In this thesis, we compare the energy efficiency of various strategies of mobile computation offloading over stochastic transmission channels where the task completion time is subject to a latency constraint. In the proposed methods, finite-state Markov chains are used to model the wireless channels between the mobile devices and the remote servers. We analyze the mechanisms of efficient mobile computation offloading under both soft and hard latency constraints. For the case of soft latency constraint, the task completion could miss the deadline below a specified probability threshold. On the other hand, under a hard deadline constraint, the task execution result must be available at the mobile device before the deadline. In order to make sure the task completes before the hard deadline, the hard deadline constraint approach requires concurrent execution in both local and cloud in specific circumstances. The closed-form solutions are often obtained using the broad Markov processes. The GE (Gilbert-Elliott) model is a more efficient method for demonstrating how the Markov chain’s structure can be used to compute the best offload initiation (Hekmati et al., 2019a).The effectiveness of the algorithms is studied under various deadline constraints and offloading methods. In this thesis, six algorithms are assessed in various scenarios. 1) Single user optimal (Zhang et al., 2013), 2) LARAC (Lagrangian Relaxation Based Aggregated Cost) (Zhang et al., 2014), 3) OnOpt (Online Optimal) algorithm (Hekmati et al., 2019a), 4) Water-Filling With Equilibrium (WF-Equ), 5) Water-Filling With Exponentiation (WFExp) (Teymoori et al., 2021), 6) MultiOPT (Multi-Decision Online Optimal). The experiment demonstrates that the studied algorithms perform dramatically different in the same setting. The various types of deadline restrictions also affect how efficiently the algorithms use energy. The experiment also highlights the trade-off between computational complexities and mobile energy savings (Teymoori et al., 2021).