Cloud-Edge-End Collaborative Task Scheduling for Multi-Robot Inspection Systems: An M/M/c Queuing-Theoretic Approach
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Abstract
This paper addresses the task scheduling problem in multi-robot inspection systems within a cloud-edge-end collaborative computing architecture. We model the edge computing layer as an M/M/c queuing system and derive the optimal server allocation using the Erlang C formula. A priority-aware scheduling framework with Earliest Deadline First (EDF) ordering and local-edge offloading is proposed to handle four classes of inspection tasks: real-time, urgent, normal, and background. An aging mechanism prevents starvation of low-priority tasks. Discrete-event simulations with 30 independent runs demonstrate that the proposed framework reduces the task drop rate by an average of 6.8 percentage points compared to FIFO, 11.0 pp compared to Round Robin, and 3.4 pp compared to Greedy scheduling, with a maximum improvement of 15.0 pp at high load. Real-time task delay improves by up to 18.4% at high arrival rates. The framework transparently manages a design tradeoff: priority-weighted delay increases by 24.8% on average, concentrated in background tasks, while energy consumption remains comparable (within 2.1% of baselines). The M/M/c analytical model provides an upper bound for simulation delay in the stable regime.
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