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Queue Data - MANAGING ATM QUEUES A branch office of...

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Mean Numbers of Customers Arriving for ATM Service Hour Sunday Monday Tuesday Wednesday Thursday Friday Saturday Midnight-1 a.m. 0.6 4.8 17.8 10.4 11.6 18.2 17.0 1-2 a.m. 0.8 0.2 9.6 3.2 10.2 4.0 16.2 2-3 a.m. 0.2 3.6 2.4 8.0 8.0 5.8 6.8 3-4 a.m. 0.2 0.6 6.4 4.4 5.0 2.4 8.4 4-5 a.m. 0.4 0.8 3.0 13.8 2.8 6.4 1.4 5-6 a.m. 0.2 4.2 2.2 3.8 11.2 6.6 3.6 6-7 a.m. 1.0 7.0 21.6 12.0 26.4 42.0 2.0 7-8 a.m. 1.8 69.4 55.8 53.2 80.4 86.8 11.6 8-9 a.m. 5.8 111.2 120.4 136.6 137.0 162.2 4.6 9-10 a.m. 5.0 72.6 93.2 91.2 68.6 114.6 14.2 10-11 a.m. 4.6 78.2 58.0 68.8 85.6 106.4 8.8 11 a.m.-Noon 8.2 97.2 78.8 99.0 147.6 121.6 14.4 Noon-1 p.m. 5.4 161.6 98.4 183.2 166.4 168.0 18.0 1-2 p.m. 3.8 154.0 98.2 170.4 172.2 181.8 21.6 2-3 p.m. 6.6 149.2 90.6 151.4 148.0 141.2 12.2 3-4 p.m. 4.0 125.8 67.2 82.6 105.8 119.2 17.8 4-5 p.m. 7.8 88.0 72.2 96.8 98.6 124.2 13.8 5-6 p.m. 6.2 133.0 82.4 89.4 84.0 148.0 14.2 6-7 p.m. 3.0 57.4 70.0 59.0 61.4 89.6 7.4 7-8 p.m. 0.8 36.4 33.8 50.6 53.8 40.8 8.0 8-9 p.m. 5.2 25.2 24.8 8.8 49.8 24.4 5.6 9-10 p.m. 2.4 11.6 25.2 19.2 21.0 29.8 2.6 10-11 p.m. 3.6 4.0 9.0 8.0 9.4 11.2 0.0 11 p.m.-Midnight 1.2 16.4 7.4 5.4 21.2 1.4 1.2 Arrival Times After the Hour Week 1 Service Times A branch office of People's Bank has a set of three automatic teller machines ( ATMs ) least one of which is available to the public 24 hours a day, 7 days a week. The manager has complete records of ATM usage and service times for five weeks. MANAGING ATM QUEUES Our Class Project will analyze the data from the 9 a.m. and 9 p.m. hours on Friday. The arrival times of all ATM customers are shown below. The times are in minutes after the start of the hour. 7,634 customers used the ATM's during the first week that records were kept. The time, in minutes , between each customer's start of service and his or her departure from the ATM was recorded for each customer.
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Number Time 1 1.09 Week 1 Week 1 2 0.64 0.02 0.36 3 3.23 0.53 6.70 4 1.80 2.36 7.63 5 1.28 2.50 11.52 6 0.62 2.79 11.54 7 1.71 3.85 14.89 8 3.21 4.39 15.47 9 3.27 4.41 20.70 10 1.26 5.74 23.17 11 0.81 6.20 23.22 12 0.95 6.48 23.81 13 1.31 7.04 25.88 14 0.88 7.88 26.39 15 2.15 7.91 26.91 16 1.68 7.94 30.96 17 0.61 8.71 32.64 18 3.14 9.00 32.84 19 0.50 9.31 33.05 20 1.41 9.54 34.94 21 1.32 9.55 35.23 22 1.25 10.10 35.58 23 0.84 10.42 35.69 24 1.04 10.57 36.67 25 2.08 10.64 37.45 26 3.24 10.70 38.98 27 1.01 11.89 41.16 28 1.17 12.55 42.71 29 1.29 13.09 42.79 30 1.22 14.45 44.64 31 0.97 14.61 46.40 32 0.76 17.28 48.84 33 1.33 18.41 51.34 34 0.54 19.17 53.05 35 0.56 19.66 53.57 36 0.82 21.01 56.22 37 1.71 21.07 Week 2 38 1.64 22.00 0.63 39 1.20 22.41 3.71 40 0.80 22.94 9.62 41 0.71 23.21 11.27 42 1.23 23.41 12.87 43 1.64 9-10 a.m. Friday 9-10 p.m. Friday
