Scheduling of real-time applications is an important research topic. We consider a large-scale application consisting of 100-1000 tasks with inter-task communications, which can be represented by a task graph. For scheduling these applications, previous research results have shown that the timetriggered scheduling approach is capable to effectively utilize real-time platforms. However, the time-triggered scheduling approach only supports periodically activated tasks. Sporadic (aperiodic) tasks, which are also common in industrial applications, require additional treatments in time-triggered approaches.In this paper, we present a method to handle the sporadic tasks (that are not periodic) by shifting the time-triggered schedule. This method improves the responsiveness of the real-time sporadic tasks, whereas the schedule of the timetriggered tasks remains feasible. We define a time-triggered server to handle sporadic events and reserve time slots to ensure a safe recovery of the delayed time-triggered schedule. If a sporadic task arrives, this task starts its execution during the time-triggered server slot and the current time-triggered schedule is shifted. This paper provides the feasibility analysis for the time-triggered and the sporadic tasks under this slot shifting method. We determine time-triggered scheduling parameters to maximize the performance of the timetriggered server. Experiments confirm higher reachable system utilization by using our slot shifting approach.