Un modelo de colas
May 24, 2022
1 Un modelo de colas
[1]: from math import*
import numpy as np
import sympy as sp
from sympy import Matrix
from numpy import matrix
from sympy import poly
from sympy.abc import x,y
[2]: m = 10
p = 0.45
q = 0.4
[3]: M = np.zeros((m+1, m+1)); M
[3]: array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
[4]: M[0,0] = 1-p
M[1,0] = p
M[m-1,m] = q
M[m,m] = 1-q
[5]: M
[5]: array([[0.55, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0.45, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
1
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.4 ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.6 ]])
[6]: for i in range(1,m):
M[i-1,i] = (1-p)*q
M[i,i] = (1-p)*(1-q)+p*q
M[i+1,i] = p*(1-q)
[7]: M
[7]: array([[0.55, 0.22, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0.45, 0.51, 0.22, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0.27, 0.51, 0.22, 0. , 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0.27, 0.51, 0.22, 0. , 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0.27, 0.51, 0.22, 0. , 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0.27, 0.51, 0.22, 0. , 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0.27, 0.51, 0.22, 0. , 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0.27, 0.51, 0.22, 0. , 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.27, 0.51, 0.22, 0. ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.27, 0.51, 0.4 ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.27, 0.6 ]])
[8]: N = Matrix(M)
[9]: N
[9]: 0.55 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.45 0.51 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.27 0.51 0.22 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.27 0.51 0.22 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.27 0.51 0.22 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.27 0.51 0.22 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.27 0.51 0.22 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.27 0.51 0.22 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.27 0.51 0.22 0.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.27 0.51 0.4
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.27 0.6
[10]: np.linalg.eig(M)
2
[10]: (array([0.03204345, 0.06772821, 0.1390245 , 0.24516746, 0.37766687,
0.52413948, 0.670461 , 0.8023994 , 1. , 0.97428661,
0.90708302]),
array([[-0.070205 , -0.11193243, -0.1349204 , -0.14573681, 0.15106326,
0.153918 , 0.15555664, -0.15653309, -0.05177876, -0.15741577,
0.1571097 ],
[ 0.16528699, 0.24537205, 0.25204081, 0.20193328, -0.11833275,
-0.01809273, 0.08517504, -0.17958571, -0.1059111 , -0.30358819,
0.25500549],
[-0.21548978, -0.26432521, -0.14903085, 0.05501391, -0.2378142 ,
-0.3159951 , -0.25606008, 0.08149606, -0.1299818 , -0.3187038 ,
0.13890448],
[ 0.26530574, 0.23024149, -0.05801921, -0.31405209, 0.28827518,
0.0018956 , -0.29129507, 0.32871611, -0.15952312, -0.30000498,
-0.06224942],
[-0.31191989, -0.13846141, 0.28073652, 0.31053389, 0.11846127,
0.387934 , 0.1017942 , 0.33687479, -0.19577837, -0.24199213,
-0.28282907],
[ 0.35205274, -0.00421649, -0.4021872 , 0.01161174, -0.4250484 ,
0.02260623, 0.43174395, 0.04431199, -0.24027346, -0.14251074,
-0.43408764],
[-0.38203428, 0.17840643, 0.3336488 , -0.39508781, 0.11028838,
-0.47464791, 0.18997105, -0.3545427 , -0.29488106, -0.00376341,
-0.43638629],
[ 0.39791612, -0.35348035, -0.06902267, 0.46134972, 0.45531029,
-0.0582498 , -0.39130873, -0.52560141, -0.36189949, 0.16695726,
-0.25489966],
[-0.39562436, 0.49165751, -0.29308844, -0.07048505, -0.40922953,
0.5787787 , -0.51855443, -0.26345003, -0.44414937, 0.35696427,
0.07549077],
[ 0.37115409, -0.55457524, 0.57893069, -0.48135314, -0.31263252,
0.10868669, 0.10202544, 0.29490795, -0.54509241, 0.54843306,
0.44908642],
[-0.17644238, 0.28131364, -0.33908806, 0.36627234, 0.37965903,
-0.38683369, 0.390952 , 0.39340604, -0.36793738, 0.39562443,
0.39485521]]))
[11]: T=np.array([[ 0.13749776, 0.21923474, 0.25125616, 0.26279646, 0.26754052,
0.12251924, -0.26956108],
