Queueing-Theory Integrated Cyber-Physical Systems Architecture for Agricultural Automation: Analytical Modeling of Latency, Throughput, and State-Dependent Cloud Escalation

Cyber-physical systems for agricultural automation require predictable performance across sensing, communication, edge, fog, and cloud resources, yet buffer sizes and offloading decisions are often selected empirically. This paper presents a five-tier Queueing-Theoretic Cyber-Physical Systems (QI-CPS) architecture with finite-buffer edge processing and state-dependent cloud escalation. The edge is modeled as M/M/1/K, the fog as a First-Come, First-Served (FCFS) M/M/c system, and the cloud as M/G/1. An arrival is admitted when the instantaneous edge occupancy Ne(t) satisfies Ne(t) < K, where K is the total capacity of the finite edge system, and is routed directly to the cloud when Ne(t) = K. The stationary Blocking Probability PB therefore determines the long-run overflow fraction and couples edge capacity to fog and cloud arrival rates. Because finite-capacity overflow and general cloud service do not satisfy classical Jackson product-form assumptions, the tiers are linked through a route-conditioned analytical decomposition and evaluated using end-to-end Discrete-Event Simulation (DES). The experiment covers K = 1–15, edge utilization ρe = 0.5–0.9, and c = 1, 2, 4, and 8 fog servers, with five independent replications, 3000 warm-up arrivals, 30,000 measured arrivals per replication, and 95% confidence intervals. For ρe = 0.8 and c = 4, K = 1 overloads the cloud; the analytical point minimum occurs at K = 4, while K = 4-5 form a near-optimal DES suitable range (121.2 ± 2.7 and 120.7 ± 3.2 ms, respectively). The results show that suitable edge capacity depends on workload and fog capacity and must satisfy both fog and cloud stability constraints. QI-CPS therefore provides a transparent method for screening feasible buffer capacities and quantifying the trade-off between local queueing and cloud overflow.