Hybrid Metaheuristic Approach for Scheduling of Aperiodic OS Tasks - Complex System Modelling and Control Through Intelligent Soft Computations - page 838

Running Example

To more illustrate this point and according to the expression ( 13 ), we have the
following expression after changing the variables WCETi, i , WCET j and WCET k by
0.3, 0.2 and 0.5:

) : a þ : b þ : c

0 3 0 2 0 5 1

in this case and in order to keep and guarantee this disparity, thus mathematically
the following conditions must be satis ed:

a has to be ≤ 3, that means a 2f 0 ; 1 ; 2 ; 3 g

b has to be ≤ 5, that means b 2f 0 ; 1 ; 2 ; 3 ; 4 ; 5 g

ʳ has to be ≤ 2, that means c 2f 0 ; 1 ; 2 g

In this case, we shall have 72 triplet (4 × 6 × 3), that means 72 possibilities for a , b

and c combinations.

Example (0, 0, 0); (0, 0, 1); (3, 0, 0); (1, 1, 1). But, not all

these mentioned combinations satisfy the basic condition for real-time task
scheduling. There are some combinations, which cannot satisfy the basic utilization
condition. So, the intelligent proposed agent will propose to the user the appropriate
combinations which can

… (2, 2, 0); (2, 1, 0); …

fit to the basic condition.

Second solution

The agent proceeds as a second solution to of the Poisson

distribution to model the arrival of aperiodic tasks. Indeed, according to the law of
mathematical probability, to have certain event it is necessary that the following
formula should be satis

nd the parameter k

ed:

n 2 Þþ

n i 1 Þþ n 3 Þ ¼

P ð X i ¼ P ð X j ¼ P ð X k ¼ 1 ð 14 Þ

By applying the Poisson law during one time unit with a mean of k . We will nd

the value of this parameter in order to reach the system ' s feasibility after a

λ

recon guration scenario was applied.

According to the law of mathematical probability and in order to have certain
event, the following expression must be veri ed: