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Lecture 11 - Queue - Waitingtimes 450 400 350 300 250 Wq(n...

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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 50 100 150 200 250 300 350 400 450 Waiting times Job number, n Wq(n)
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0 Bin Frequency 30 0 1217 60 30 2020 90 60 1647 120 90 1232 150 120 944 180 150 741 210 180 556 240 210 418 270 240 318 300 270 229 330 300 120 360 330 115 390 360 76 420 390 53 450 420 59 480 450 87 510 480 69 540 510 29 570 540 10 600 570 38 600 17 More 5 0 60 120 180 240 0 500 1000 1500 2000 2500 Histo Frequency
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300 360 420 480 540 600 ogram Column D Bin
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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 20 40 60 80 100 120 Running average of Wq(k) k
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Lambda (arr. rate Mu (service rate)   1/15   1/13 Average Average Average Average For arrivals: For services: 15.043 12.944 69.021 81.965 Uniform (0,1) Uniform (0,1) k T(k) S(k) Wq(k) Wsys(k) 0 0.66 1 0.000 13.841 0 13.841 0.3 0.67 2 5.454 14.610 8.387 22.998 0.11 0.52 3 1.693 9.449 21.304 30.754 0.49 0.6 4 10.090 11.992 20.663 32.655 0.37 0.26 5 6.929 3.856 25.726 29.582 0.37 0.83 6 7.031 22.702 22.552 45.254 0.17 0.3 7 2.844 4.596 42.410 47.006 0.64 0.79 8 15.473 20.268 31.533 51.800 0.99 0.8 9 66.123 20.961 0.000 20.961 0.46 0.54 10 9.361 10.066 11.600 21.666 0.63 0.25 11 14.733 3.739 6.934 10.673 0.7 0.72 12 18.256 16.378 0.000 16.378 0.98 0.33 13 58.326 5.187 0.000 5.187 0.45 0.71 14 8.844 16.021 0.000 16.021 0.74 0.17 15 20.200 2.466 0.000 2.466 0.02 0.78 16 0.237 19.837 2.229 22.066 0.04 0.6 17 0.631 11.829 21.435 33.263 0.25 0.56 18 4.230 10.569 29.034 39.603 0.52 0.4 19 10.861 6.585 28.742 35.328 0.18 0.65 20 3.024 13.498 32.303 45.802 0.72 0.3 21 18.910 4.729 26.891 31.620 0.97 0.83 22 53.366 23.386 0.000 23.386 0.39 0.7 23 7.417 15.865 15.970 31.835 0.13 0.61 24 2.011 12.167 29.824 41.991 0.55 0.7 25 11.947 15.646 30.043 45.690 0.9 0.4 26 35.149 6.573 10.540 17.113 0.83 0.62 27 26.786 12.526 0.000 12.526 0.02 0.37 28 0.244 6.110 12.282 18.391 0.11 0.56 29 1.741 10.680 16.651 27.331 0.37 0.15 30 6.935 2.110 20.396 22.507 0.8 0.07 31 24.422 0.973 0.000 0.973 0.09 0.2 32 1.344 2.851 0.000 2.851 0.9 0.55 33 34.297 10.357 0.000 10.357 0.49 0.38 34 10.068 6.136 0.289 6.425 0.1 0.45 35 1.579 7.853 4.846 12.698 0.31 0.38 36 5.533 6.154 7.165 13.319 0.12 0.95 37 1.963 37.801 11.356 49.157 0.79 0.43 38 23.550 7.405 25.607 33.013 0.57 0.02 39 12.501 0.277 20.512 20.789 0.96 0.16 40 48.394 2.260 0.000 2.260 0.35 0.75 41 6.439 17.953 0.000 17.953 0.72 0.83 42 19.102 23.196 0.000 23.196 0.18 0.7 43 3.033 15.588 20.163 35.752 0.05 0.99 44 0.804 61.590 34.947 96.537 0.03 0.16 45 0.464 2.272 96.073 98.346 0.99 0.68 46 78.147 14.678 20.199 34.876 0.04 0.24 47 0.600 3.592 34.277 37.869 0.64 0.16 48 15.293 2.234 22.576 24.810 0.91 0.44 49 35.973 7.511 0.000 7.511
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0.86 0.5 50 29.744 8.968 0.000 8.968 0.16 0.78 51 2.676 19.737 6.292 26.029 0 0.8 52 0.055 20.703 25.974 46.677 0.29 0.13 53 5.204 1.809 41.472 43.281 0.22 0.45 54 3.691 7.767 39.590 47.358 0.24 0.74 55 4.183 17.580 43.175 60.755 0.71 0.28 56 18.774 4.303 41.981 46.284 0.21 0.67 57 3.529 14.503 42.755 57.259 0.6 0.88 58 13.743 27.617 43.516 71.132 0.21 0.13 59 3.623 1.862 67.509 69.371 0.56 0.99 60 12.245 57.113 57.127 114.240 0.43 0.38 61 8.471 6.176 105.769 111.946 0.06 0.29 62 0.934 4.372 111.012 115.384 0.73 0.22 63 19.390 3.268 95.994 99.262 0.35 0.42 64 6.504 7.172 92.758 99.930 0.38 0.79 65 7.167 20.208 92.764 112.972 0.91 0.63 66 36.553 12.942 76.419 89.361 0.48 0.57 67 9.719 10.974 79.642 90.616 0.62 0.75 68 14.655 17.968 75.961 93.929 0.9 0.4 69 34.787 6.731 59.142 65.873 0.35 0.05 70 6.492 0.664 59.381 60.045 0.44 0.45 71 8.626 7.872 51.419 59.291 0.17 0.65 72 2.821 13.830 56.470 70.300 0.92 0.79 73 38.224 20.277 32.076 52.353 0.95 0.92 74 44.775 33.122 7.578 40.700 0.93 0.66 75 40.440 14.039 0.260 14.300 0.5 0.63 76 10.334 12.943 3.966 16.909 0.97 0.06 77 52.845 0.752 0.000 0.752 0.03 0.32 78 0.433 4.961 0.319 5.280 0.61 0.65 79 14.132 13.660 0.000 13.660 0.12 0.6 80 1.878 11.832 11.782 23.614 0.59 0.71 81 13.217 16.301 10.397 26.698 0.9 0.82 82 35.308 22.600 0.000 22.600 0.28 0.1 83 4.935 1.441 17.666 19.106 0.74 0.92 84 20.320 33.234 0.000 33.234 0.59 0.91 85 13.388 30.951 19.846 50.797 0.01 0.75 86 0.176 17.851 50.621 68.473 0.63 0.84 87 14.896 24.000 53.576 77.577 0.34 0.8 88 6.153 21.113 71.423 92.537 0.24 0.01 89 4.213 0.185 88.324 88.509 0.89 0.68 90 33.580 14.782 54.929 69.711 0.81 0.11 91 25.005 1.516 44.706 46.222 0.06 0.03 92 0.855 0.396 45.367 45.763 0.27 0.63 93 4.807 12.952 40.955 53.907 0.08 0.46 94 1.222 7.912 52.685 60.597 0.91 0.25 95 36.140 3.821 24.458 28.279 0.05 0.12 96 0.769 1.729 27.510 29.239 0.77 0.93 97 22.084 33.922 7.156 41.077 0.82 0.47 98 26.041 8.370 15.037 23.407 0.28 0.76 99 4.981 18.721 18.426 37.147 0.15 0.85 100 2.467 24.570 34.680 59.250 0.97 0.37 101 52.845 6.072 6.405 12.478 0.74 0.4 102 20.089 6.570 0.000 6.570
