# Joint Optimization of Service Migration and Resource Allocation in Mobile Edge-Cloud Computing
## 1 Introduction  
### Motivation  
In recent years, the rapid expansion of Internet of Things (IoT) devices and mobile applications has catalyzed the development of mobile edge-cloud computing (MECC). This innovative paradigm combines the extensive computational resources of cloud computing with the immediacy of edge computing to meet essential requirements for low latency, high reliability, and superior quality of service (QoS) [1]. By harnessing the robust data handling and computational capabilities of cloud data centers, MECC efficiently manages large datasets and executes complex computations beyond the processing power of edge devices alone [2, 3]. Additionally, MECC significantly reduces latency by processing data closer to their source, enhancing performance for latency-sensitive applications such as autonomous driving, augmented reality (AR), virtual reality (VR), and real-time gaming [4, 5, 6, 7, 8]. MECC also improves system reliability by enabling edge nodes to autonomously manage critical operations, ensuring uninterrupted service even during network disruptions. Furthermore, the architecture of MECC supports dynamic and scalable resource allocation, optimizing cloud resources for computationally intensive tasks while delegating real-time processing to edge servers (ESs) [9]. This adaptability makes MECC highly suitable formodern digital ecosystems, capable of efficiently handling variable network loads and diverse application demands while seamlessly integrating smart technologies. Despite its advancements MECC faces significant challenges, primarily stemming from user mobility and the dynamic computational demands of contemporary mobile applications, which can lead to potential delays and instabilities, adversely impacting QoS [10; 11]. Common issues arise when users move to locations farther from their current ES, necessitating the offloading of tasks back to the original server to maintain service continuity. This often results in increased communication delays and can substantially degrade user experience, particularly in latency-sensitive applications. While recent advancements in dynamic computational offloading and resource allocation have significantly mitigated issues related to user mobility by optimizing offloading and allocation decisions to minimize response times, there remains a notable gap in fully addressing the dependencies of task execution on the underlying environments and user contexts at ESs. Current research has responded to these operational challenges by prioritizing service migration strategies that relocate task execution environments and user contexts to ESs closer to the user's real-time location, thereby maintaining or enhancing QoS [12]. However, these studies often overlook the critical impact of the reduction in computational time caused by migration processes, which can be detrimental to the performance of time-sensitive services. Furthermore, the interplay between service migration decisions and resource allocation strategies remains underexplored. Effective strategies should not only minimize data transfer delays by considering user proximity but also assess the computational capacities of various ESs to ensure that after migration the resources are adequate to handle the relocated services without causing service timeouts. Although some studies have acknowledged the complex interdependence between service migration and resource allocation, they often fail to account for scenarios where tasks are not completed before migration. This oversight can lead to data loss, increased delays, and significantly compromised QoS. In summary, while significant progress has been made in addressing various aspects of migrating services and allocating resources within MECC environments, critical gaps remain. Developing comprehensive strategies that simultaneously enhance the efficiency of service migration and resource distribution, considering unfinished tasks and their contexts, is crucial.