Performance modeling and analysis for randomly walking mobile users with Markov chains

We treat user equipments (UEs) and mobile edge clouds (MECs) as M/G/1 queueing systems, which are the most suitable, powerful, and manageable models. We propose a computation offloading strategy which can satisfy all UEs served by an MEC and develop an efficient method to find such a strategy. We use discrete-time Markov chains, continuous-time Markov chains, and semi-Markov processes to characterize the mobility of UEs, and calculate the joint probability distribution of the locations of UEs at any time. We extend our Markov chains to incorporate mobility cost into consideration, and are able to obtain the average response time of a UE with location change penalty. We can algorithmically predict the overall average response time of tasks generated on a UE and also demonstrate numerical data and examples. We consider the power constrained MEC speed setting problem and develop an algorithm to solve the problem for two power consumption models.