Quantitative causality

Events generated by the execution of a distributed system are related by causality and concurrency. While providing a means of reasoning about the relative occurrence of events, this partial order fails to represent the timeliness of occurrence. In this paper, we develop a novel means of assigning weights to events where the weights are reduced as the temporal proximity to an anchor event decreases. This weight quantifies the strength of the causal or concurrent relationship with respect to an anchor event. Those events that causally succeed the anchor are the focus of this paper with concurrency and causally preceding being part of future work plans. Three methods of computing event weights for causally succeeding events are defined. Each contains a tunable parameter to determine the rate of weight decrease. The methods are piece-wise linear, exponential, and relevant vector difference decay. A case study has been performed that applied quantitative causality to the well-known software engineering problem of feature location. A summary of the case study results is provided to illustrate the utility of quantitative causality for succeeding events.