This paper presents a graph-theoretic model that supports the design andanalysis of data flow within digital musical instruments (DMIs). The state ofthe art in DMI design fails to provide any standards for the scheduling ofcomputations within a DMI's data flow. It does not provide a theoreticalframework within which we can analyze different scheduling protocols and theirimpact on the DMI's performance. Indeed, the mapping between the DMI's sensoryinputs and sonic outputs is classically treated as a black box. DMI designersand builders are forced to design and schedule the flow of data through thisblack box on their own. Improper design of the data flow can produceundesirable results, ranging from overflowing buffers that cause system crashesto misaligned sensory data that result in strange or disordered sonic events.In this paper, we attempt to remedy this problem by providing a framework forthe design and analysis of the DMI data flow. We also provide a schedulingalgorithm built upon that framework that guarantees desirable properties forthe resulting DMI.