Activities on Arrow (AOA) diagrams are a traditional network representation technique used in project management to plan, schedule, and control projects. In an AOA diagram, activities are represented by arrows, while events or milestones are represented by nodes (also called circles). Each arrow shows a specific activity that consumes time and possibly resources, and the direction of the arrow indicates the sequence in which activities must be performed. The nodes at the beginning and end of an arrow signify the start and completion of that activity. Thus, in AOA networks, emphasis is placed on activities rather than events, and the logic of the project is conveyed through the connections between arrows. A key feature of AOA diagrams is the use of dummy activities. Dummy activities are represented by dashed arrows and have zero duration. They do not represent actual work but are used to maintain correct precedence relationships between activities when the logic of the project cannot be shown clearly using only real activities. Dummy activities ensure that dependencies are accurately reflected without affecting the overall project duration. This makes AOA diagrams particularly useful for complex projects where multiple activities depend on different combinations of preceding activities. For drawing project networks using AOA diagrams, certain essential information is required. The first requirement is a complete list of activities involved in the project. Each activity should be clearly defined so that there is no ambiguity regarding what work it represents. Second, the sequence or precedence relationships among activities must be known. This information specifies which activities must be completed before others can begin, which activities can be performed concurrently, and which depend on multiple preceding activities. Third, an estimate of the time duration required for each activity is necessary. These durations may be deterministic (single time estimate) or probabilistic, depending on the project management technique being applied. Fourth, identification of the start and end points of the project is required, ensuring that all activities logically connect from the initial event to the terminal event. In some cases, additional information such as resource requirements or cost estimates may also be included, but for basic network construction and time analysis, activity list, precedence relationships, and durations are the most critical inputs. Once the AOA network is drawn, time analysis of the network is carried out to determine the project schedule. Time analysis helps in identifying the earliest and latest times at which activities can start and finish without delaying the project. The core components of time analysis are the forward pass, backward pass, and the calculation of different types of slack or float. The forward pass is the process used to determine the earliest possible start