The demand for stringent interactive Quality of Service has intensified in both mobile-edge computing (MEC) and cloud systems, driven by the imperative to improve user experiences. As a result, the processing of computation-intensive tasks in these systems necessitates adherence to specific deadlines or achieving extremely low latency. To optimize task scheduling performance, existing research has mainly focused on reducing the number of late jobs whose deadlines are not met. However, the primary challenge with these methods lies in the total search time and scheduling efficiency. In this article, we present the optimal job scheduling algorithm designed to determine the optimal task order for a given set of tasks. In addition, users are enabled to make informed decisions for offloading tasks based on the information provided by servers. The details of performance analysis are provided to show its optimality and low complexity with the linearithmic time $\mathcal {O}(n\log n)$ , where n is the number of tasks. To tackle the uncertainty of the randomly arriving tasks, we further develop an online approach with fast outage detection that achieves rapid acceptance times with time complexity of $\mathcal {O}(n)$ . Extensive numerical results are provided to demonstrate the effectiveness of the proposed algorithm in terms of the service ratio and scheduling cost.