|
24 |
|
|
–среднее число приборов свободных от работы; |
|
|
–годовой фонд рабочего времени (6000 часов). |
|
1. |
Табулировать функцию (2.47) при = 1,9 |
(m=10-S); |
2. |
Построить график зависимости затрат от |
числа обслуживающих каналов, и |
найти оптимальное число обслуживающих каналов для данной задачи.
ПРАКТИЧЕСКИЕ ЗАДАНИЯ К РАЗДЕЛУ 3: Сети систем массового обслуживания
Практическое задание 8: Сети систем массового обслуживания 1
Пусть матрица переходных вероятностей P=||pij||, сети СМО имеет вид:
Записать систему уравнений для интенсивностей потоков 1, 2, 3, 4, где через 1, 2, 3 обозначены суммарные интенсивности потоков на входе i-й СМО, а через 4 интенсивность потока запросов от СМО 4.
Указание к решению. Пример задания сети СМО:
24
25
Рисунок 3.1. Граф задания сети СМО
Практическое задание 9: Сети систем массового обслуживания 2
Технологическая система (участок) S состоит из двух станкков, каждый из которых в случайный момент времени может выйти из строя (отказать), после чего мгновенно начинается ремонт узла, тоже продолжающийся заранее неизвестное, случайное время. Перечислить возможные состояния системы, интерпретировать геометрической схемой – графом состояний.
Указание к решению. S0 - оба станка исправны; S1 - первый станок ремонтируется, второй исправен; S2 - втторой станок ремонтируется, первый испправен; S3 - оба станка ремонтируются.
Рисунок 3.1. Граф состояний системы
Не забывайте проверять а) условие существования стационарного режима для 
текущей итерации; б) согласованность единиц измерения.
25
26
ПРИЛОЖЕНИЕ 1
Таблица значений квантилей ,
n\ε |
0,01 |
0,025 |
0,05 |
0,1 |
0,2 |
0,3 |
0,4 |
0,5 |
0,6 |
0,7 |
0,8 |
0,9 |
0,95 |
0,975 |
0,99 |
1 |
0,0002 |
0,0010 |
0,0039 |
0,0158 |
0,0642 |
0,1485 |
0,2750 |
0,4549 |
0,7083 |
1,0742 |
1,6424 |
2,7055 |
3,8415 |
5,0239 |
6,6349 |
2 |
0,0201 |
0,0506 |
0,1026 |
0,2107 |
0,4463 |
0,7133 |
1,0217 |
1,3863 |
1,8326 |
2,4079 |
3,2189 |
4,6052 |
5,9915 |
7,3778 |
9,2103 |
3 |
0,1148 |
0,2158 |
0,3518 |
0,5844 |
1,0052 |
1,4237 |
1,8692 |
2,3660 |
2,9462 |
3,6649 |
4,6416 |
6,2514 |
7,8147 |
9,3484 |
11,3449 |
4 |
0,2971 |
0,4844 |
0,7107 |
1,0636 |
1,6488 |
2,1947 |
2,7528 |
3,3567 |
4,0446 |
4,8784 |
5,9886 |
7,7794 |
9,4877 |
11,1433 |
13,2767 |
5 |
0,5543 |
0,8312 |
1,1455 |
1,6103 |
2,3425 |
2,9999 |
3,6555 |
4,3515 |
5,1319 |
6,0644 |
