Give the taxonomy of real-time application and briefly explain with suitable examples.

Real-time applications can be classified into two main categories: Hard Real-Time Systems and Soft Real-Time Systems.

1. Hard Real-Time Systems: These are systems where it is absolutely critical that responses occur within the required deadline. In these systems, failure to respond in time is considered a system failure. For example, in an air traffic control system, the real-time response to incoming data (like the position of an aircraft) is critical. If the system fails to respond in time, it could lead to catastrophic results.

2. Soft Real-Time Systems: These are systems where the performance of the system degrades if responses do not occur in a timely manner, but it does not fail completely. For example, in a video streaming application, if the data is not processed in real time, the video playback may be choppy or delayed, but it does not cause a complete system failure.

Each of these categories can be further divided based on other factors such as the predictability of tasks, the criticality of tasks, and the nature of the tasks (periodic, aperiodic, or sporadic).

For example, within hard real-time systems, there can be a further classification into mission-critical systems (like air traffic control or nuclear reactor control) and safety-critical systems (like a car's braking system or a pacemaker).

Similarly, within soft real-time systems, there can be a further classification into time-sensitive systems (like a video streaming service or an online gaming platform) and non-time-sensitive systems (like an email server or a file download service).

In summary, the taxonomy of real-time applications can be quite complex, with many different factors influencing the classification. However, the most basic classification is into hard and soft real-time systems, based on the criticality of timely responses.