A.6-1
Table A.6
Probability that All Processors Are BusyNumber of Processors, M
r 1 2 3 4 5 6 7 8 9 10.02 .0200 .0008 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .04 .0400 .0031 .0003 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .06 .0600 .0068 .0009 .0001 .0000 .0000 .0000 .0000 .0000 .0000 .08 .0800 .0119 .0020 .0003 .0001 .0000 .0000 .0000 .0000 .0000 .10 .1000 .0182 .0037 .0008 .0002 .0000 .0000 .0000 .0000 .0000 .12 .1200 .0257 .0062 .0016 .0004 .0001 .0000 .0000 .0000 .0000 .14 .1400 .0344 .0094 .0027 .0008 .0002 .0001 .0000 .0000 .0000 .16 .1600 .0441 .0136 .0044 .0015 .0005 .0002 .0001 .0000 .0000 .18 .1800 .0549 .0186 .0066 .0024 .0009 .0003 .0001 .0001 .0000 .20 .2000 .0667 .0247 .0096 .0038 .0016 .0006 .0003 .0001 .0000 .22 .2200 .0793 .0317 .0133 .0057 .0025 .0011 .0005 .0002 .0001 .24 .2400 .0929 .0397 .0178 .0082 .0039 .0018 .0009 .0004 .0002 .26 .2600 .1073 .0488 .0232 .0114 .0057 .0029 .0015 .0008 .0004 .28 .2800 .1225 .0589 .0296 .0153 .0081 .004 3 .0023 .0013 .0007 .30 .3000 .1385 .0700 .0370 .0201 .0111 .0062 .0035 .0020 .0012 .32 .3200 .1552 .0822 .0455 .0259 .0150 .0088 .0052 .0031 .0019 .34 .3400 .1725 .0954 .0551 .0326 .0197 .0120 .0074 .0046 .0029 .36 .3600 .1906 .1097 .0658 .0405 .0254 .0161 .0103 .0066 .0043 .38 .3800 .2093 .1249 .0777 .0495 .0321 .0211 .0139 .0093 .0062 .40 .4000 .2286 .1412 .0907 .0597 .0400 .0271 .0185 .0127 .0088 .42 .4200 .2485 .1584 .1049 .0712 .0490 .0342 .0241 .0171 .0122 .44 .4400 .2689 .1766 .1204 .0839 .0595 .0426 .0308 .0224 .0164 .46 .4600 .2899 .1958 .1370 .0980 .0712 .0523 .0388 .0289 .0217 .48 .4800 .3114 .2159 .1549 .1135 .0844 .0635 .0482 .0368 .0282 .50 .5000 .3333 .2368 .1739 .1304 .0991 .0762 .0590 .0460 .0361 .52 .5200 .3558 .2587 .1942 .1487 .1154 .0905 .0715 .0569 .0455 .54 .5400 .3787 .2815 .2156 .1684 .1332 .1065 .0857 .0695 .0566 .56 .5600 .4021 .3051 .2383 .1895 .1527 .1242 .1018 .0839 .0695 .58 .5800 .4258 .3295 .2621 .2121 .1738 .1437 .1197 .1002 .0843 .60 .6000 .4500 .3547 .2870 .2362 .1966 .1651 .1395 .1186 .1013 .62 .6200 .4746 .3808 .3132 .2616 .2210 .1883 .1615 .1392 .1205 .64 .6400 .4995 .4076 .3404 .2886 .2472 .2135 .1855 .1620 .1420 .66 .6600 .5248 .4351 .3687 .3169 .2751 .2406 .2116 .1871 .1660 .68 .6800 .5505 .4634 .3982 .3467 .3047 .2697 .2400 .2146 .1926 .70 .7000 .5765 .4923 .4287 .3778 .3360 .3007 .2706 .2445 .2217 .72 .7200 .6028 .5220 .4602 .4104 .3690 .3338 .3034 .2770 .2536 .74 .7400 .6294 .5523 .4928 .4443 .4037 .3689 .3386 .3119 .2882 .76 .7600 .6564 .5833 .5263 .4796 .4400 .4059 .3760 .3494 .3257 .78 .7800 .6836 .6150 .5609 .5162 .4781 .4449 .4157 .3895 .3660 .80 .8000 .7111 .6472 .5964 .5541 .5178 .4859 .4576 .4322 .4092 .82 .8200 .7389 .6800 .6329 .5933 .5591 .5289 .5019 .4775 .4553 .84 .8400 .7670 .7135 .6703 .6338 .6020 .5738 .5485 .5254 .5043 .86 .8600 .7953 .7474 .7086 .6755 .6465 .6206 .5972 .5759 .5562 .88 .8800 .8238 .7820 .7477 .7184 .6925 .6694 .6483 .6289 .6110 .90 .9000 .8526 .8171 .7878 .7625 .7401 .7200 .7015 .6845 .6687 .92 .9200 .8817 .8527 .8286 .8078 .7892 .7724 .7570 .7427 .7293 .94 .9400 .9109 .8888 .8703 .8542 .8398 .8267 .8146 .8033 .7928 .96 .9600 .9404 .9254 .9128 .9017 .8918 .8827 .8743 .8665 .8591 .98 .9800 .9701 .9625 .9560 .9503 .9452 .9405 .9361 .9320 .9282
A.6-2
Table A.6(Continued) Probability that All Processors Are BusyNumber of Processors, M
A.6-3 r 11 12 13 14 15 16 17 18 19 20
.24 .0001 .0001 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000
.26 .0002 .0001 .0001 .0000 .0000 .0000 .0000 .0000 .0000 .0000
.28 .0004 .0002 .0001 .0001 .0000 .0000 .0000 .0000 .0000 .0000
.30 .0007 .0004 .0002 .0001 .0001 .0000 .0000 .0000 .0000 .0000
.32 .0011 .0007 .0004 .0003 .0002 .0001 .0001 .0000 .0000 .0000
.34 .0018 .0011 .0007 .0005 .0003 .0002 .0001 .0001 .0000 .0000
.36 .0028 .0018 .0012 .0008 .0005 .0003 .0002 .0002 .0001 .0001
.38 .0042 .0028 .0019 .0013 .0009 .0006 .0004 .0003 .0002 .0001
.40 .0061 .0043 .0030 .0021 .0015 .0010 .0007 .0005 .0004 .0003
.42 .0087 .0063 .0045 .0033 .0024 .0017 .0013 .0009 .0007 .0005
.44 .0121 .0089 .0066 .0049 .0036 .0027 .0020 .0015 .0011 .0009
.46 .0164 .0124 .0094 .0072 .0055 .0042 .0032 .0025 .0019 .0015
.48 .0218 .0168 .0131 .0102 .0079 .0062 .0049 .0038 .0030 .0024
.50 .0284 .0225 .0178 .0142 .0113 .0090 .0072 .0058 .0046 .0037
.52 .0365 .0295 .0238 .0193 .0157 .0128 .0104 .0085 .0070 .0057
.54 .0463 .0380 .0313 .0258 .0213 .0177 .0147 .0122 .0102 .0085
.56 .0578 .0482 .0404 .0339 .0285 .0240 .0203 .0171 .0145 .0123
.58 .0712 .0604 .0513 .0438 .0374 .0320 .0274 .0235 .0202 .0174
.60 .0868 .0747 .0644 .0557 .0482 .0419 .0364 .0317 .0276 .0241
.62 .1047 .0913 .0798 .0699 .0613 .0539 .0475 .0419 .0370 .0328
.64 .1250 .1103 .0976 .0866 .0769 .0685 .0611 .0545 .0488 .0437
.66 .1478 .1320 .1182 .1060 .0953 .0858 .0774 .0699 .0632 .0572
.68 .1733 .1565 .1416 .1284 .1166 .1061 .0967 .0882 .0806 .0737
.70 .2017 .1839 .1681 .1539 .1412 .1297 .1193 .1099 .1013 .0936
.72 .2329 .2144 .1977 .1827 .1691 .1568 .1455 .1353 .1258 .1172
.74 .2671 .2480 .2307 .2151 .2008 .1877 .1756 .1646 .1544 .1449
.76 .3043 .2849 .2672 .2511 .2362 .2225 .2099 .1981 .1872 .1771
.78 .3446 .3252 .3073 .2908 .2756 .2615 .2484 .2362 .2247 .2140
.80 .3881 .3688 .3510 .3345 .3192 .3049 .2915 .2790 .2672 .2561
.82 .4348 .4160 .3985 .3822 .3670 .3527 .3393 .3267 .3147 .3035
.84 .4848 .4667 .4498 .4340 .4192 .4052 .3920 .3795 .3677 .3564
.86 .5379 .5209 .5049 .4900 .4758 .4624 .4497 .4377 .4261 .4152
.88 .5943 .5787 .5640 .5501 .5369 .5244 .5125 .5012 .4903 .4799
.90 .6539 .6400 .6269 .6145 .6026 .5913 .5806 .5702 .5603 .5508
.92 .7168 .7050 .6938 .6831 .6729 .6632 .6538 .6448 .6362 .6279
