Multi-stage systems are processes that involve several distinct stages or steps, each contributing to the overall outcome. These systems are commonly found in various fields, such as engineering, manufacturing, and biology. Each stage typically has specific functions and outputs that feed into the next stage, creating a chain of operations that enhances efficiency and effectiveness. In a multi-stage system, the performance of each stage can significantly impact the entire process. For example, in a production line, if one stage is delayed, it can cause bottlenecks that affect subsequent stages. Understanding and optimizing each stage is crucial for improving the overall performance of the system.