Fog computing is an emerging paradigm which extends the functionality of the cloud near to the end users. Its introduction helped in running different real-time applications where latency is a critical factor. This paradigm is motivated by the fast growth of Internet of Things (IoT) applications in different fields. By running Virtual Machines (VMs) on fog devices, different users will be able to offload their computational tasks to fog devices to get them done in a smooth, transparent, and faster manner. Nevertheless, the performance of real-time applications might suffer if no proper live virtual machine migration mechanism is adopted. Live VM migration aims to move the running VM from one physical fog node to another with minimal or zero downtime due to mobility issues. Many efforts have been made in this field to solve the challenges facing live VM migration in fog computing. However, there are remaining issues that require solutions and improvements. In this paper, the following presents the research outcomes: An extensive survey of existing literature on live VM migration mechanisms in fog computing. Also, a new novel classification approach for categorizing live VM migration mechanisms based on conventional and Artificial Intelligence (AI) approaches to address live VM migration challenges is presented. Moreover, an identification of research gaps and in the existing literature and highlighting the areas where further investigation is required is done and finally a conclusion with a discussion of potential future research directions is drawn.

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