Discrete ConvolutionalFixedSum

The ConvolutionalFixedSum (CFS) algorithm provides a generalization of the Unifast and RandFixedSum algorithms enabling the generation of vectors of uniformly sampled random values that sum to a specified total, while respecting upper and lower constraints on each individual element. ConvolutionalFixedSum provides a foundational technique that is used in the generation of synthetic tasks sets that underpin the performance evaluation of real-time scheduling algorithms and schedulability analysis techniques. The CFS algorithm generates continuous values; however, some use cases, for example considering message and packet scheduling on communications networks, require solutions that are constrained to discrete values. Adapting the CFS algorithm to the discrete case is non-trivial, with simple rounding to the nearest lattice point producing a non-uniform distribution. In this paper, we present the Discrete-ConvolutionalFixedSum (DCFS) algorithm, which solves this problem.