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In conventional bit-rate control, the buffer level is controlled by adapting the quantization step size with a fixed frame rate and spatial resolution. We consider a multidimensional (M-D) bit-rate control where the frame rate, spatial resolution and quantization step size are jointly adapted for buffer control. We introduce a fundamental framework to formalize the description of the M-D buffer-constrained allocation problem. Given a set of operating points on a M-D grid to code a nonstationary source in a buffer-constrained environment, we formulate the optimal solution. The formulation allows a skipped frame to be reconstructed from one coded frame using any temporal interpolation method and is shown to be a generalization of formulations considered in the literature. In the case of intraframe coding, a dynamic programming algorithm is introduced to find the optimal solution. The algorithm allows one to compare operational rate-distortion bounds of the M-D and conventional approaches. We also discuss how a solution can be obtained for the case of interframe coding using the optimal dynamic programming algorithm for intraframe coding by making an independent allocation approximation. We illustrate that the M-D approach can provide bit-rate reductions over 50%. We also show that the M-D approach with limited-lookahead provides a slightly suboptimal solution that consistently outperforms the conventional approach with full-lookahead.