This paper addresses the pressing issue of delay uncertainty that plagues cloud-edge computing environments, particularly where real-time processing and adherence to Quality of Service (QoS) standards are imperative for tasks that come with stringent timing constraints. The advent of diverse and voluminous tasks due to the digital transformation across various sectors has escalated the complexity and intensity of resource competition. This escalation, in turn, has rendered conventional scheduling methods, which primarily rely on static and heuristic approaches, largely inefficient in managing the heightened risk of delays, thereby undermining the reliability and performance of cloud-edge computing systems. In response to these challenges, we propose a novel deterministic timing task scheduling model tailored for the cloud-edge computing paradigm to precisely address the issue of delay uncertainties. Furthermore, we introduce an scheduling algorithm based on the Deep Q-Network (DQN) framework. This algorithm intelligently schedules tasks across multiple time slots, tightly monitoring task completion relative to established timing constraints, with the ultimate goal of enhancing task acceptance rates while meticulously meeting specific timing requirements. Through a series of comprehensive simulations, our findings reveal that the DQN-based scheduling approach achieves substantial improvements in ensuring task timeliness.