This paper presents a joint rate allocation scheme for statistical multiplexing of multiprogram video coding in broadcasting systems. The scheme is based on a scalable video coding (SVC) platform that does not require computationally expensive re-encoding or transcoding to adjust the bit-rate of each video program. A piecewise linear model is used to estimate the rate-distortion relationship in SVC enhancement layers. Based on the model, a joint rate allocation scheme is developed to dynamically allocate the available bandwidth by taking into consideration both inter-program fairness and intraprogram smoothness constraints. Experiments have been carried out to compare the performance of existing methods with our proposed scheme. Results demonstrate that the proposed scheme achieves a fine balance in picture quality across all statistical multiplexed programs as well as within each program.