7,2893 |
9,2364 |
11,0705 |
12,8325 |
15,0863 |
6 |
0,8721 |
1,2373 |
1,6354 |
2,2041 |
3,0701 |
3,8276 |
4,5702 |
5,3481 |
6,2108 |
7,2311 |
8,5581 |
10,6446 |
12,5916 |
14,4494 |
16,8119 |
7 |
1,2390 |
1,6899 |
2,1673 |
2,8331 |
3,8223 |
4,6713 |
5,4932 |
6,3458 |
7,2832 |
8,3834 |
9,8032 |
12,0170 |
14,0671 |
16,0128 |
18,4753 |
8 |
1,6465 |
2,1797 |
2,7326 |
3,4895 |
4,5936 |
5,5274 |
6,4226 |
7,3441 |
8,3505 |
9,5245 |
11,0301 |
13,3616 |
15,5073 |
17,5345 |
20,0902 |
9 |
2,0879 |
2,7004 |
3,3251 |
4,1682 |
5,3801 |
6,3933 |
7,3570 |
8,3428 |
9,4136 |
10,6564 |
12,2421 |
14,6837 |
16,9190 |
19,0228 |
21,6660 |
10 |
2,5582 |
3,2470 |
3,9403 |
4,8652 |
6,1791 |
7,2672 |
8,2955 |
9,3418 |
10,4732 |
11,7807 |
13,4420 |
15,9872 |
18,3070 |
20,4832 |
23,2093 |
11 |
3,0535 |
3,8157 |
4,5748 |
5,5778 |
6,9887 |
8,1479 |
9,2373 |
10,3410 |
11,5298 |
12,8987 |
14,6314 |
17,2750 |
19,6751 |
21,9200 |
24,7250 |
12 |
3,5706 |
4,4038 |
5,2260 |
6,3038 |
7,8073 |
9,0343 |
10,1820 |
11,3403 |
12,5838 |
14,0111 |
15,8120 |
18,5493 |
21,0261 |
23,3367 |
26,2170 |
13 |
4,1069 |
5,0088 |
5,8919 |
7,0415 |
8,6339 |
9,9257 |
11,1291 |
12,3398 |
13,6356 |
15,1187 |
16,9848 |
19,8119 |
22,3620 |
24,7356 |
27,6882 |
14 |
4,6604 |
5,6287 |
6,5706 |
7,7895 |
9,4673 |
10,8215 |
12,0785 |
13,3393 |
14,6853 |
16,2221 |
18,1508 |
21,0641 |
23,6848 |
26,1189 |
29,1412 |
15 |
5,2293 |
6,2621 |
7,2609 |
8,5468 |
10,3070 |
11,7212 |
13,0297 |
14,3389 |
15,7332 |
17,3217 |
19,3107 |
22,3071 |
24,9958 |
27,4884 |
30,5779 |
16 |
5,8122 |
6,9077 |
7,9616 |
9,3122 |
11,1521 |
12,6243 |
13,9827 |
15,3385 |
16,7795 |
18,4179 |
20,4651 |
23,5418 |
26,2962 |
28,8454 |
31,9999 |
17 |
6,4078 |
7,5642 |
8,6718 |
10,0852 |
12,0023 |
13,5307 |
14,9373 |
16,3382 |
17,8244 |
19,5110 |
21,6146 |
24,7690 |
27,5871 |
30,1910 |
33,4087 |
18 |
7,0149 |
8,2307 |
9,3905 |
10,8649 |
12,8570 |
14,4399 |
15,8932 |
17,3379 |
18,8679 |
20,6014 |
22,7595 |
25,9894 |
28,8693 |
31,5264 |
34,8053 |
19 |
7,6327 |
8,9065 |
10,1170 |
11,6509 |
13,7158 |
15,3517 |
16,8504 |
18,3377 |
19,9102 |
21,6891 |
23,9004 |
27,2036 |
30,1435 |
32,8523 |
36,1909 |
20 |
8,2604 |
9,5908 |
10,8508 |
12,4426 |
14,5784 |
16,2659 |
17,8088 |
19,3374 |
20,9514 |
22,7745 |
25,0375 |
28,4120 |
31,4104 |
34,1696 |
37,5662 |
21 |
8,8972 |
10,2829 |
11,5913 |
13,2396 |
15,4446 |
17,1823 |
18,7683 |