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24.52 16.68 44 1.33 24.67 18.82 45 0.47 24.81 20.22 46 1.17 24.86 22.75 47 0.48 25.08 25.41 48 0.68 25.40 25.70 49 0.73 25.43 27.05 50 1.03 25.96 27.49 51 1.26 26.49 27.97 52 1.21 27.36 28.67 53 1.98 27.72 29.10 54 1.01 28.77 33.78 55 1.09 29.47 34.25 56 1.15 29.66 36.54 57 0.75 29.87 40.99 58 1.01 29.88 41.39 59 1.03 30.12 46.72 60 1.13 30.19 46.87 61 2.75 30.31 48.99 62 1.17 30.97 50.34 63 0.99 31.42 51.82 64 0.93 32.38 57.66 65 1.59 33.08 57.69 66 1.46 33.42 Week 3 67 0.99 34.06 0.46 68 1.46 34.33 4.22 69 1.01 34.50 9.30 70 3.04 35.21 10.10 71 0.72 37.68 11.59 72 1.05 37.91 12.85 73 0.62 38.82 13.01 74 1.13 40.22 13.09 75 1.15 40.55 15.59 76 2.66 41.45 17.08 77 0.96 41.90 18.09 78 1.93 43.11 23.72 79 1.72 45.13 24.78 80 2.32 45.22 28.30 81 1.38 46.22 28.60 82 0.84 46.89 31.10 83 0.76 46.90 33.84 84 0.91 46.99 36.38 85 1.11 47.75 38.89 86 0.65 48.56 41.28 87 1.09
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48.76 41.58 88 0.84 48.80 43.17 89 0.97 49.28 43.56 90 1.81 49.50 44.71 91 1.14 49.60 45.96 92 1.07 49.68 47.53 93 0.85 49.98 51.11 94 0.92 50.68 54.28 95 1.80 50.77 59.06 96 1.00 50.87 59.95 97 1.14 50.92 Week 4 98 1.74 51.38 0.19 99 0.61 53.15 0.20 100 1.69 54.93 0.25 101 0.75 55.92 2.21 102 0.87 56.18 6.91 103 1.24 56.58 9.74 104 1.68 57.65 11.00 105 3.43 57.71 11.69 106 0.86 57.92 12.13 107 1.14 58.40 14.25 108 0.60 Week 2 15.64 109 0.92 0.10 15.68 110 1.09 0.38 16.35 111 1.06 0.94 16.39 112 4.57 2.66 16.53 113 2.15 2.89 16.85 114 0.92 3.13 19.55 115 0.98 3.56 21.71 116 1.44 3.62 28.42 117 1.24 4.13 35.03 118 1.43 4.40 37.29 119 0.95 5.66 38.21 120 0.70 5.74 42.07 121 1.47 5.83 46.60 122 1.13 7.11 48.39 123 1.17 7.23 48.48 124 4.59 7.26 50.88 125 1.25 7.34 52.34 126 1.05 7.55 54.73 127 0.80 8.73 56.59 128 0.85 8.82 57.12 129 0.74 9.15 Week 5 130 0.78 9.23 0.80 131 0.99
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9.95 10.18 132 1.26 10.07 10.69 133 2.46 10.17 11.90 134 1.05 10.37 15.20 135 1.20 10.80 19.16 136 1.85 11.19 19.35 137 0.68 11.67 20.57 138 0.80 12.16 20.67 139 1.21 12.38 31.04 140 1.19 12.45 31.71 141 0.63 12.62 32.12 142 1.10 12.77 34.81 143 0.90 13.05 34.95 144 1.35 14.22 34.98 145 1.09 15.71 39.17 146 0.98 16.52 40.55 147 1.07 17.26 49.41 148 0.63 17.47 50.73 149 1.17 17.64 51.90 150 1.03 17.73 53.27 151 0.61 18.38 53.55 152 1.85 18.94 54.25 153 0.98 19.21 54.54 154 1.82 19.48 55.29 155 1.05 19.56 156 1.01 20.01 157 0.88 20.70 158 1.16 20.94 159 0.59 21.03 160 1.95 22.09 161 1.39 22.18 162 1.36 22.31 163 1.10 22.32 164 1.03 23.22 165 1.41 23.69 166 2.20 24.76 167 4.05 25.44 168 2.40 25.50 169 1.09 25.78 170 1.42 26.42 171 1.42 27.15 172 1.40 27.57 173 0.69 28.53 174 2.40 28.87 175 1.29
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29.27 176 1.19 29.32 177 1.91 29.44 178 1.53 31.01 179 0.95 32.10 180 0.80 32.54 181 1.10 33.02 182 0.70 33.05 183 1.25 33.37 184 1.22 33.66 185 0.84 34.49 186 1.07 35.00 187 1.01 35.16 188 0.95 35.26 189 3.02 36.72 190 1.13 37.31 191 1.08 38.45 192 1.15 38.46 193 1.03 39.76 194 0.71 40.19 195 0.64 40.87 196 1.17 41.63 197 1.08 41.70 198 1.98 41.86 199 1.03 42.11 200 1.09 42.42 201 0.62 42.56 202 0.44 42.66 203 0.83 43.05 204 2.96 44.91 205 1.15 45.99 206 1.45 46.22 207 1.21 46.79 208 1.07 47.17 209 2.05 47.91 210 0.58
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