Stability Analysis for Fog Computing via Lyapunov Function

Publication Date

1-12-2026

Document Type

Article

Publication Title

Internet of Things the Netherlands

Volume

36

DOI

10.1016/j.iot.2026.101871

Abstract

Fog computing is an emerging paradigm for the Internet of Things (IoT), where system stability directly impacts reliability, performance, and user experience. Existing stability models often ignore application-level service completion or fail to capture dynamic interactions among sensors and fog nodes. This study addresses these gaps by establishing necessary conditions for fog nodes to process application services within finite time. First, we introduce a fluid model based on a partial differential equation (PDE) to quantify the dynamics of service counts for each sensor when fog nodes are shared. Second, we design a Lyapunov function derived from the PDE solution to analyze system stability and convergence. Third, we apply this Lyapunov function to derive conditions that guarantee timely service completion. Finally, numerical experiments validate the fluid model, investigate PDE solution behavior, and assess the convergence speed of the Lyapunov function under various system parameters. These results provide actionable insights for ensuring stability and efficiency in fog computing systems for IoT applications.

Keywords

Fog computing, Lyapunov function, Partial differential equations (PDE), Sensor networks, Stability analysis

Department

Applied Data Science

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