<p>Fog Computing’s core principle revolves around task redistribution to alleviate device workload, thereby optimizing both efficiency and latency. However, ensuring consistent service quality amidst shifting user locations requires strategic service migration. The unpredictability of this dynamic environment poses significant challenges in maintaining uninterrupted Quality of Service (QoS), especially in highly heterogeneous regions with varying multi-resource capacities and bandwidth. These conditions make the migration decision for workflows more complex. Additionally, managing tasks with various deadline requirements further intensifies the complexity of resource allocation within the Fog Computing framework. The challenge is not only to meet QoS but also to ensure the satisfaction of strict timed requirements. Balancing these timed constraints while dealing with resource heterogeneity and dynamic migration becomes crucial for optimal system management. This study explores the optimization of workflow partial offloading and migration in hybrid Fog and Cloud environments, with a specific focus on meeting timed constraints associated with tasks and their dependencies. The problem is formulated to minimize the overall delay and energy consumption while addressing timed constraints. To tackle this challenge, we propose a Deep Q-Network-based solution, aiming to find an optimal policy for workflow partial offloading and migration in a highly heterogeneous Fog environment. The proposed solution not only enhances overall QoS but also ensures compliance with timed constraints imposed by tasks. The simulation results highlight the superior performance of the proposed approach, demonstrating significant efficiency improvements in terms of delay and energy consumption. Notably, the solution consistently achieves a higher satisfaction ratio for timed constraints, outperforming existing offloading and migration strategies.</p>