In the field of the Internet of Things (IoT), Edge computing has emerged as a revolutionary paradigm that offers unprecedented benefits by serving the IoT at the network edge. One of the primary advantages of edge computing is that it reduces the job completion time by offloading tasks at the edge server from the IoT. Typically, a job is made up of dependent tasks in which the output of one task is required as the input to the other. This work proposes a directed cyclic graph model that represents the dependencies among these tasks focusing on jointly optimizing task dependencies with deadline constraints for tasks that are delay-sensitive. Thus, dependent tasks are scheduled while considering their deadlines using priority-aware scheduling. For tasks with no deadlines, the processing is done with First-Come-First-Serve (FCFS) scheduling. The tasks with a priority are offloaded to the suitable edge server for processing by using a priority queue to enhance the task satisfaction rate under deadline constraints. To model the suitable edge server decision, we use the Markov decision process (MDP) that minimizes the total completion time. Additionally, we model the mobility of users while offloading tasks to the edge servers. The throughput results demonstrate that the proposed strategy outperforms random offloading, the highest data rate offloading (HDR), the highest computing device (HCD), and delay-dependent priority-aware offloading (DPTO), by 66.67%, 43.75%, 27.78%, and 4.55%, respectively. Furthermore, the proposed strategy surpasses random, HDR, and HCD offloading in terms of task satisfaction rate by 20.48%, 16.28%, and 12.36%, respectively.