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MM3&H2H23
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###The following portion contains code to evaluate RT of M/M/3 queues (enveloped between portions to read the lambda and mu values from our specific data files (.csv files))
import pandas as pd
import numpy as np
import math
inp_fn = "allfitw92-SH-iodepth16-clsize4-L2"
df_iat = pd.read_csv(inp_fn+"_IAT.csv")
df_iat1 = df_iat
df_st = pd.read_csv(inp_fn+"_ST.csv")
f_out = open(inp_fn+".csv","w")
df_exp_iat = df_iat[df_iat.DistName == "exponential"]
df_exp_st = df_st[df_st.DistName == "exponential"]
#Exponential (M/M/3) code here
subtrace = 0
r_line = ""
while True:
df_exp_subtrace_iat = df_exp_iat[df_exp_iat.fname.str.contains("_"+str(subtrace))]
df_exp_subtrace_st = df_exp_st[df_exp_st.fname.str.contains("_"+str(subtrace))]
if not df_exp_subtrace_st.shape[0]:
break
lam = 1/df_exp_subtrace_iat.Params_1.values[0]
mu = 1/df_exp_subtrace_st.Params_1.values[0]
k = 3
rho = lam/(k*mu)
if rho > 1 :
rt = "Unstable"
#print("Unstable queue")
else :
p0 = 0
for i in range(k) :
p0 += ((lam/mu)**i)/math.factorial(i)
p0 += (pow(k,k)/math.factorial(k)) * pow(rho, k)/ (1 - rho)
p0 = 1 / p0
#print("p0 is : {}" .format(p0))
p1 = p0 * ((lam/mu)**1)/math.factorial(1)
#print("p1 is : {}" .format(p1))
p2 = p0 * ((lam/mu)**2)/math.factorial(2)
#print("p2 is : {}" .format(p2))
#Compute expected long term length L
pi_w = 1 - p0 - p1 - p2
L = (lam/mu) + (rho*pi_w)/ (1 - rho)
#print("Long term expected length : ", L)
#Compute long term expected response time
W = L/lam
#print("Long term expected response time : ", W)
rt = W
r_line += str(rt)+", "
subtrace = subtrace +1
print("Exponential M/M/3")
print(r_line)
###Here ends the M/M/3 code
###The following portion contains code to evaluate RT of H2/H2/3 queues (enveloped between portions to read the lambda and mu values from our specific data files (.csv files))
subtrace = 0
r_line = ""
while True:
df_hyperexp_subtrace_iat = df_hyperexp_iat[df_hyperexp_iat.fname.str.contains("_"+str(subtrace))]
df_hyperexp_subtrace_st = df_hyperexp_st[df_hyperexp_st.fname.str.contains("_"+str(subtrace))]
if not df_hyperexp_subtrace_st.shape[0]:
break
#Declaring parameters
lam1 = 1/df_hyperexp_subtrace_iat.Params_1.values[0]
lam2 = 1/df_hyperexp_subtrace_iat.Params_2.values[0]
mu1 = 1/df_hyperexp_subtrace_st.Params_1.values[0]
mu2 = 1/df_hyperexp_subtrace_st.Params_2.values[0]
p = df_hyperexp_subtrace_iat.Params_3.values[0]
q = df_hyperexp_subtrace_st.Params_3.values[0]
b1 = 3*mu1*(1-q)
b2 = 3*mu2*(1-q)
b3 = 3*mu1*q
b4 = 3*mu2*q
f1 = lam1*(1-p)
f2 = lam2*(1-p)
f3 = lam1*p
f4 = lam2*p
#Initializing forward, backward and initial arrays
L_0 = np.transpose(np.array([[-(lam1), 0],
[0, -(lam2)]]))