20,3372 |
21,9915 |
23,8578 |
26,1711 |
29,6151 |
32,6706 |
35,4789 |
38,9322 |
22 |
9,5425 |
10,9823 |
12,3380 |
14,0415 |
16,3140 |
18,1007 |
19,7288 |
21,3370 |
23,0307 |
24,9390 |
27,3015 |
30,8133 |
33,9244 |
36,7807 |
40,2894 |
23 |
10,1957 |
11,6886 |
13,0905 |
14,8480 |
17,1865 |
19,0211 |
20,6902 |
22,3369 |
24,0689 |
26,0184 |
28,4288 |
32,0069 |
35,1725 |
38,0756 |
41,6384 |
24 |
10,8564 |
12,4012 |
13,8484 |
15,6587 |
18,0618 |
19,9432 |
21,6525 |
23,3367 |
25,1063 |
27,0960 |
29,5533 |
33,1962 |
36,4150 |
39,3641 |
42,9798 |
25 |
11,5240 |
13,1197 |
14,6114 |
16,4734 |
18,9398 |
20,8670 |
22,6156 |
24,3366 |
26,1430 |
28,1719 |
30,6752 |
34,3816 |
37,6525 |
40,6465 |
44,3141 |
26 |
12,1981 |
13,8439 |
15,3792 |
17,2919 |
19,8202 |
21,7924 |
23,5794 |
25,3365 |
27,1789 |
29,2463 |
31,7946 |
35,5632 |
38,8851 |
41,9232 |
45,6417 |
27 |
12,8785 |
14,5734 |
16,1514 |
18,1139 |
20,7030 |
22,7192 |
24,5440 |
26,3363 |
28,2141 |
30,3193 |
32,9117 |
36,7412 |
40,1133 |
43,1945 |
46,9629 |
28 |
13,5647 |
15,3079 |
16,9279 |
18,9392 |
21,5880 |
23,6475 |
25,5093 |
27,3362 |
29,2486 |
31,3909 |
34,0266 |
37,9159 |
41,3371 |
44,4608 |
48,2782 |
29 |
14,2565 |
16,0471 |
17,7084 |
19,7677 |
22,4751 |
24,5770 |
26,4751 |
28,3361 |
30,2825 |
32,4612 |
35,1394 |
39,0875 |
42,5570 |
45,7223 |
49,5879 |
30 |
14,9535 |
16,7908 |
18,4927 |
20,5992 |
23,3641 |
25,5078 |
27,4416 |
29,3360 |
31,3159 |
33,5302 |
36,2502 |
40,2560 |
43,7730 |
46,9792 |
50,8922 |
31 |
15,6555 |
17,5387 |
19,2806 |
21,4336 |
24,2551 |
26,4397 |
28,4087 |
30,3359 |
32,3486 |
34,5981 |
37,3591 |
41,4217 |
44,9853 |
48,2319 |
52,1914 |
32 |
16,3622 |
18,2908 |
20,0719 |
22,2706 |
25,1478 |
27,3728 |
29,3763 |
31,3359 |
33,3809 |
35,6649 |
38,4663 |
42,5847 |
46,1943 |
49,4804 |
53,4858 |
26
27
|
Продолжение таблицы значений квантилей |
|
|
|
|
|
|
|
|
|
|||||
33 |
17,0735 |
19,0467 |
20,8665 |
23,1102 |
26,0422 |
28,3069, |
30,3444 |
32,3358 |
34,4126 |
36,7307 |
39,5718 |
43,7452 |
47,3999 |
50,7251 |
54,7755 |
34 |
17,7891 |
19,8063 |
21,6643 |
23,9523 |
26,9383 |
29,2421 |
31,3130 |
33,3357 |
35,4438 |
37,7954 |
40,6756 |
44,9032 |
48,6024 |
51,9660 |
56,0609 |
35 |
18,5089 |
20,5694 |
22,4650 |
24,7967 |
27,8359 |
30,1782 |
32,2821 |
34,3356 |
36,4746 |
38,8591 |
41,7780 |
46,0588 |
49,8018 |
53,2033 |
57,3421 |
36 |
19,2327 |
21,3359 |
