Jackson

Jackson

%パラメタ設定
N = 3;
P = [0 0 1; 0 0 0.6; 0.5 0 0]
lambda = [2; 1; 0]
mu = [5; 4; 6]

%[p^t-E]α = -λ
A = P.' - eye(N)
alpha = linsolve(A, -lambda)
rho = alpha ./ mu

%平均系内人数
L = rho ./ (1 - rho)
fplot(@(x) x/(1-x), [0 0.97])

%人数分布
n = [6, 1, 2]
%nとした場合の定常分布(周辺)を求める
for i = 1:N
    i
    rho(i)
    n(i)
    pi(i) = (1-rho(i))*rho(i)^n(i);
end
pi
%rho(i)を使い、人数を変化させた時の定常分布のグラフ
figure
hold on
for i = 1:N
    fplot(@(x) (1-rho(i))*rho(i)^x, [0 30])
end
legend
hold off
%Jackson定常分布
jpi = 1;
for i = 1:N
    jpi = jpi * pi(i);
end
jpi