# print(L_0)
#F_0 = np.array([[lam1*p*q, lam1*(1-p)*q, lam1*p*(1-q), lam1*(1-p)*(1-q)],
# [lam2*(1-p)*(1-q), lam2*p*(1-q), lam2*p*q, lam2*(1-p)*q]])
F_0 = np.array([[lam1*p*q, lam1*(1-p)*q, lam1*p*(1-q), lam1*(1-p)*(1-q)],
#[lam2*p*q, lam2*(p)*(1-q), lam2*(1-p)*(q), lam2*(1-p)*(1-q)],
[lam2*(p)*(q), lam2*(1-p)*(q), lam2*(p)*(1-q), lam2*(1-p)*(1-q)]])
# print(F_0)
B_0 = np.array([[mu1, 0],
[mu1, 0],
[0, mu2],
[0, mu2]])
# print(B_0)
L = np.array([[-(lam1 + 3*mu1), 0, 0, 0],
[0, -(lam2 + 3*mu1), 0, 0],
[0, 0, -(lam1 + 3*mu2), 0],
[0, 0, 0, -(lam2 + 3*mu2)]])
L_1 = np.array([[-(lam1 + mu1), 0, 0, 0],
[0, -(lam2 + mu1), 0, 0],
[0, 0, -(lam1 + mu2), 0],
[0, 0, 0, -(lam2 + mu2)]])
L_2 = np.array([[-(lam1 + 2*mu1), 0, 0, 0],
[0, -(lam2 + 2*mu1), 0, 0],
[0, 0, -(lam1 + 2*mu2), 0],
[0, 0, 0, -(lam2 + 2*mu2)]])
# print(L)
# print(L_1)
# print(L_2)
F = np.array([[f3, f1, 0, 0],
[f4, f2, 0, 0],
[0, 0, f3, f1],
[0, 0, f4, f2]])
# print(F)
B = np.array([[b3, 0, b1, 0],
[0, b3, 0, b1],
[b4, 0, b2, 0],
[0, b4, 0, b2]])
B_1 = np.array([[2*mu1*q, 0, 2* mu1*(1-q), 0],
[0, 2*mu1*q, 0, 2*mu1*(1-q)],
[2*mu2*q, 0, 2*mu2*(1-q), 0],
[0, 2*mu2*q, 0, 2*mu2*(1-q)]])
# print(B)
# print(B_1)
R_0 = np.zeros((4, 4))
# print(R_0)
# Computing matrix R
R_prev = R_0
n = 0
flag = 0
while flag == 0 :
diff = []
if n > 0:
R_prev = R
R_2 = np.matmul(R_prev,R_prev)
R_mid = -(np.matmul(R_2,B) + F)
#print(R_mid)
R = np.matmul(R_mid, np.linalg.inv(L))
for (i,j) in zip(R_prev, R) :
for (k,l) in zip(i,j) :
diff.append(abs(k-l))
max = np.max(diff)
#print("Max is", max)
if (max < 10**-7) :
flag =1
break
n += 1
#print(R,n)
#Computing steady state distribution for state 0 and 1 and 2
#Creating (I - R)^-1 = psi
I = np.eye(4)
psi_full = np.linalg.inv(I - R)
psi = np.matmul(psi_full, np.ones((4,1), dtype=np.int64))
psi = np.vstack([np.ones((10,1), dtype=np.int64), psi])
# print("Psi :",psi)
#Creating L + RB
RB = np.matmul(R, B)
LRB = np.add(L, RB)
# print(LRB)
#Creating stacked version of [0 0 F L+RB]T = phi
phi_3 = np.vstack([np.zeros((2, 4)), np.zeros((4, 4)), F, LRB])
#Creating stacked version of [0 F L2 B]T = phi
phi_2 = np.vstack([np.zeros((2, 4)), F, L_2, B])
#Creating stacked version of [F_0 L_1 B_1 0]
phi_1 = np.vstack([F_0, L_1, B_1, np.zeros((4, 4))])
phi = np.hstack([phi_1, phi_2, phi_3])
# print("Phi :",phi)
#Solving for pi_0 and pi_1 and pi_2
A = np.array([0, -(lam2), 0, 0, mu2, mu2, 0, 0, 0, 0, 0, 0, 0, 0])
A = A[..., None]
A = np.hstack([psi,A, phi])
b = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
# print(A,b)
"""
steady_pi = np.linalg.solve(np.transpose(A), b)
print(steady_pi)
"""
steady_pi = np.matmul(b, np.linalg.inv(A))
# print(steady_pi)
# print(b.shape)
lam_avg = (p/(lam1) + (1-p)/(lam2))
pi_1 = [steady_pi[2], steady_pi[3], steady_pi[4], steady_pi[5]]
