A Continuous-Time Markov Chain (CTMC) is a mathematical model used to describe systems that transition between different states over continuous time. In a CTMC, the future state of the system depends only on its current state and not on the sequence of events that preceded it. This property is known as the Markov property. The transitions between states occur at random times, which are typically modeled using exponential distributions. CTMCs are widely used in various fields, including queueing theory, reliability engineering, and population dynamics. They help analyze systems where events happen continuously, such as customer arrivals at a service center or failures in machinery. By understanding the behavior of CTMCs, researchers can predict long-term behavior and optimize system performance.