A priority waiting system assigns arriving customers to one of four classes. Arrival rates (Poisson) of the classes are shown in the following table: Use Table 18.4 Arrivals per Hour Class 1 2 4 Five servers process the customers, and each can handle 6 customers per hour. a. What is the system utilization? (Round your answer to 2 decimal places.) b. What is the average wait for service by customers in the various classes? How many are waiting in each class, on average? (Round your answers to 3 decimal places.) W W2 W3 WA L1 L2 L3 L4 c. If the arrival rate of the second priority class could be reduced to 3 units per hour by shifting some arrivals into the third priority class, how would your answers to part b change? (Round your answers to 3 decimal places.) W1 W2 W3 WA L1 L2 L3 L4 TABLE 18.4 Infinite-source values for Lg and Po given Nu and M Lg La Po LO Po 0.15 1 0.026 .850 1.1 2 0.477 .290 6 0.021 100 2 0.001 .860 3 0.066 327 2.4 3 2.589 .056 0.20 1 0.050 .800 4 0.011 332 4 0.431 083 2 0.002 SIS 1.22 0.675 -250 5 0.105 089 0.25 1 0.083 .750 3 0.094 294 6 0.027 090 2 0.004 .778 4 0.016 .300 7 0.007 .091 0.30 1 0.129 .700 5 0.003 -301 2.5 3 3.511 .045 2 0.007 .739 1.3 2 0.951 212 4 0.533 .074 0.35 1 0. ISS .650 3 0.130 .264 5 0.130 OSO 2 0.011 .702 4 0.023 .271 6 0.034 082 0.40 1 0.267 .600 5 0.004 .272 7 0.009 OS2 2 0.017 .667 1.4 2 1.345 176 2.6 3 4.933 .035 0.45 1 0.368 550 3 0.177 .236 4 0.658 .065 2 0.024 .633 4 0.032 .245 5 0.161 .072 3 0.002 .637 5 0.006 .246 6 0.043 074 0.50 1 0.500 .500 1.5 2 1.929 .143 7 0.011 074 2 0.033 .600 3 0.237 211 | 2.7 3 7.354 025 3 0.003 606 4 0.045 221 4 0.811 .057 0.55 1 0.672 450 5 0.009 .223 5 0.198 065 2 0.045 569 1.6 2 2.844 .111 6 0.053 .067 3 0.004 .576 3 0.313 .187 7 0.014 .067 0.60 1 0.900 400 4 0.060 .1992.8 3 12.273 016 2 0.059 -538 5 0.012 201 4 1.000 050 3 0.006 548 1.7 2 4.426 OS1 5 0.241 .058 0.65 1 1.207 -350 3 0.409 .166 6 0.066 .060 2 0.077 509 4 0.080 .180 7 0.018 .061 + | 3 0.008 521 5 0.017 .182 2.9 3 27.193 .00S 0.70 1 1.633 .300 1.8 2 7.674 053 4 1.234 044 2 0.095 481 cm + 3 0.532 .146 5 0.293 .052 3 0.011 495 4 0.105 .162 6 0.081 .054 0.75 1 2.250 250 5 0.023 .165 7 0.023 055 2 0.123 455 1.9 2 17.587 026 3.0 4 1.528 .03S 3 0.015 471 3 0.6SS .128 5 0.354 047 0.SO 1 3.200 .200 4 0.136 .145 6 0.099 .049 20.152 429 5 0.030 .149 7 0.028 050 3 0.019 447 6 0.007 .149 S 0.008 .050 0.85 1 4.817 150 2.0 3 0.889 .111 3.1 4 1.902 .032 2 0.187 404 4 0.174 130 5 0.427 042 3 0.024 425 5 0.040 134 6 0.120 044 4 0.003 427 6 0.009 .135 7 0.035 045 0.90 1 S. 100 .100 2.1 3 1.149 .096 S 0.010 .045 2 0.229 379 4 0.220 .117 3.2 4 2.386 .027 3 0.030 403 5 0.052 .121 5 0.513 .037 4 0.004 406 6 0.012 .122 6 0.145 .040 0.95 1 18.050 .050 2.23 1.491 OS1 7 0.043 .040 2 0.277 .356 4 0.277 .105 S 0.012 .041 3 0.037 383 5 0.066 .109 3.3 4 3.027 .023 4 0.005 .386 6 0.016 .111 5 0.615 033 1.0 2 0.333 333 2.3 3 1.951 .068 6 0.174 .036 3 0.045 -364 4 0.346 093 7 0.052 .037 4 0.007 .367 5 0.084 .099 8 0.015 .037 3.4 4 3.906 .019 4.3 7 0.289 130 5.2 6 4.301 .003 5 0.737 .029 S 0.097 013 7 1.081 .005 6 0.209 .032 9 0.033 014 8 0.368 .005 7 0.063 .033 10 0.011 .014 9 0.135 .005 S 0.019 033 4.4 5 5.268 .006 10 0.049 .005 3.5 4 5.165 .015 6 1.078 010 11 0.018 .006 5 0.882 026 7 0.337 .0125.3 6 5.303 .003 6 0.248 .029 S 0.114 012 7 1.249 .004 7 0.076 .030 9 0.039 012 8 0.422 2005 8 0.023 .030 10 0.013 012 9 0.155 2005 9 0.007 030 4.5 5 6.862 005 10 0.057 .005 3.6 4 7.090 2011 6 1.265 .009 11 0.021 005 5 1.055 023 7 0.391 .010 12 0.007 2005 6 0.295 .026 S 0.134 011 5.4 6 6.661 .002 7 0.019 .027 9 0.046 011 7 1.444 004 S 0.028 027 10 0.015 .011 S 0.483 .004 9 0.008 .027 46 5 9.289 .004 9 0.178 .004 3.7 4 10.347 .008 6 1.487 .008 10 0.066 .004 5 1.265 .020 7 0.453 .009 11 0.024 .005 6 0.349 .023 S 0.156 010 12 0.009 2005 7 0.109 .024 9 0.054 .010 5.5 6 8.590 002 8 0.034 025 10 0.018 .010 1.674 .003 9 0.010 .025 47 5 13.382 .003 S 0.553 004 3.S 4 16.937 .005 6 1.752 007 9 0.204 2004 5 1.519 017 7 0.525 .008 10 0.077 2004 6 0.412 .021 S 0.181 2009 11 0.028 .004 7 0.129 .022 9 0.064 .009 12 0.010 2004 S 0.041 .022 10 0.022 .009 5.6 6 11.519 .001 9 0.013 022 4.8 5 21.641 .002 7 1.944 003 3.9 4 36.859 .002 6 2.071 .006 8 0.631 2003 5 1.830 015 7 0.607 .008 9 0.233 004 6 0.485 .019 S 0.209 .00S 10 0.0SS 004 7 0.153 .020 9 0.074 .00S 11 0.033 .004 S 0.050 .020 10 0.026 .008 12 0.012 .004 9 0.016 .020 4.9 5 46.566 .001 5.7 6 16.446 .001 4.0 5 2.216 2013 6 2.459 .005 7 2.264 .002 6 0.570 .017 7 0.702 .007 S 0.721 .003 7 0.1 SO .018 S 0.242 .007 9 0.266 .003 S 0.059 2018 9 0.087 .007 10 0.102 .003 9 0.019 018 10 0.031 007 11 0.038 003 4.1 5 2.703 011 11 0.011 .007 12 0.014 .003 6 0.668 0155.0 6 2.938 .005 5.5 6 26.373 001 7 0.212 016 7 0.810 006 7 2.648 002 S 0.070 016 S 0.279 .006 8 0.823 .003 9 0.023 .017 9 0.101 .007 9 0.303 .003 4.2 5 3.327 .009 10 0.036 .007 10 0.116 .003 6 0.784 .013 11 0.013 .007 11 0.044 .003 7 0.248 014 5.1 6 3.536 004 12 0.017 .003 S 0.083 .015 7 0.936 .005 5.9 6 56.300 .000 9 0.027 .015 S 0.321 .006 7 3.113 .002 10 0.009 .015 9 0.117 .006 S 0.939 .002 4.3 5 4.149 .008 10 0.042 006 9 0.345 .003 6 0.919 012 11 0.015 .006 10 0.133 .003