Characterizing Effective Computing Capacity and Online Task Assignment in Heterogeneous Oilfield Cloud–Edge Systems

Online allocation of oilfield analytics depends on which resources can execute each task and when those resources are available. We develop Effective-Capacity-aware Lyapunov Online Assignment (EC-LyOA), which links task-specific execution eligibility to a state-conditioned workload capacity region that accounts jointly for computation and shared communication demands. A base controller (EC-LyOA-B) prices these demands through resource-accounting debts; under bounded independent slot observations and strict resource slack, it achieves accounting-queue stability with an O(1/V) cost gap and an O(V) debt bound, and an explicit rejection option limits the long-run rejection rate to O(1/V) inside the capacity region. A guarded implementation (EC-LyOA-G) adds runtime memory and deadline reservations and is evaluated empirically. In trace-driven experiments, task releases are constructed from Petrobras 3W oil-well records, while execution and communication follow parameterized profiles. Concentrating demand in restricted service states reduces effective capacity, and an independence approximation overestimates capacity by 87.6% in the evaluated case. In a medium deployment, EC-LyOA-G operating points obtained by varying the control weight dominate MaxWeight, a CPU-only drift-plus-penalty controller and three adapted learning-based policies; at matched on-time completion (92.9% versus 93.0%), cost per on-time task is 5.8% lower than under the CPU-queue policy. Ablations identify memory reservations and deadline checks as decisive for valid completion. These results provide a quantitative basis for aligning service deployment, resource provisioning and online assignment with the workload each infrastructure can support.