[-0.31816529, -0.42322399, -0.28559976, -0.02014612, 0.26197428,
0.25060753, -0.4720845 ],
[ 0.39713031, 0.29163269, -0.24122259, -0.53965673, -0.24308644,
0.30756379, -0.361224 ],
[-0.45626532, 0.00945001, 0.58084486, -0.03202424, -0.6037404 ,
0.37746465, -0.11891517],
[ 0.48543837, -0.37443754, -0.25858507, 0.65893839, -0.40261706,
0.46325208, 0.21344233],
3
[-0.47506485, 0.64315957, -0.46594009, 0.10859489, 0.27351051,
0.56853664, 0.55855231],
[ 0.22942902, -0.36581547, 0.41924649, -0.43850264, 0.4464186 ,
0.38376223, 0.44979011]])
[12]: S=Matrix(T); S
[12]: 0.13749776 0.21923474 0.25125616 0.26279646 0.26754052 0.12251924 −0.26956108
−0.31816529 −0.42322399 −0.28559976 −0.02014612 0.26197428 0.25060753 −0.4720845
0.39713031
0.29163269 −0.24122259 −0.53965673 −0.24308644 0.30756379 −0.361224
−0.45626532 0.00945001 0.58084486 −0.03202424 −0.6037404 0.37746465 −0.11891517
0.48543837 −0.37443754 −0.25858507 0.65893839 −0.40261706 0.46325208 0.21344233
−0.47506485 0.64315957 −0.46594009 0.10859489 0.27351051 0.56853664 0.55855231
0.22942902 −0.36581547 0.41924649 −0.43850264 0.4464186 0.38376223 0.44979011
[13]: N**100
[13]: 0.0258821157612462 0.025423395551323 0.0243291245855139 0.0228219552248823 0.0211226968436521 0
0.0520023999913425 0.0511181512886818 0.0490086815844942 0.0461029879436538 0.042826559914862 0
0.0610741453954532 0.0601470183082429 0.0579349725673421 0.0548872785200201 0.0514496500141923 0
0.0703112548039316 0.0694402442374455 0.0673616600018429 0.0644967851084575 0.0612637430194901 0
0.0798660947374334 0.0791655877915316 0.0774933778106326 0.0751873209784652 0.0725829518145979 0
0.0901596340846592 0.0897494859408904 0.0887698080810226 0.0874173096772594 0.0858875936110017 0
0.101953674807636 0.101946631712671 0.101928856868114 0.101901960857317 0.101867939520083
0.116413773000679 0.116901084581957 0.118063364665396 0.119663720766125 0.121467301149395
0.135157030835663 0.136193399806297 0.138666599365879 0.142075373205673 0.145922223062756
0.16027996561853 0.161869253525022 0.165662683014818 0.170892943093563 0.17679817167447
0.106899910963431 0.108045747255944 0.110780871454949 0.114552364624588 0.118811169375504
[14]: B=np.array([0.04092726, 0.1252987 , 0.29992873, 0.53313468, 0.76542285,
1. , 0.93528778])
A=Matrix(B)
A
[14]: 0.04092726
0.1252987
0.29992873
0.53313468
0.76542285
1.0
0.93528778
[15]: U=np.ones([m,m]); U
[15]: array([[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
4
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[1., 1., 1., 1., 1., 1., 1., 1., 1., 1.]])
[16]: for i in range(1,m): # esta sentencia indica los valores que tomarÃą i
U[0,0] = 1 # Se define la entrada de la fila 0, columna 0 como 1
U[i,i] = U[i-1,i-1] + i+1 # Para generar cualqier entrada [i,i] se usa la␣
,→entrada [i-1,i-1] y se suma i+1
[17]: U
[17]: array([[ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
[ 1., 3., 1., 1., 1., 1., 1., 1., 1., 1.],
[ 1., 1., 6., 1., 1., 1., 1., 1., 1., 1.],
[ 1., 1., 1., 10., 1., 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 15., 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1., 21., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1., 1., 28., 1., 1., 1.],
[ 1., 1., 1., 1., 1., 1., 1., 36., 1., 1.],
[ 1., 1., 1., 1., 1., 1., 1., 1., 45., 1.],
[ 1., 1., 1., 1., 1., 1., 1., 1., 1., 55.]])
[18]: V = Matrix(U); V
[18]: 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 3.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 6.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 10.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 15.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 21.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 28.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 36.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 45.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 55.0
[ ]: print("Ingrese un NÞmero : ")
num = int(input())
cont = 0
suma = 0
while cont <= num:
suma = suma+cont
cont = cont+1
print("La Suma es : ",suma)
Ingrese un NÞmero :