23,2686 |
25,6433 |
28,7350 |
31,1152 |
33,2517 |
35,3356 |
37,5049 |
39,9220 |
42,8788 |
47,2122 |
50,9985 |
54,4373 |
58,6192 |
37 |
19,9602 |
22,1056 |
24,0749 |
26,4921 |
29,6355 |
32,0532 |
34,2216 |
36,3355 |
38,5348 |
40,9839 |
43,9782 |
48,3634 |
52,1923 |
55,6680 |
59,8925 |
38 |
20,6914 |
22,8785 |
24,8839 |
27,3430 |
30,5373 |
32,9919 |
35,1920 |
37,3355 |
39,5643 |
42,0451 |
45,0763 |
49,5126 |
53,3835 |
56,8955 |
61,1621 |
39 |
21,4262 |
23,6543 |
25,6954 |
28,1958 |
31,4405 |
33,9315 |
36,1628 |
38,3354 |
40,5935 |
43,1053 |
46,1730 |
50,6598 |
54,5722 |
58,1201 |
62,4281 |
40 |
22,1643 |
24,4330 |
26,5093 |
29,0505 |
32,3450 |
34,8719 |
37,1340 |
39,3353 |
41,6222 |
44,1649 |
47,2685 |
51,8051 |
55,7585 |
59,3417 |
63,6907 |
41 |
22,9056 |
25,2145 |
27,3256 |
29,9071 |
33,2506 |
35,8131 |
38,1055 |
40,3353 |
42,6506 |
45,2236 |
48,3628 |
52,9485 |
56,9424 |
60,5606 |
64,9501 |
42 |
23,6501 |
25,9987 |
28,1440 |
30,7654 |
34,1574 |
36,7550 |
39,0774 |
41,3352 |
43,6786 |
46,2817 |
49,4560 |
54,0902 |
58,1240 |
61,7768 |
66,2062 |
43 |
24,3976 |
26,7854 |
28,9647 |
31,6255 |
35,0653 |
37,6975 |
40,0496 |
42,3352 |
44,7063 |
47,3390 |
50,5480 |
55,2302 |
59,3035 |
62,9904 |
67,4593 |
44 |
25,1480 |
27,5746 |
29,7875 |
32,4871 |
35,9743 |
38,6408 |
41,0222 |
43,3352 |
45,7336 |
48,3957 |
51,6389 |
56,3685 |
60,4809 |
64,2015 |
68,7095 |
45 |
25,9013 |
28,3662 |
30,6123 |
33,3504 |
36,8844 |
39,5847 |
41,9950 |
44,3351 |
46,7607 |
49,4517 |
52,7288 |
57,5053 |
61,6562 |
65,4102 |
69,9568 |
46 |
26,6572 |
29,1601 |
31,4390 |
34,2152 |
37,7955 |
40,5292 |
42,9682 |
45,3351 |
47,7874 |
50,5071 |
53,8177 |
58,6405 |
62,8296 |
66,6165 |
71,2014 |
47 |
27,4158 |
29,9562 |
32,2676 |
35,0814 |
38,7075 |
41,4744 |
43,9417 |
46,3350 |
48,8139 |
51,5619 |
54,9056 |
59,7743 |
64,0011 |
67,8206 |
72,4433 |
48 |
28,1770 |
30,7545 |
33,0981 |
35,9491 |
39,6205 |
42,4201 |
44,9154 |
47,3350 |
49,8401 |
52,6161 |
55,9926 |
60,9066 |
65,1708 |
69,0226 |
73,6826 |
49 |
28,9406 |
31,5549 |
33,9303 |
36,8182 |
40,5344 |
43,3664 |
45,8895 |
48,3350 |
50,8660 |
53,6697 |
57,0786 |
62,0375 |
66,3386 |
70,2224 |
74,9195 |
50 |
29,7067 |
32,3574 |
34,7643 |
37,6886 |
41,4492 |
44,3133 |
46,8638 |
49,3349 |
51,8916 |
54,7228 |
58,1638 |
63,1671 |
67,5048 |
71,4202 |
76,1539 |
27
ПРИЛОЖЕНИЕ 2 Таблица значений
28
критич.
