Math Problem Statement

Exhibit 10.10 Finite Queuing Tables

Population 4

X S Pw F .015 1 .045 .999 .022 1 .066 .998 .030 1 .090 .997 .034 1 .102 .996 .038 1 .114 .995 .042 1 .126 .994 .046 1 .137 .993 .048 1 .143 .992 .052 1 .155 .991 .054 1 .161 .990 .058 1 .173 .989 .060 1 .179 .988 .062 1 .184 .987 .064 1 .190 .986 .066 1 .196 .985 .070 2 .014 .999 .070 1 .208 .984 .075 2 .016 .999 .075 1 .222 .981 .080 2 .018 .999 .080 1 .237 .978 .085 2 .021 .999 .085 1 .251 .975 .090 2 .023 .999 .090 1 .265 .972 .095 2 .026 .999 .095 1 .280 .969 .100 2 .028 .999 .100 1 .294 .965 .105 2 .031 .998 .105 1 .308 .962 .110 2 .034 .998 .110 1 .321 .958 .115 2 .037 .998 .115 1 .335 .954 .120 2 .041 .997 .120 1 .349 .950 .125 2 .044 .997 .125 1 .362 .945 .130 2 .047 .997 .130 1 .376 .941 .135 2 .051 .996 .135 1 .389 .936 .140 2 .055 .996 .140 1 .402 .931 .145 2 .058 .995 .145 1 .415 .926 .150 2 .062 .995 .150 1 .428 .921 .155 2 .066 .994 .155 1 .441 .916 .160 2 .071 .994 .160 1 .454 .910 .165 2 .075 .993 .165 1 .466 .904 .170 2 .079 .993 .170 1 .479 .899 .180 2 .088 .991 .180 1 .503 .887 .190 2 .098 .990 .190 1 .526 .874 .200 3 .008 .999 .200 2 .108 .988 .200 1 .549 .862 .210 3 .009 .999 .210 2 .118 .986 .210 1 .572 .849 .220 3 .011 .999 .220 2 .129 .984 .220 1 .593 .835 .230 3 .012 .999 .230 2 .140 .982 .230 1 .614 .822 .240 3 .014 .999 .240 2 .151 .980 .240 1 .634 .808 .250 3 .016 .999 .250 2 .163 .977 .250 1 .654 .794 .260 3 .018 .998 .260 2 .175 .975 .260 1 .673 .780 X S Pw F .270 3 .020 .998 .270 2 .187 .972 .270 1 .691 .766 .280 3 .022 .998 .280 2 .200 .968 .280 1 .708 .752 .290 3 .024 .998 .290 2 .213 .965 .290 1 .725 .738 .300 3 .027 .997 .300 2 .226 .962 .300 1 .741 .724 .310 3 .030 .997 .310 2 .240 .958 .310 1 .756 .710 .320 3 .033 .997 .320 2 .254 .954 .320 1 .771 .696 .330 3 .036 .996 .330 2 .268 .950 .330 1 .785 .683 .340 3 .039 .996 .340 2 .282 .945 .340 1 .798 .670 .360 3 .047 .994 .360 2 .312 .936 .360 1 .823 .644 .380 3 .055 .993 .380 2 .342 .926 .380 1 .846 .619 .400 3 .064 .992 .400 2 .372 .915 .400 1 .866 .595 .420 3 .074 .990 .420 2 .403 .903 .420 1 .884 .572 .440 3 .085 .986 .440 2 .435 .891 .440 1 .900 .551 .460 3 .097 .985 .460 2 .466 .878 .460 1 .914 .530 .480 3 .111 .983 .480 2 .498 .864 .480 1 .926 .511 .500 3 .125 .980 .500 2 .529 .850 .500 1 .937 .492 .520 3 .141 .976 .520 2 .561 .835 .520 1 .947 .475 .540 3 .157 .972 .540 2 .592 .820 .540 1 .956 .459 .560 3 .176 .968 .560 2 .623 .805 .560 1 .963 .443 .580 3 .195 .964 .580 2 .653 .789 .580 1 .969 .429 .600 3 .216 .959 .600 2 .682 .774 .600 1 .975 .415 .650 3 .275 .944 .650 2 .752 .734 .650 1 .985 .384 .700 3 .343 .926 .700 2 .816 .695 .700 1 .991 .357 .750 3 .422 .905 .750 2 .871 .657 .750 1 .996 .333 .800 3 .512 .880 .800 2 .917 .621 .800 1 .998 .312 .850 3 .614 .852 .850 2 .954 .587 .850 1 .999 .294 .900 3 .729 .821 .900 2 .979 .555 .950 3 .857 .786 .950 2 .995 .526

Solution

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Math Problem Analysis

Mathematical Concepts

Queuing Theory
Probability
Systems Analysis

Formulas

Utilization Factor (X = λ / μ)
Probability of Waiting (Pw)
Probability of Full Utilization (F)

Theorems

Little's Law
Erlang B Formula
Erlang C Formula

Suitable Grade Level

Undergraduate (College Level)