\(D_i = \max\{A_i, D_{i-1}\} + S_i\)
num = 10
X = rng.exponential(scale=1 / labda, size=num)
S = rng.exponential(scale=1 / mu, size=num)
X[0] = S[0] = 0
A = X.cumsum()
D = np.zeros_like(X)
for i in range(1, num):
D[i] = max(A[i], D[i - 1]) + S[i]
J = D - A # sojourn times
W = J - S # waiting times
print(J.mean(), J.var())
Define:
Assuming the limits for \(t \to \infty\) exist
Expected waiting time for \(G/G/1\) queue: \(\E W \approx \frac{C_a^2+C_e^2}2 \frac\rho{1-\rho} \E S\)
Modify \(C_a^2\) and \(\E S\) for systems with