Mobile Edge Computing (MEC) brings resourceful mobile edge servers to a network’s edge. The latest wireless communication technologies provide high bandwidth. The combination of state-of-the-art communication technologies and MEC enables a multitude of real-time communication and computing use cases, such as connected cars, augmented reality, etc.. Offloaded tasks most often belong to real-time applications, hence a mobile edge server needs to complete execution of such tasks within defined latency requirements. To satisfy these latency requirements, admission control and scheduling algorithms are presented here. The admission control algorithm ascertains that only those tasks’ offloading requests are admitted for execution on a mobile server whose latency requirements can be satisfied, and that the admission of a new task does not result in missing execution latency deadlines of already offloaded tasks. The admission control algorithm also allocates a time-slice (per unit-time) for offloaded tasks corresponding to each core on which tasks execute. Afterwards, our scheduling algorithm schedules offloaded tasks on cores selected by the admission control algorithm, and it ascertains that each task’s execution latency requirements are satisfied. We show how the proposed admission control and scheduling algorithms outperform existing algorithms.