DYNAMIC PRIORITY SERVERS - Hard Real-Time Computing Systems: Predictable Scheduling Algorithms and Applications - page 199

110

100 without overhead

with overhead

90

80

70

60

50

40

0 20 40 60 80 100 120

Server period

Figure 6.21 Worst-case response time of a CBS as a function of the period.

Figure 6.21 illustrates the worst-case response time of a CBS as a function of the
period, with and without overhead. Equation (6.9) has been plotted for C i =10,
U s =0 . 25, and =0 . 2. As is clear from the plot, the overhead prevents using
small values of the period; hence, it is interesting to find the value of the server period
that minimizes the response time. Note that for computing the probability distribution
function of the response time, we actually need to express the response time as a
function of the job execution time C i .

Figure 6.22 illustrates the worst-case response time of a CBS as a function of the job
execution time. As shown in Figure 6.22, the response time R i can be upper bounded
by the following linear function

T s
Q s −

R ub
i

= T s − Q s + +

C i

(6.10)

and lower bounded by

T s
Q s −

R l i

=

C i .

(6.11)