HANDLING OVERLOAD CONDITIONS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 333

Although these approaches may lead to interesting results in specific applications, a
more general framework can be used to avoid a proliferation of policies and treat
different applications in a uniform fashion.

The elastic model presented in this section (originally proposed by Buttazzo, Abeni,
and Lipari [BAL98] and later extended by Buttazzo, Lipari, Caccamo, and Abeni
[BLCA02]), provides a novel theoretical framework for flexible workload manage-
ment in real-time applications.

EXAMPLES

To better understand the idea behind the elastic model, consider a set of three periodic
tasks, with computation times C 1 =10, C 2 =10, and C 3 =15and periods T 1 =20,
T 2 =40, and T 3 =70. Clearly, the task set is schedulable by EDF because

U p = 10

20 + 10 40 + 15

70 =0 . 964 < 1 .

To allow a certain degree of flexibility, suppose that tasks are allowed to run with
periods ranging within two values, reported in Table 9.2.

T i min T i max

τ 1 20 25

τ 2 40 50

τ 3 35 80

Table 9.2 Period ranges for the task set considered in the example.

Now, suppose that a new task τ 4 , with computation time C 4 =5and period T 4 =30,
enters the system at time t . The total processor utilization of the new task set is

10

20 + 10 40 + 15

5
30 =1 . 131 > 1 .

U p =

70 +

In a rigid scheduling framework, τ 4 should be rejected to preserve the timing behavior
of the previously guaranteed tasks. However, τ 4 can be accepted if the periods of the
other tasks can be increased in such a way that the total utilization is less than one. For
example, if T 1 can be increased up to 23, the total utilization becomes U p =0 . 989,

and hence τ 4 can be accepted.