BASIC CONCEPTS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 28

D i

th

first k

instance

instance

C

i

τ i

t

φ φ + (k-1) T i

i i

T i

(a)

D D i

i

C i C i

J

i

t

a d i1 a d i2

i1 i2

(b)

Figure 2.5 Sequence of instances for a periodic task (a) and an aperiodic job (b).

Another timing characteristic that can be specified on a real-time task concerns the
regularity of its activation. In particular, tasks can be defined as periodic or aperiodic .
Periodic tasks consist of an infinite sequence of identical activities, called instances or
jobs , that are regularly activated at a constant rate. For the sake of clarity, from now
on, a periodic task will be denoted by τ i , whereas an aperiodic job by J i . The generic
k th job of a periodic task τ i will be denoted by τ i,k .

The activation time of the first periodic instance ( τ i, 1 ) is called phase .If φ i is the phase
of task τ i , the activation time of the k th instance is given by φ i +( k 1) T i , where T i

is the activation period of the task. In many practical cases, a periodic process can be
completely characterized by its phase φ i , its computation time C i , its period T i , and
its relative deadline D i .

−

Aperiodic tasks also consist of an infinite sequence of identical jobs (or instances);
however, their activations are not regularly interleaved. An aperiodic task where con-
secutive jobs are separated by a minimum inter-arrival time is called a sporadic task .
Figure 2.5 shows an example of task instances for a periodic and an aperiodic task.

2.2.2 PRECEDENCE CONSTRAINTS

In certain applications, computational activities cannot be executed in arbitrary order
but have to respect some precedence relations defined at the design stage. Such prece-
dence relations are usually described through a directed acyclic graph G , where tasks