utilities in Future Networks via Market Equilibrium with Externalities

Mandar Datar, Mattia Merluzzi

TL;DR

The paper addresses sustainable, fair allocation of heterogeneous radio and computing resources under global energy/CO$_2$ budgets by casting the problem as a Fisher market with externalities. It extends classical market equilibrium analysis with Pigouvian pricing and proves that the equilibrium can be found via a convex optimization problem that maximizes $\sum_n B_n \log(U_n(\mathbf{x}_n))$, yielding prices $p_k^* = \gamma_k^* + \sum_i \lambda_{ik}^*$ and dual feasibility that enforce regulatory and capacity constraints. The approach links Nash welfare and proportional fairness to the market outcome, and numerical experiments with two service providers demonstrate that the ME-based allocation is more robust and fair than a social-optimum allocation under varying energy costs and budgets. The framework offers a scalable, sustainability-aware mechanism for orchestrating edge, MEC, and cloud resources in future networks, integrating external costs directly into resource pricing and allocation.

Abstract

We study the problem of market equilibrium (ME) in future wireless networks, with multiple actors competing and negotiating for a pool of heterogeneous resources (communication and computing) while meeting constraints in terms of global cost. The latter is defined in a general way but is associated with energy and/or carbon emissions. In this direction, service providers competing for network resources do not acquire the latter, but rather the right to consume, given externally defined policies and regulations. We propose to apply the Fisher market model, and prove its convergence towards an equilibrium between utilities, regulatory constraints, and individual budgets. The model is then applied to an exemplary use case of access network, edge computing, and cloud resources, and numerical results assess the theoretical findings of convergence, under different assumptions on the utility function and more or less stringent constraints.

Balancing Costs and Utilities in Future Networks via Market Equilibrium with Externalities

TL;DR

The paper addresses sustainable, fair allocation of heterogeneous radio and computing resources under global energy/CO budgets by casting the problem as a Fisher market with externalities. It extends classical market equilibrium analysis with Pigouvian pricing and proves that the equilibrium can be found via a convex optimization problem that maximizes , yielding prices and dual feasibility that enforce regulatory and capacity constraints. The approach links Nash welfare and proportional fairness to the market outcome, and numerical experiments with two service providers demonstrate that the ME-based allocation is more robust and fair than a social-optimum allocation under varying energy costs and budgets. The framework offers a scalable, sustainability-aware mechanism for orchestrating edge, MEC, and cloud resources in future networks, integrating external costs directly into resource pricing and allocation.

Abstract

We study the problem of market equilibrium (ME) in future wireless networks, with multiple actors competing and negotiating for a pool of heterogeneous resources (communication and computing) while meeting constraints in terms of global cost. The latter is defined in a general way but is associated with energy and/or carbon emissions. In this direction, service providers competing for network resources do not acquire the latter, but rather the right to consume, given externally defined policies and regulations. We propose to apply the Fisher market model, and prove its convergence towards an equilibrium between utilities, regulatory constraints, and individual budgets. The model is then applied to an exemplary use case of access network, edge computing, and cloud resources, and numerical results assess the theoretical findings of convergence, under different assumptions on the utility function and more or less stringent constraints.

Paper Structure

This paper contains 9 sections, 1 theorem, 24 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Utility and costs
  4. Resource Allocation and Pricing Problem
  5. Equilibrium Solution
  6. Nash welfare and fairness
  7. Examples of utility
  8. Numerical Experiments
  9. Conclusions and future directions

Key Result

Theorem 1

If each agent's utility function within market $\mathcal{M}$ is continuous, concave, and homogeneous of degree one (CCH), and $e_{i}(\overline{\mathbf{x}})$ is convex and increasing function in $\overline{\mathbf{x}}$, $\forall i \in \mathcal{I}$, the market equlibrium can be computed by solving an

Figures (2)

  • Figure 1: Sensitivity of the agents' utility to various factors: (a) the CPU energy function, (b) the Radio energy function, and (c) agents' budgets
  • Figure 2: Variation in the usage of: (a) radio, (b) CPU, and the utility derived from both MEC and cloud facilities vs. local energy consumption constraints.

Theorems & Definitions (3)

  • Definition 1
  • Theorem 1
  • Proof 1