This paper addresses the problem of multiplexing pre-encoded video sequences to be transmitted across a bandwidth constrained channel. At each time instant, the available bit budget needs to be optimally allocated to the sequences. We seek for a solution that minimizes the output distortion variance, in order to keep the quality of the reconstructed sequences as similar as possible, by formulating the problem in the ρ-domain. In addition, by enabling a shared video buffer, we show that it is possible to smooth the overall video quality along time. Experimental results on H.264/AVC compressed video data validate the performance of the proposed algorithm.