The transparent transport of real-time periodic traffic through a broadband packet network requires the recovery of source clock frequency at the destination. The arriving packet stream at the destination buffer contains the source clock frequency information, which can be recovered by monitoring the buffer level, and using it to adjust the destination clock frequency without buffer under- or overflow. However, the inherently stochastic nature of packet transport in a broadband packet network makes the recovery difficult. The authors illustrate the packet jitter phenomenon, and develop algorithms to construct the destination clock frequency such that it asymptotically follows the source clock frequency with minimal variation. They provide a systematic design procedure for the implementation of these algorithms, and apply them to a computer model of a single stage FCFS multiplexer to demonstrate their effectiveness and different design trade-offs. They also discuss the application of the algorithms to the audio and video services.>