.94 .7829 .7735 .7645 .7560 .7478 .7399 .7324 .7251 .7181 .7113
.96 .8521 .8455 .8391 .8331 .8273 .8217 .8163 .8111 .8060 .8011
.98 .9245 .9210 .9177 .9144 .9114 .9084 .9055 .9027 .9000 .8973
Number of Processors, M
Number of Processors, M
r 25 30 35 40 45 50 55 60
.42 .0001 .0000 .0000 .0000 .0000 .0000 .0000 .0000
.44 .0002 .0001 .0000 .0000 .0000 .0000 .0000 .0000
.46 .0004 .0001 .0000 .0000 .0000 .0000 .0000 .0000
.48 .0007 .0002 .0001 .0000 .0000 .0000 .0000 .0000
.50 .0013 .0004 .0002 .0001 .0000 .0000 .0000 .0000
.52 .0021 .0008 .0003 .0001 .0000 .0000 .0000 .0000
.54 .0035 .0015 .0006 .0003 .0001 .0000 .0000 .0000
.56 .0055 .0025 .0011 .0005 .0002 .0001 .0001 .0000
.58 .0084 .0041 .0020 .0010 .0005 .0003 .0001 .0001
.60 .0124 .0065 .0035 .0019 .0010 .0006 .0003 .0002
.62 .0180 .0101 .0057 .0033 .0019 .0011 .0006 .0004
.64 .0255 .0151 .0091 .0055 .0034 .0021 .0013 .0008
.66 .0352 .0221 .0141 .0090 .0058 .0038 .0025 .0016
.68 .0478 .0315 .0211 .0142 .0097 .0066 .0045 .0031
.70 .0636 .0439 .0307 .0217 .0154 .0110 .0079 .0057
.72 .0831 .0599 .0437 .0322 .0238 .0178 .0133 .0100
.74 .1070 .0801 .0607 .0464 .0357 .0276 .0215 .0168
.76 .1356 .1053 .0826 .0654 .0521 .0417 .0335 .0270
.78 .1695 .1360 .1102 .0900 .0739 .0610 .0506 .0421
.80 .2091 .1729 .1442 .1212 .1024 .0870 .0741 .0634
.82 .2549 .2166 .1856 .1601 .1388 .1208 .1056 .0926
.84 .3074 .2678 .2351 .2076 .1842 .1641 .1467 .1314
.86 .3668 .3270 .2935 .2648 .2399 .2181 .1989 .1818
.88 .4336 .3947 .3615 .3325 .3070 .2843 .2639 .2456
.90 .5079 .4714 .4396 .4116 .3865 .3639 .3433 .3246
.92 .5901 .5574 .5286 .5028 .4794 .4581 .4385 .4204
.94 .6802 .6530 .6287 .6067 .5866 .5680 .5507 .5346
.96 .7785 .7585 .7405 .7240 .7087 .6945 .6811 .6686
.98 .8851 .8742 .8642 .8549 .8463 .8383 .8306 .8234
r 65 70 75 80 85 90 95 100
.60 .0001 .0001 .0000 .0000 .0000 .0000 .0000 .0000
.62 .0002 .0001 .0001 .0000 .0000 .0000 .0000 .0000
.64 .0005 .0003 .0002 .0001 .0001 .0000 .0000 .0000
.66 .0011 .0007 .0005 .0003 .0002 .0001 .0001 .0001
.68 .0022 .0015 .0010 .0007 .0005 .0004 .0002 .0002
.70 .0041 .0030 .0022 .0016 .0012 .0009 .0006 .0005
.72 .0075 .0057 .0043 .0033 .0025 .0019 .0015 .0011
.74 .0131 .0103 .0081 .0064 .0050 .0040 .0032 .0025
.76 .0219 .0178 .0145 .0118 .0096 .0079 .0065 .0053
.78 .0351 .0294 .0247 .0207 .0174 .0147 .0124 .0105
.80 .0544 .0468 .0403 .0348 .0301 .0261 .0226 .0196
.82 .0814 .0717 .0633 .0560 .0496 .0440 .0391 .0348
.84 .1181 .1064 .0960 .0867 .0785 .0711 .0646 .0587
.86 .1666 .1530 .1407 .1296 .1195 .1104 .1021 .0945
.88 .2290 .2139 .2001 .1874 .1758 .1650 .1551 .1459
.90 .3073 .2914 .2767 .2631 .2504 .2385 .2274 .2169
.92 .4036 .3879 .3732 .3594 .3464 .3342 .3226 .3116
.94 .5195 .5052 .4918 .4790 .4669 .4554 .4444 .4339
.96 .6567 .6454 .6346 .6244 .6145 .6051 .5960 .5873
.98 .8165 .8099 .8035 .7974 .7916 .7859 .7804 .7751