Based on the concept that task progress is the growth of developments in a structured work and activity process, mathematical models ore developed to define, identify, and follow work progress and resourco utilization patterns. These models ore developed from the Pearl-Roed Logistic function and describe operating characteristics in the micro resource allocation and control problem. The model3 are the Task Operating Characteristic (TOC) curve and the Resource Operating Characteristic (ROC) curve. A second paper extends the theoretical results and gives examples (Braswell 1971).