FIXED-PRIORITY SERVERS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 136

1

0.95 DS bound

RM bound

0.9

0.85

0.8

0.75

0.7

0.65

0.6

0 0.2 0.4 0.6 0.8 1

Server Utilization factor Us

Figure 5.11 Schedulability bound for periodic tasks and DS as a function of the server
utilization factor U s .

In summary, given a set of n periodic tasks with utilization U p and a Deferrable Server
with utilization U s , respectively, the schedulability of the periodic task set is guaran-
teed under RM if

n K 1 /n 1 . U p ≤ − (5.13)

where

U s +2
2 U s +1 ,

K =

Using the Hyperbolic Bound, the guarantee test for a task set in the presence of a
Deferrable Server can be performed as follows:

n

U s +2
2 U s +1 .

( U i +1) ≤ (5.14)

i =1