A Mobile Edge Cloud (MEC) system consists of mobile devices, edge devices and the cloud. In the wide range of applications supported by MEC, AI applications are an important type. In a typical scenario of AI applications, the inferences of the deployed AI models form a type of streaming tasks. The offloading technique is often desired when the resource that the task executions are generated in (such as the mobile devices in MEC) is overloaded or has limited capacity. In this thesis, the offloading strategies are investigated systematically for handing streaming tasks in the Mobile Edge Cloud systems. In particular, the following research is conducted.

First, a two-tier offloading model is first established based on the queueing theory for handling streaming tasks in a Mobile Cloud (MC) system. Then a three-tier offloading model is developed for MEC to process streaming tasks. The offloading models constructed for handling streaming tasks in MC and MEC systems can be used for capacity planning in MEC.
Second, given the distributed nature of MEC and the incoming data, a decentralised offloading scheme is developed for streaming tasks in MEC. The offload model is constructed based on the game theory. It can determine the arrival rate of the tasks that each resource will end up handling when the Nash Equilibrium is reached.
Finally, although a decentralised offloading scheme is a natural choice in MEC, the MEC may be set up by a company for a particular application. Therefore, it is possible that all information about the tasks and the MEC system is known in advance. Envisaging this possibility, the centralised offloading schemes are also developed for MEC: first for process a batch of tasks and then being extended to handle streaming tasks. The centralised schemes can orchestrate the task-to-resource allocations in MEC.