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0.77 0.68 103 22.106 14.863 0.000 14.863 0.43 0.09 104 8.469 1.281 6.394 7.675 0.91 0.85 105 35.663 24.814 0.000 24.814 0.28 0.22 106 4.829 3.232 19.985 23.217 0.79 0.41 107 23.680 6.795 0.000 6.795 0.63 0.14 108 15.024 1.961 0.000 1.961 0.94 0.13 109 41.750 1.837 0.000 1.837 0.11 0.73 110 1.712 17.010 0.125 17.134 0.31 0.86 111 5.574 25.414 11.560 36.974 0.48 0.29 112 9.819 4.541 27.155 31.696 0.15 0.73 113 2.388 16.902 29.308 46.209 0.37 0.32 114 6.974 5.036 39.236 44.271 0.66 0.02 115 16.225 0.209 28.046 28.256 0.86 0.9 116 29.948 30.500 0.000 30.500 0.62 0.13 117 14.586 1.781 15.914 17.695 0.79 0.2 118 23.247 2.897 0.000 2.897 0.28 0.84 119 4.951 23.930 0.000 23.930 0.9 0.74 120 34.162 17.479 0.000 17.479 0.61 0.4 121 13.965 6.707 3.514 10.221 0.66 0.96 122 16.065 40.389 0.000 40.389 0.29 0.57 123 5.181 10.962 35.209 46.171 0.85 0.76 124 28.509 18.447 17.662 36.109 0.53 0.18 125 11.215 2.629 24.894 27.523 0.73 0.51 126 19.885 9.287 7.639 16.926 0.97 0.38 127 50.350 6.178 0.000 6.178 0.96 0.24 128 48.086 3.601 0.000 3.601 0.9 0.02 129 34.069 0.197 0.000 0.197 0.97 0.45 130 52.954 7.682 0.000 7.682 0.06 0.43 131 0.957 7.281 6.725 14.006 0.11 0.31 132 1.743 4.784 12.264 17.047 0.09 0.09 133 1.463 1.265 15.584 16.849 0.14 0.7 134 2.215 15.636 14.634 30.270 0.05 0.29 135 0.747 4.380 29.523 33.902 0.39 0.79 136 7.524 20.592 26.378 46.971 0.01 0.36 137 0.099 5.846 46.872 52.718 0.32 0.64 138 5.798 13.256 46.919 60.176 0.19 0.71 139 3.101 16.094 57.075 73.169 0.55 0.53 140 11.926 9.692 61.243 70.936 0.57 0 141 12.738 0.029 58.197 58.227 0.29 0.51 142 5.208 9.375 53.019 62.394 0.5 0.82 143 10.311 22.639 52.083 74.721 0.26 0.94 144 4.447 37.274 70.275 107.549 0.17 0.28 145 2.789 4.273 104.760 109.033 0.76 0.28 146 21.457 4.205 87.576 91.781 0.6 0.66 147 13.750 14.048 78.031 92.079 0.34 0.12 148 6.169 1.706 85.910 87.617 0.9 0.78 149 34.717 19.785 52.900 72.684 0.48 0.78 150 9.860 19.905 62.824 82.729 0.43 0.07 151 8.446 0.982 74.284 75.266 0.8 0.16 152 24.225 2.259 51.041 53.299 0.74 0.02 153 20.430 0.221 32.869 33.090 0.26 0.37 154 4.615 6.019 28.475 34.494 0.83 0.03 155 26.329 0.448 8.165 8.613
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0.78 0.93 156 23.050 34.128 0.000 34.128 0.58 0.4 157 12.907 6.652 21.221 27.873 0.84 0.8 158 27.422 20.854 0.451 21.305 1 0.3 159 92.665 4.675 0.000 4.675 0.36 0.22 160 6.686 3.221 0.000 3.221 0.08 0.61 161 1.327 12.156 1.894 14.050 0.6 0.58 162 13.792 11.336 0.258 11.594 0.86 0.46 163 29.454 8.105 0.000 8.105 0.21 0.26 164 3.619 3.855 4.486 8.341 0.53 0.3 165 11.410 4.693 0.000 4.693 0.23 0.68 166 4.017 14.943 0.676 15.619 0.25 0.35 167 4.371 5.654 11.248 16.902 0.21 0.58 168 3.627 11.162 13.275 24.436 0.42 0.25 169 8.196 3.720 16.240 19.960 0.21 0.59 170 3.508 11.635 16.452 28.087 0.03 0.84 171 0.478 23.887 27.609 51.497 0.84 0.29 172 27.205 4.507 24.292 28.799 0.01 0.78 173 0.171 19.859 28.628 48.487 0.15 0.77 174 2.356 19.051 46.131 65.183 0.03 0.01 175 0.423 0.107 64.759 64.866 0.48 0.74 176 9.680 17.304 55.186 72.490 0.73 0.68 177 19.610 14.626 52.880 67.506 0.07 0.48 178 1.088 8.423 66.418 74.841 0.89 0.69
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