The problem of scheduling a set of dependent tasks from a user mobile device to several servers in communication cells while the user is moving along these cell in various speed is studied in this thesis. The challenging issue is the execution speed of each server and the speed of user?s movement are not compatible. This leads to the difficulty of assigning and finishing the subset of scheduled dependent tasks to each server within the limitation of execution time during passing a cell. Another concern involved this study is the constraints on the length of makespan in terms of minimum communication time among servers in the same cell and the energy consumed by the servers as well as the energy spent by user?s mobile device. This study proposed a new algorithm to schedule a set of dependent tasks under the constraints from these issues. Three new concepts of (1) selecting cells for executing scheduled tasks proposed algorithm, (2) partitioning and scheduling tasks to be assigned to the servers in the selected cell, and (3) shuffling the tentatively assigned tasks of all servers to minimize the makespan and energy consumption were proposed in this study. The experimental results were compared with the current practically used algorithms, i.e. HEFT, PEFT, HETS based on several complex synthetic task flow graphs. The obtained results showed that the most of makespan lengths found by our algorithm are shorter than those found by the other algorithms. But in terms of energy consumption, all results scheduled by our algorithm significantly consume less energy than those from the other algorithms.?