Question

Benny the Barber owns a one-chair shop. At Barber College, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at the rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following:

d. The average utilization of Benny’s time.

Short answer

Utilization rates are a way to degree the productivity and efficiency of a person (or indeed a whole PSO) in producing income against accessible transmission capacity, partitioned over a set time. In less complicated terms, a utilization rate reflects the rate of a team member’s work hours that can be charged to a client versus their general accessibility.

Step-by-step solution

Utilization rate 

Theutilization rate is the rate of a person’s added up working hours that are going through on work that can be charged to a client. No matter how propelled or beneficial a representative is, time will continuously be their restricting calculation no matter how decided they are to do their most extreme. There are, as it were, 24 hours within the day – and as we’ve investigated in profundity some time recently, human creatures don’t do well when we endeavour towards being “always on.”

The average utilization of Benny’s time

Utilization

$$\begin{gathered} \mathrm{\rho }=\frac{\mathrm{\lambda }}{\mathrm{\mu }} \\ =\frac{2}{3} \\ =0.667\mathrm{or}66.7\mathrm{percent}\mathrm{of}\mathrm{all}\mathrm{time} \end{gathered}$$