In the framework of supervisory control of timed discrete event systems, this paper addresses the design problem of a real-time scheduler that meets stringent time constraints of periodic tasks and sporadic tasks which exclusively access shared resources. For this purpose, we present the timed discrete event models of execution of periodic tasks and sporadic tasks and resource access for shared resources. Based on these models, we present the notion of deadlock-free and schedulable languages that contain only deadline-meeting sequences which do not reach deadlock states. In addition, we present the method of systematically computing the largest deadlock-free and schedulable language, and it is also shown that schedulability analysis can be done using this language. We further show that the real-time scheduler achieving the largest deadlock-free and schedulable language is optimal in the sense that there are no other schedulers to achieve schedulable cases more than those achieved by the optimal scheduler. (C) 2009 Elsevier Ltd. All rights reserved.