Adaptive Service Migration in Hybrid MEC–Cloud Environments: A Queueing-Theoretic Framework for Split-User Offloading

Resource-constrained Multi-Access Edge Computing (MEC) nodes cannot fully replace cloud infrastructure, yet existing service placement models treat edge hosting as an all-or-nothing decision. This paper proposes a queueing-theoretic framework for split-user offloading in hybrid MEC–cloud environments. The system is modeled as a Continuous-Time Markov Chain (CTMC) over a load-vector state space that admits a product-form stationary distribution. A delay-aware greedy orchestration policy determines, at every arrival and departure event, which service occupies the MEC node and how many of its users are offloaded from the cloud. Closed-form expressions are derived for average end-to-end (E2E) delay, MEC occupancy and saturation probabilities, per-service hosting probabilities, and delay-saving indicators. Numerical analysis of a five-service industrial scenario shows that the proposed split-user mechanism keeps the MEC node occupied for most of the observation time (around 97% at the baseline load), naturally prioritizes services with the largest aggregate latency benefit, and substantially reduces the average delay compared with a cloud-only configuration. The analytical results are validated by discrete-event simulation, which matches the CTMC values with relative discrepancy below 1% under the Poisson/exponential assumptions; additional simulations quantify the sensitivity to alternative arrival and service-time distributions. The framework provides analytically tractable, interpretable decision logic with negligible runtime overhead, making it a suitable analytical foundation for cloud service orchestration platforms that must meet strict QoS targets in next-generation edge networks.