# print("pi_1 : ", pi_1)
pi_2 = [steady_pi[6], steady_pi[7], steady_pi[8], steady_pi[9]]
# print("pi_2 : ", pi_2)
pi_3 = [steady_pi[10], steady_pi[11], steady_pi[12], steady_pi[13]]
# print("pi_3 : ", pi_3)
squareI_R = np.matmul((I - R), (I - R))
W_num_1 = np.matmul(np.linalg.inv(squareI_R), np.ones((4,1), dtype=int))
W_num_1 = np.matmul(R, W_num_1)
#print(W_num_1)
W_num_2 = 3*np.matmul(np.linalg.inv(I - R), np.ones((4,1), dtype=int))
#print(W_num_2)
W_num = np.dot(pi_3, W_num_1 + W_num_2)
W_num = W_num + np.matmul(pi_1, np.ones((4,1), dtype=int)) + 2*np.matmul(pi_2, np.ones((4,1), dtype=int))
W = W_num * lam_avg
#print("The mean response time is: ", W)
subtrace+=1
r_line += str(W[0])+", "
print("H2/H2/3 mean RT :")
print(r_line)
###Here ends the H2/H2/3 code
###Remember you can execute M/H2/3 through simple changes in the input of the H2/H2/1 code (i.e., lam1 = lam2)
###The following portion contains code to evaluate RT of M/H2/3 queues (enveloped between portions to read the lambda and mu values from our specific data files (.csv files))
subtrace = 0
r_line = ""
while True:
#df_hyperexp_subtrace_iat = df_hyperexp_iat[df_hyperexp_iat.fname.str.contains("_"+str(subtrace))]
df_exp_subtrace_iat = df_exp_iat[df_exp_iat.fname.str.contains("_"+str(subtrace))]
df_hyperexp_subtrace_st = df_hyperexp_st[df_hyperexp_st.fname.str.contains("_"+str(subtrace))]
if not df_hyperexp_subtrace_st.shape[0]:
break
#print(df_exp_subtrace_iat.Params_1.values)
#Declaring parameters
lam1 = 1/df_exp_subtrace_iat.Params_1.values[0]
lam2 = 1/df_exp_subtrace_iat.Params_1.values[0]
mu1 = 1/df_hyperexp_subtrace_st.Params_1.values[0]
mu2 = 1/df_hyperexp_subtrace_st.Params_2.values[0]
#p = df_hyperexp_subtrace_iat.Params_3.values[0]
q = df_hyperexp_subtrace_st.Params_3.values[0]
b1 = 3*mu1*(1-q)
b2 = 3*mu2*(1-q)
b3 = 3*mu1*q
b4 = 3*mu2*q
f1 = lam1*(1-p)
f2 = lam2*(1-p)
f3 = lam1*p
f4 = lam2*p
#Initializing forward, backward and initial arrays
L_0 = np.transpose(np.array([[-(lam1), 0],
[0, -(lam2)]]))
# print(L_0)
#F_0 = np.array([[lam1*p*q, lam1*(1-p)*q, lam1*p*(1-q), lam1*(1-p)*(1-q)],
# [lam2*(1-p)*(1-q), lam2*p*(1-q), lam2*p*q, lam2*(1-p)*q]])
F_0 = np.array([[lam1*p*q, lam1*(1-p)*q, lam1*p*(1-q), lam1*(1-p)*(1-q)],
#[lam2*p*q, lam2*(p)*(1-q), lam2*(1-p)*(q), lam2*(1-p)*(1-q)],
[lam2*(p)*(q), lam2*(1-p)*(q), lam2*(p)*(1-q), lam2*(1-p)*(1-q)]])
# print(F_0)
B_0 = np.array([[mu1, 0],
[mu1, 0],
[0, mu2],
[0, mu2]])
# print(B_0)
L = np.array([[-(lam1 + 3*mu1), 0, 0, 0],
[0, -(lam2 + 3*mu1), 0, 0],
[0, 0, -(lam1 + 3*mu2), 0],
[0, 0, 0, -(lam2 + 3*mu2)]])
L_1 = np.array([[-(lam1 + mu1), 0, 0, 0],
[0, -(lam2 + mu1), 0, 0],
[0, 0, -(lam1 + mu2), 0],
[0, 0, 0, -(lam2 + mu2)]])
L_2 = np.array([[-(lam1 + 2*mu1), 0, 0, 0],
[0, -(lam2 + 2*mu1), 0, 0],
