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# Waiting Line Tables for pharmacist at Arnold Palmer Hospital

The pharmacist at Arnold Palmer Hospital, Saad Alwan, receives 12 requests for prescriptions each hour, Poisson distributed. It takes him a mean time of 4 minutes to fill each, following a negative exponential distribution. Use the waiting line table, Table D.5 and Wq = Lq/^, to answer these questions:

a) What is the average number of prescriptions in the queue?
b) How long will the average prescription spend in the queque
c) Alwan decides to hire a second pharmacist, Ajay Aggerwal, whom he went to
school with and who operates at the same speed in filling prescriptions. How
will the answers to parts (a) and (b) change?

TABLE D.5 WAITING LINE TABLE

Passion Arrivals, Exponential Service Times
Number of Service Channels, M

p 1 2 3 4 5

.10 .0111
.15 .0264 .0008
.20 .0500 .0020
.25 .0833 .0039
.30 .1285 .0069
.35 .1884 .0110
.40 .2666 .0166
.45 .3681 .0239 .0019
.50 .5000 .0333 .0030
.55 .6722 .0449 .0043
.60 .9000 .0593 .0061
.65 1.2071 .0767 .0084
.70 1.6333 .0976 .0112
.75 2.2500 .1227 .0147
.80 3.2000 .1523 .0189
.85 4.8166 .1873 .0239 .0031
.90 8.1000 .2285 .0300 .0041
.95 18.0500 .2767 .0371 .0053
1.0 .3333 .0454 .0067
1.2 .6748 .0904 .0158
1.4 1.3449 .1778 .0324 .0059
1.6 2.8444 .3128 .0604 .0121
1.8 7.6734 .5320 .1051 .0227
2.0 .8888 .1739 .0398
2.2 1.4907 .2770 .0659
2.4 2.1261 .4305 .1047
2.6 4.9322 .6581 .1609
2.8 12.2724 1.0000 .2411
3.0 1.5282 .3541
3.2 2.3856 .5128
3.4 3.9060 .7365
3.6 7.0893 1.0550
3.8 16.9366 1.5184
4.0 2.2164
4.2 3.3269
4.4 5.2675
4.6 9.2885
4.8 21.6384

#### Solution Summary

The expert examines the waiting line tables for pharmacist at Arnold Palmer Hospital. The average prescriptions in the queue and second pharmacist is examined.

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