The efficient migration of virtual machines (VMs) is critical for optimizing resource management, ensuring service continuity, and enhancing resiliency in cloud and edge computing environments, particularly as 6G networks demand higher reliability and lower latency. This study addresses the challenges of dynamically balancing server loads while minimizing downtime and migration costs under stochastic task arrivals and variable processing times. We propose a queuing theory-based model employing continuous-time Markov chains (CTMCs) to capture the interplay between VM migration decisions, server resource constraints, and task processing dynamics. The model incorporates two migration policies—one minimizing projected post-migration server utilization and another prioritizing current utilization—to evaluate their impact on system performance. The numerical results show that the blocking probability for the first VM for Policy 1 is 2.1% times lower than for Policy 2 and the same metric for the second VM is 4.7%. The average server’s resource utilization increased up to 11.96%. The framework’s adaptability to diverse server–VM configurations and stochastic demands demonstrates its applicability to real-world cloud systems. These results highlight predictive resource allocation’s role in dynamic environments. Furthermore, the study lays the groundwork for extending this framework to multi-access edge computing (MEC) environments, which are integral to 6G networks.

The rapid growth of 5G networks has increased the need for effective resource management, especially in multi-operator environments, where the spectrum is shared between mobile network operators (MNOs) and mobile virtual network operators (MVNOs). This study focuses on the challenge of dynamic spectrum management in 5G New Radio (NR) networks, emphasizing network slicing and frequency reallocation to ensure slice isolation and revenue maximization. Unlike static allocation methods that fail to adapt to real-time traffic fluctuations, our proposed framework dynamically divides the spectrum between MNO and MVNO slices. It uses a resource queuing model that accounts for random user distributions and session arrivals, integrating spatial randomness and temporal variability. This allows for the precise quantification of slice performance in dynamic resource sharing. A frequency reallocation algorithm adjusts spectrum partitions in real-time, prioritizing proximity-based bitrate enhancements, while guaranteeing minimum bitrates for all users. The framework incorporates revenue-driven optimization, balancing the MNO’s income from spectrum leasing, while ensuring slice isolation. The numerical results show that the pricing ratio provides a tunable parameter for operators to prioritize either user capacity or leasing income based on market conditions. The highest average revenue forMNOis achieved by prioritizing its own users, while increasing the resource reallocation signal rate boosts average revenue by 3–3.7% and reduces average user device losses, maintaining strict isolation. However, real-world adoption faces challenges, including computational complexity from large state-space growth, and signaling overhead increasing energy consumption. Additionally, unresolved technical hurdles, such as interoperability between multi-vendor equipment, and standardization gaps in spectrum sharing protocols hinder network slicing deployment. This study bridges the gap between technical and economic goals, offering a scalable solution for 5G and beyond.

Fifth-generation (5G) networks provide network slicing capabilities, enabling the deployment of multiple logically isolated network slices on a single infrastructure platform to meet specific requirements of users. This paper focuses on modeling and analyzing resource capacity planning and reallocation for network slicing, specifically between two providers transmitting elastic traffic, such during as web browsing. A controller determines the need for resource reallocation and plans new resource capacity accordingly. A Markov decision process is employed in a controllable queuing system to find the optimal resource capacity for each provider. The reward function incorporates three network slicing principles: maximum matching for equal resource partitioning, maximum share of signals resulting in resource reallocation, and maximum resource utilization. To efficiently compute the optimal resource capacity planning policy, we developed an iterative algorithm that begins with maximum resource utilization as the starting point. Through numerical demonstrations, we show the optimal policy and metrics of resource reallocation for two services: web browsing and bulk data transfer. The results highlight fast convergence within three iterations and the effectiveness of the balanced three-principle approach in resource capacity planning for 5G network slicing.

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.