What is a real-time system?

This book is about the design of certain kinds of reactive systems. A reactive system interacts with its environment by reacting to inputs from the environment with certain outputs. Usually, a reactive system is not supposed to stop but should be continuously ready for such interactions. In the real world there are plenty of reactive systems around. A vending machine for drinks should be continuously ready for interacting with its customers. When a customer inputs suitable coins and selects “coffee” the vending machine should output a cup of hot coffee. A traffic light should continuously be ready to react when a pedestrian pushes the button indicating the wish to cross the street. A cash machine of a bank should continuously be ready to react to customers' desire for extracting money from their bank account.

Reactive systems are seen in contrast to transformational systems, which are supposed to compute a single input–output transformation that satisfies a certain relation and then terminate. For example, such a system could input two matrices and compute its product.

We wish to design reactive systems that interact in a well-defined relation to the real, physical time. A real-time system is a reactive system which, for certain inputs, has to compute the corresponding outputs within given time bounds. An example of a real-time system is an airbag. When a car is forced into an emergency braking its airbag has to unfold within 300 milliseconds to protect the passenger's head. Thus there is a tight upper time bound for the reaction. However, there is also a lower time bound of 100 milliseconds.