FIXED-PRIORITY SERVERS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 141

C T

Server i i

τ

2 10 C = 1

1

s

τ

12 20 T

s = 5

2

aperiodic
requests

2 1

C

s

1

τ

1

1

2
1

τ

2

0 2 4 6 8 10 12 14 16 18 20

Figure 5.15 Example of aperiodic service under a PE server.

lowest-priority level and τ 1 is still active, J 1 is preempted by τ 1 and is resumed at time
t =13, when τ 1 completes.

5.5.1 SCHEDULABILITY ANALYSIS

Considering that, in the worst case, a PE server behaves as a periodic task, the schedu-
lability bound for a set of periodic tasks running along with a Priority Exchange server
is the same as the one derived for the Polling Server. Hence, assuming that PE is the
highest-priority task in the system, we have
U lub = U s + n K 1 /n 1 . − (5.17)

where

K = 2

U s +1 .
Thus, given a set of n periodic tasks and a Priority Exchange server with utilization
factors U p and U s , respectively, the schedulability of the periodic task set is guaranteed
under RM if

n 2
U s +1

1 .

1 /n

U p ≤ − (5.18)