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Find a Doctor (FaD) is a small startup that helps people find a physician that best meets their...

Question:

Find a Doctor (FaD) is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc.) During a "slow" time for FaD 7, staff members take calls from customers. On average, one call arrives every 5 minutes. On average, each staff member spends 20 minutes with each customer. How Long (in minutes) does a customer spend on average waiting on hold before he or she can start speaking to a representative?

a. 1.2 mins

b. 0.7 mins

c. 11.4 mins

d. 15.2 mins

Queue

Queue refers to the line of customer waiting for the consumption of service of a partcular product. It is the line of people thoes are waiting for their chance of seeking the service from the service render or producer.

Answer and Explanation:

The option a. 1.2 mins closest, therefore, it is the correct answer.

{eq}\begin{align*} {\rm{Utilization}} &= \dfrac{{{\rm{Arrival}}\,{\rm{Rate}}}}{{{\rm{Service}}\,{\rm{Rate \times Number}}\,{\rm{Of}}\,{\rm{Servers}}}}\\ &= \dfrac{{1/5}}{{1/20 \times 7}}\\ &= \dfrac{{0.2}}{{0.05 \times 7}}\\ &= \dfrac{{0.2}}{{0.35}}\\ &= 0.6\% \,(approx) \end{align*} {/eq}

The average waiting time for the customers assuming that the coefficients of variation for the arrival process and the service process are both 1.

{eq}\begin{align*} {\rm{Time}} &= \left[ {\dfrac{{{\rm{Processing}}\,{\rm{Time}}}}{{{\rm{Number}}\,{\rm{Of}}\,{\rm{Server}}}}} \right] \times \left[ {\dfrac{{{\rm{Utilizatio}}{{\rm{n}}^{\sqrt {2[(m + 1)} - 1}}}}{{{\rm{1 - }}\,{\rm{Utilization}}}}} \right] \times \left[ {\dfrac{{{\rm{CO}}{{\rm{V}}_{\rm{a}}}^2{\rm{ + CO}}{{\rm{V}}_{\rm{p}}}^2}}{{\rm{2}}}} \right]\\ &= \left[ {\dfrac{{20}}{7}} \right] \times \left[ {\dfrac{{{{0.6}^3}}}{{1 - 0.6}}} \right] \times \left[ {\dfrac{{1 + 1}}{2}} \right]\\ &= 2.8 \times \dfrac{{0.216}}{{0.4}} \times 1\\ &= 2.8 \times 0.54 \times 1\\ &= 1.512 \end{align*} {/eq}


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