n/ε |
0.40 |
0.25 |
0.10 |
0.05 |
0.025 |
0.01 |
0.005 |
0.0005 |
1 |
0.324920 |
1.000000 |
3.077684 |
6.313752 |
12.70620 |
31.82052 |
63.65674 |
636.6192 |
2 |
0.288675 |
0.816497 |
1.885618 |
2.919986 |
4.30265 |
6.96456 |
9.92484 |
31.5991 |
3 |
0.276671 |
0.764892 |
1.637744 |
2.353363 |
3.18245 |
4.54070 |
5.84091 |
12.9240 |
4 |
0.270722 |
0.740697 |
1.533206 |
2.131847 |
2.77645 |
3.74695 |
4.60409 |
8.6103 |
5 |
0.267181 |
0.726687 |
1.475884 |
2.015048 |
2.57058 |
3.36493 |
4.03214 |
6.8688 |
6 |
0.264835 |
0.717558 |
1.439756 |
1.943180 |
2.44691 |
3.14267 |
3.70743 |
5.9588 |
7 |
0.263167 |
0.711142 |
1.414924 |
1.894579 |
2.36462 |
2.99795 |
3.49948 |
5.4079 |
8 |
0.261921 |
0.706387 |
1.396815 |
1.859548 |
2.30600 |
2.89646 |
3.35539 |
5.0413 |
9 |
0.260955 |
0.702722 |
1.383029 |
1.833113 |
2.26216 |
2.82144 |
3.24984 |
4.7809 |
10 |
0.260185 |
0.699812 |
1.372184 |
1.812461 |
2.22814 |
2.76377 |
3.16927 |
4.5869 |
11 |
0.259556 |
0.697445 |
1.363430 |
1.795885 |
2.20099 |
2.71808 |
3.10581 |
4.4370 |
12 |
0.259033 |
0.695483 |
1.356217 |
1.782288 |
2.17881 |
2.68100 |
3.05454 |
4.3178 |
13 |
0.258591 |
0.693829 |
1.350171 |
1.770933 |
2.16037 |
2.65031 |
3.01228 |
4.2208 |
14 |
0.258213 |
0.692417 |
1.345030 |
1.761310 |
2.14479 |
2.62449 |
2.97684 |
4.1405 |
15 |
0.257885 |
0.691197 |
1.340606 |
1.753050 |
2.13145 |
2.60248 |
2.94671 |
4.0728 |
16 |
0.257599 |
0.690132 |
1.336757 |
1.745884 |
2.11991 |
2.58349 |
2.92078 |
4.0150 |
17 |
0.257347 |
0.689195 |
1.333379 |
1.739607 |
2.10982 |
2.56693 |
2.89823 |
3.9651 |
18 |
0.257123 |
0.688364 |
1.330391 |
1.734064 |
2.10092 |
2.55238 |
2.87844 |
3.9216 |
19 |
0.256923 |
0.687621 |
1.327728 |
1.729133 |
2.09302 |
2.53948 |
2.86093 |
3.8834 |
20 |
0.256743 |
0.686954 |
1.325341 |
1.724718 |
2.08596 |
2.52798 |
2.84534 |
3.8495 |
21 |
0.256580 |
0.686352 |
1.323188 |
1.720743 |
2.07961 |
2.51765 |
2.83136 |
3.8193 |
22 |
0.256432 |
0.685805 |
1.321237 |
1.717144 |
2.07387 |
2.50832 |
2.81876 |
3.7921 |
23 |
0.256297 |
0.685306 |
1.319460 |
1.713872 |
2.06866 |
2.49987 |
2.80734 |
3.7676 |
24 |
0.256173 |
0.684850 |
1.317836 |
1.710882 |
2.06390 |
2.49216 |
2.79694 |
3.7454 |
25 |
0.256060 |
0.684430 |
1.316345 |
1.708141 |
2.05954 |
2.48511 |
2.78744 |
3.7251 |
26 |
0.255955 |
0.684043 |
1.314972 |
1.705618 |
2.05553 |
2.47863 |
2.77871 |
3.7066 |
27 |
0.255858 |
0.683685 |
1.313703 |
1.703288 |
2.05183 |
2.47266 |
2.77068 |
3.6896 |
28 |
0.255768 |
0.683353 |
1.312527 |
1.701131 |
2.04841 |
2.46714 |
2.76326 |
3.6739 |
29 |
0.255684 |
0.683044 |
1.311434 |
1.699127 |
2.04523 |
2.46202 |
2.75639 |
3.6594 |
30 |
0.255605 |
0.682756 |
1.310415 |
1.697261 |
2.04227 |
2.45726 |
2.75000 |
3.6460 |
∞ |
0.253347 |
0.674490 |
1.281552 |
1.644854 |
1.95996 |
2.32635 |
2.57583 |
3.2905 |
28