Distributed Allocation and Resource Scheduling Algorithms Resilient to Link Failure

TL;DR

This work addresses resilient distributed resource allocation (DRA) in networks subject to link failures, packet drops, and heterogeneous time delays. It introduces a graph-theoretic, percolation-theory-based algorithm that guarantees all-time feasibility and exact convergence under uniformly-connected topologies, accommodating sector-bound nonlinearities and quantized communications. Convergence is established under bounds tied to the network's Laplacian spectra and percolation thresholds, with explicit trade-offs between failure probability, delay, and convergence speed. Simulations and a distributed economic-dispatch example validate robustness to severe disruptions, offering practical resilience improvements over prior delay- and connectivity-dependent methods.

Abstract

Distributed resource allocation (DRA) is fundamental to modern networked systems, spanning applications from economic dispatch in smart grids to CPU scheduling in data centers. Conventional DRA approaches require reliable communication, yet real-world networks frequently suffer from link failures, packet drops, and communication delays due to environmental conditions, network congestion, and security threats. We introduce a novel resilient DRA algorithm that addresses these critical challenges, and our main contributions are as follows: (1) guaranteed constraint feasibility at all times, ensuring resource-demand balance even during algorithm termination or network disruption; (2) robust convergence despite sector-bound nonlinearities at nodes/links, accommodating practical constraints like quantization and saturation; and (3) optimal performance under merely uniformly-connected networks, eliminating the need for continuous connectivity. Unlike existing approaches that require persistent network connectivity and provide only asymptotic feasibility, our graph-theoretic solution leverages network percolation theory to maintain performance during intermittent disconnections. This makes it particularly valuable for mobile multi-agent systems where nodes frequently move out of communication range. Theoretical analysis and simulations demonstrate that our algorithm converges to optimal solutions despite heterogeneous time delays and substantial link failures, significantly advancing the reliability of distributed resource allocation in practical network environments.

Figures (7)

• Figure 2: Convergence behaviour under dynamic network topology. Left: Evolution of cost residual with penalty term $\sigma([x_i-M_i]^++[m_i-x_i]^+)$ for both linear and nonlinear (log-scale quantization) models in a non-persistently connected network. Right: State trajectories of all agents under log-scale quantization, demonstrating constant average values and confirming the all-time feasibility of the proposed solution.
• Figure 3: Algorithm performance with logarithmic penalty function. Left: Convergence of cost residual with smoothed penalty term $\frac{1}{\mu}(\log(1+\exp(\mu(x_i-M_i)))+\log(1+\exp(\mu(m_i-x_i))))$ under dynamic network conditions. Right: State evolution of all agents maintaining constant average value, confirming all-time feasibility with logarithmic constraints.
• Figure 4: Network topology under varying link failure conditions. (a) Original Erdős--Rényi network with 20% linking probability. (b)-(c) Networks with failure rates below percolation threshold ($p_l < p_c$), maintaining connectivity with probability 1. (d)-(e) Networks with failure rates exceeding percolation threshold ($p_l > p_c$), becoming disconnected. (f)-(g) Union networks over $T=2$ and $T=4$ time steps respectively, demonstrating uniform connectivity when $p_l^{T+1} < p_c$ despite instantaneous disconnections.
• Figure 5: Impact of link failure probability on convergence performance. The plot shows cost residual evolution under varying link failure rates (50%-92%), demonstrating that higher failure probabilities require longer time windows for uniform connectivity, resulting in slower but still guaranteed convergence to optimal solutions.
• Figure 6: Algorithm resilience to communication delays. Left: Convergence behaviour with step-rate $\eta=2$, showing successful convergence for delays $\overline{\tau}=2$ but divergence for larger delays. Right: Improved resilience with reduced step-rate $\eta=0.5$, achieving convergence for all tested delay bounds ($\overline{\tau}\in\{2,4,6\}$), illustrating the fundamental trade-off between delay tolerance and convergence speed.

Theorems & Definitions (28)

• Lemma 1
• Corollary 1
• proof
• Lemma 2
• proof
• Definition 1
• Remark 1
• Corollary 2
• Definition 2
• Definition 3