BASIC CONCEPTS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 42

v(f )
i

v(f )
i

soft

non real−time

f i f i

d

i

v(f )
i

v(f )
i

on−time

firm

f i f i

d d

i i

Figure 2.17 Example of cost functions for different types of tasks.

In other cases (d), executing a task after its deadline does not cause catastrophic con-
sequences, but there is no benefit for the system, thus the utility function is zero after
the deadline.

When utility functions are defined on the tasks, the performance of a scheduling al-
gorithm can be measured by the cumulative value , given by the sum of the utility
functions computed at each completion time:

n

Cumulative value = v ( f i ) .

i =1

This type of metrics is very useful for evaluating the performance of a system during
overload conditions, and it is considered in more detail in Chapter 9.

2.4 SCHEDULING ANOMALIES

In this section we describe some singular examples that clearly illustrate that real-
time computing is not equivalent to fast computing, since, for example, an increase of
computational power in the supporting hardware does not always cause an improve-
ment of performance. These particular situations, called Richard's anomalies, were
described by Graham in 1976 and refer to task sets with precedence relations executed
in a multiprocessor environment.