The successful operation of mission critical systems requires a sophisticated control network which provides for the real-time delivery of data from a very large number of diverse sources such as sensors, audio/video surveillance, computational sources, etc., as well as remote monitoring and diagnosis sources. It is expected that many of the traffic sources will be in the form of periodic sources with real-time requirements. In this study, we propose fast scheduling algorithms for multiplexing periodic source flows with real-time delivery requirements. We assume a single switch environment with periodic source flows being supported over a constant bit rate (CBR) type circuit. We undertake a systematic study beginning from the simplest scenario where all traffic flows consist of data frames of the same size and with the same real-time delay requirement. In this case, we prove that the FCFS algorithm is optimal. We conclude with the most difficult case of examining CBR flows of variable bandwidth requirements and variable delay requirements. Algorithms and analysis are presented for all the cases. The simulation results show the substantial performance gains provided by the proposed algorithms.