41 lines
1.4 KiB
Mathematica
41 lines
1.4 KiB
Mathematica
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function [nstates, Qav, Qre, pi0, av_indx] = CTMC_CR(nm,n,lambdaB,lambdaR,muB,muR)
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%CTMC_CR infinitesimal generator matrix and initial probability vector
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% of the Component Redundancy (CR) Continuous Time Markov Chain (CTMC)
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% nm : number of hot standby (n+m>=n+1)
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% n : number of required rectifiers or batteries to address load
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% lambdaB : battery failure rate
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% lambdaR : rectifier failure rate
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% muB : battery recovery rate
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% muR : rectifier recovery rate
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aus = nm-n+2;% number of states only considering rectifiers
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nstates = (nm-n+2)^2;
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eaus = zeros(1,nm-n+2);
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eaus(end) = 1;
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av_indx = find(kron(ones(1,nm-n+2), eaus)+kron(eaus, ones(1,nm-n+2))<1);
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% define rectifiers' and batteries' behavior
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Rr_failure = diag(lambdaR*[nm:-1:n],1);
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Rb_failure = diag(lambdaB*[nm:-1:n],1);
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Rre = kron(Rr_failure, eye(aus, aus)) + kron(eye(aus, aus), Rb_failure);
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Rre(av_indx(2:end),1) = muB;
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Rav = Rre;
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Rav(2:end,1) = muB;
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% % Plotting reliability model
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% D= digraph(Rre);
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% Plot = plot(D);
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% highlight(Plot,[5,10,15,20,21,22,23,24,25],'NodeColor','r');
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% highlight(Plot,'Edges',[inedges(D,5)',inedges(D,10)',inedges(D,15)',inedges(D,20)',...
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% inedges(D,21)',inedges(D,22)',inedges(D,23)',inedges(D,24)',inedges(D,25)'],'EdgeColor','r');
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Qav = Rav - diag(Rav*ones(nstates,1));
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Qre = Rre - diag(Rre*ones(nstates,1));
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pi0 = zeros(1,nstates);
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pi0(1) = 1;
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end
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