[0, 0, -(lam1 + 2*mu2), 0],
[0, 0, 0, -(lam2 + 2*mu2)]])
# print(L)
# print(L_1)
# print(L_2)
F = np.array([[f3, f1, 0, 0],
[f4, f2, 0, 0],
[0, 0, f3, f1],
[0, 0, f4, f2]])
# print(F)
B = np.array([[b3, 0, b1, 0],
[0, b3, 0, b1],
[b4, 0, b2, 0],
[0, b4, 0, b2]])
B_1 = np.array([[2*mu1*q, 0, 2* mu1*(1-q), 0],
[0, 2*mu1*q, 0, 2*mu1*(1-q)],
[2*mu2*q, 0, 2*mu2*(1-q), 0],
[0, 2*mu2*q, 0, 2*mu2*(1-q)]])
# print(B)
# print(B_1)
R_0 = np.zeros((4, 4))
# print(R_0)
# Computing matrix R
R_prev = R_0
n = 0
flag = 0
while flag == 0 :
diff = []
if n > 0:
R_prev = R
R_2 = np.matmul(R_prev,R_prev)
R_mid = -(np.matmul(R_2,B) + F)
#print(R_mid)
R = np.matmul(R_mid, np.linalg.inv(L))
for (i,j) in zip(R_prev, R) :
for (k,l) in zip(i,j) :
diff.append(abs(k-l))
max = np.max(diff)
#print("Max is", max)
if (max < 10**-7) :
flag =1
break
n += 1
#print(R,n)
#Computing steady state distribution for state 0 and 1 and 2
#Creating (I - R)^-1 = psi
I = np.eye(4)
psi_full = np.linalg.inv(I - R)
psi = np.matmul(psi_full, np.ones((4,1), dtype=np.int64))
psi = np.vstack([np.ones((10,1), dtype=np.int64), psi])
# print("Psi :",psi)
#Creating L + RB
RB = np.matmul(R, B)
LRB = np.add(L, RB)
# print(LRB)
#Creating stacked version of [0 0 F L+RB]T = phi
phi_3 = np.vstack([np.zeros((2, 4)), np.zeros((4, 4)), F, LRB])
#Creating stacked version of [0 F L2 B]T = phi
phi_2 = np.vstack([np.zeros((2, 4)), F, L_2, B])
#Creating stacked version of [F_0 L_1 B_1 0]
phi_1 = np.vstack([F_0, L_1, B_1, np.zeros((4, 4))])
phi = np.hstack([phi_1, phi_2, phi_3])
# print("Phi :",phi)
#Solving for pi_0 and pi_1 and pi_2
A = np.array([0, -(lam2), 0, 0, mu2, mu2, 0, 0, 0, 0, 0, 0, 0, 0])
A = A[..., None]
A = np.hstack([psi,A, phi])
b = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
# print(A,b)
"""
steady_pi = np.linalg.solve(np.transpose(A), b)
print(steady_pi)
"""
steady_pi = np.matmul(b, np.linalg.inv(A))
# print(steady_pi)
# print(b.shape)
lam_avg = (p/(lam1) + (1-p)/(lam2))
pi_1 = [steady_pi[2], steady_pi[3], steady_pi[4], steady_pi[5]]
# print("pi_1 : ", pi_1)
pi_2 = [steady_pi[6], steady_pi[7], steady_pi[8], steady_pi[9]]
# print("pi_2 : ", pi_2)
pi_3 = [steady_pi[10], steady_pi[11], steady_pi[12], steady_pi[13]]
# print("pi_3 : ", pi_3)
squareI_R = np.matmul((I - R), (I - R))
W_num_1 = np.matmul(np.linalg.inv(squareI_R), np.ones((4,1), dtype=int))
W_num_1 = np.matmul(R, W_num_1)
#print(W_num_1)
W_num_2 = 3*np.matmul(np.linalg.inv(I - R), np.ones((4,1), dtype=int))
#print(W_num_2)
W_num = np.dot(pi_3, W_num_1 + W_num_2)
W_num = W_num + np.matmul(pi_1, np.ones((4,1), dtype=int)) + 2*np.matmul(pi_2, np.ones((4,1), dtype=int))
W = W_num * lam_avg
#print("The mean response time is: ", W)
subtrace+=1
r_line += str(W[0])+", "
print("M/H2/3 mean RT :")
print(r_line)