Each Tuesday, the new residents at an inpatient rehabilitation clinic must visit

Question

Each Tuesday, the new residents at an inpatient rehabilitation clinic must visit the medication lab and have all of their existing medications inventoried when they arrive. The interarrival times of patients to the medication lab follow a uniform distribution with an upper bound of 45 minutes and a lower bound of 30 minutes. The service times to have their medication logged follow a normal distribution with a mean of 20 minutes and a standard deviation of 5 minutes.

Using Excel, determine queuing and service statistics for the 40 patients who visit the medication lab over a one-day period. The columns of data you will need to generate include patient ID, interarrival time, arrival time, service start time, wait time, service time, service completion time, time in system, and server idle time.

Calculate the following summary statistics

a. Number of patients who wait

b. Probability of waiting

c. Average wait time

d. Maximum wait time

e. Percentage of time server is busy

f. Number waiting > 1 minute

g. Probability of waiting > 1 minute

h. Average number of patients in line

Explanation / Answer

Upper Bound 45 Number of patients who wait 0 Lower Bound 30 probability of waiting 0 average wait time 0.037003864 maximum wait time 1.480154559 Mean 20 % of time server is busy -49.35867807 Standard Deviation 5 Number waiting > 1 minute 1 probability of waiting > 1 minute 0.025 Average number of patients in line 0 Patient id interarrival time arrival time service start time wait time service time service completion time time in system server idle time 1 35.79 35.79 35.79 0 15.87 51.66 15.87 0.00 2 32.09 67.88 67.88 0 24.05 91.93 24.05 -24.05 3 30.84 98.72 98.72 0 22.25 120.97 22.25 -22.25 4 30.60 129.32 129.32 0 18.13 147.46 18.13 -18.13 5 32.66 161.99 161.99 0 12.32 174.30 12.32 -12.32 6 37.75 199.73 199.73 0 17.86 217.59 17.86 -17.86 7 33.50 233.23 233.23 0 24.35 257.58 24.35 -24.35 8 39.64 272.88 272.88 0 19.66 292.53 19.66 -19.66 9 34.80 307.67 307.67 0 8.32 315.99 8.32 -8.32 10 38.73 346.41 346.41 0 17.13 363.54 17.13 -17.13 11 39.24 385.65 385.65 0 17.37 403.01 17.37 -17.37 12 36.54 422.19 422.19 0 25.46 447.64 25.46 -25.46 13 39.32 461.50 461.50 0 22.52 484.03 22.52 -22.52 14 43.06 504.57 504.57 0 27.65 532.21 27.65 -27.65 15 35.16 539.72 539.72 0 12.08 551.80 12.08 -12.08 16 41.99 581.71 581.71 0 25.22 606.93 25.22 -25.22 17 41.99 623.70 623.70 0 20.75 644.45 20.75 -20.75 18 30.48 654.18 654.18 0 9.03 663.21 9.03 -9.03 19 31.84 686.02 686.02 0 18.92 704.94 18.92 -18.92 20 41.46 727.48 727.48 0 22.21 749.69 22.21 -22.21 21 38.54 766.03 766.03 0 16.03 782.06 16.03 -16.03 22 31.42 797.45 797.45 0 22.30 819.75 22.30 -22.30 23 44.71 842.16 842.16 0 24.74 866.89 24.74 -24.74 24 39.40 881.56 881.56 0 19.13 900.69 19.13 -19.13 25 32.18 913.74 913.74 0 25.20 938.94 25.20 -25.20 26 41.26 955.00 955.00 0 35.43 990.43 35.43 -35.43 27 33.95 988.95 990.43 1.480154559 16.99 1007.42 18.47 -16.99 28 38.91 1027.86 1027.86 0 20.09 1047.95 20.09 -20.09 29 42.41 1070.27 1070.27 0 16.17 1086.44 16.17 -16.17 30 33.38 1103.65 1103.65 0 23.79 1127.44 23.79 -23.79 31 44.11 1147.76 1147.76 0 16.26 1164.02 16.26 -16.26 32 44.83 1192.59 1192.59 0 32.03 1224.62 32.03 -32.03 33 38.57 1231.17 1231.17 0 19.11 1250.27 19.11 -19.11 34 31.10 1262.26 1262.26 0 24.27 1286.53 24.27 -24.27 35 31.73 1294.00 1294.00 0 21.16 1315.15 21.16 -21.16 36 41.39 1335.38 1335.38 0 17.79 1353.18 17.79 -17.79 37 43.80 1379.19 1379.19 0 19.38 1398.56 19.38 -19.38 38 41.91 1421.10 1421.10 0 24.80 1445.89 24.80 -24.80 39 39.64 1460.73 1460.73 0 17.55 1478.28 17.55 -17.55 40 43.87 1504.60 1504.60 0 26.90 1531.50 26.90 -26.90

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