FIXED-PRIORITY SERVERS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 146

C i T

i

Server

τ

3 10 1

C = 2

= 8

s
s

τ

4 15

2

T

τ

1

τ

2

2 2

aperiodic
requests

C s

+2 +2

2
1

0 2 4 6 8 10 12 14 16 18 20 22

Figure 5.18 Example of a high-priority Sporadic Server.

the next replenishment is set at time RT 2 =18. The corresponding replenishment
amount is established when J 2 completes and is equal to RA 2 =2.

5.6.1 SCHEDULABILITY ANALYSIS

The Sporadic Server violates one of the basic assumptions governing the execution
of a standard periodic task. This assumption requires that once a periodic task is the
highest-priority task that is ready to execute, it must execute. Like DS, in fact, SS
defers its execution and preserves its capacity when no aperiodic requests are pend-
ing. However, we show that the replenishment rule used in SS compensates for any
deferred execution and, from a scheduling point of view, SS can be treated as a normal
periodic task with a period T s and an execution time C s . In particular, the following

theorem holds [SSL89]:

Theorem 5.1 (Sprunt, Sha, Lehoczky) A periodic task set that is schedulable with a
task τ i is also schedulable if τ i

is replaced by a Sporadic Server with the same period

and execution time.