The paper presents a real-time operating system (RTOS) of a time-triggered distributed computing environment based on physical time and logical time for cyber-physical systems. In the environment, input and output tasks are activated synchronized with physical time and computation tasks are activated by the reception of timestamped messages and managed based on logical time. The control performance is affected by the jitters of input and output tasks but not affected by the jitters of computation tasks, so the jitter of the computation task activation is tolerated. However, the response time of low priority computation tasks may be increased in fixed-priority scheduling, which is used by most RTOSs. The paper presents a RTOS with mixed scheduling, in which fixed scheduling is used for input and output tasks to minimize the jitters and earliest deadline first (EDF) scheduling based on logical deadlines is used for computation tasks to minimize the response time. The logical deadline is not affected by the task activation time and higher priority is assigned to a computation task with an earlier logical deadline even if its activation is delayed, so the response time is improved. We have evaluated the performance of the RTOS and have confirmed that the performance is acceptable for practical embedded control systems.