 # Solved: Another queuing problem question from Ragsdale "Spreadsheet Modeling & Data Analysis

Another queuing problem question from Ragsdale “Spreadsheet Modeling & Data Analysis using the Q.xls template.

Setup: patients arrive to a physician’s office according to a poisson process at a rate of 6 patients per hour. The office is staffed by two physicians. Each physician spends 20 minutes (exponentially distributed) with a patient. Use the Q.xls template to answer the following question:
Question: if the physician earns \$200/hr, what is the minimum goodwill cost of waiting per hour that would make you hire an additional physician to staff the office?

Arrival rate (Lambda or A) = 6 per hour

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Service rate (Mu or S) = 20 minutes or 60/20 = 3 per hour

Number of physicians (M) = 2

A/S = 6/3 = 2.0

Total cost in case of 2 physicians =

Lq for A/S or Lambda/Mu = 2 and M = 3 is 0.889

Ls = Lq + A/S = 0.889 + 2 = 2.889

Let goodwill cost of waiting in system = x per hour

Equating physician cost to goodwill cost as 200 = 2.889*x

x = 69.2\$ per hour

Thus, goodwill cost should be minimum 69.2\$ in order to hire additional physician