Real-time systems are characterized by the fact that severe consequences will result if neither logical nor timing correctness of the system are satisfied. Task scheduling is one of the most important problem since scheduling algorithms ensure that tasks meet their deadlines. If a schedule is not feasible, then the executions of tasks can not meet their deadlines. In most time-critical systems, not only timing correctness of results but also fault-tolerance of the system are required. So, scheduling algorithms should consider the occurrences of faults, which has the objective to optimize both timeliness and reliability. Recently, it has been noted in many researches that real-time engineering is essential in multimedia computing. For example, in a tele-conferencing system in Local Area Network(LAN) of workstations, multiple streams of motion videos and audios should be handled continuously and synchronized temporally when they are captured, transmitted, and modified in the network. since the data streams of videos and audios should be presented to a CRT at a certain constant rate. All processing units like the storage unit, the computation unit, and the communication unit in a workstation should complete their processing as timely as possible. In this dissertation, we propose two algorithms, one of which is targeted to the scheduling of nonpreemptive real-time tasks and the other tries to optimize both the timeliness and the reliability. We also indicate that multimedia computing requires real-time engineerings to satisfy the timeliness and apply our scheduling algorithms to solve the scheduling problems inherent in multimedia computing. In addition, we suggest a new specification method based on Milner``s CCS. We propose a new scheduling algorithm called OFOG in the meaning that it inserts one floor to one gap and show that it is optimal for scheduling a subset among whole sets of periodic tasks and the time complexity of OFOG algorithm is analyzed to be equal...