Response time analysis WCRT Liu and Layland, implementation

I need to compute the WCRT for tasks using the Liu and Layland equation, how is this done in matlab.

Here c1=2, c2=2, c3=5. Thanks!

Answer 1

[Filip Markovic]

Hi Eli,

Maybe this can help:

Here I defined the function "rt", and it uses the "rtsum" function which is described after the "rt" function. You just need to provide the array C of task execution times, and also the array T of task periods. If you use fixed-priority scheduling, then just sort C and T arrays in the increasing priority order. I implemented this without using the recursion, I tried to optimise the code a bit. Maybe it can be optimised even more.

function [Ri] = rt(i,C,T,D_i)
% Function rt(i,C,T,D_i) computes response time of the i-th task in the taskset
% given the index of the task, array of WCET values and array of periods.
% It stops immediately if R_i is greater than D_i, and returns R_i.
%   Syntax:
%      Ri = rt(i,C,T)
%   Input:
%      i, index of the task under analysis
%      C, array of WCET values
%      T, Array of minimum inter-arrival times
%      D_i, Relative deadline of the i-th task
%   Output:
%      Ri, response time of tau_i

Ri = C(i);
R_i_next = rtsum(i,Ri,C,T);

while(Ri ~= R_i_next && Ri < D_i )
    Ri = R_i_next;
    R_i_next = rtsum(i,Ri,C,T);
end

And here is the "rtsum" function:

function [R] = rtsum(i,t,C,T)
% Function rtsum(i,t,C,T) computes the WCET workload for the i-th task, given the
% duration 't', array 'C' of WCETs values, and array 'T' of periods
%   Syntax:
%      R = Rsum(i,t,C,T)
%   Input:
%      i, index of the task under analysis
%      t, time duration under analysis
%      C, array of WCET values
%      T, Array of minimum inter-arrival times
%   Output:
%      R, response time sum 
sum = C(i);
for h = 1:i-1
    sum = sum + ceil(t/T(h)) * C(h);
end
R = sum;