Question

A person repairing cycles finds that the time spent on the cycles has exponential distribution with mean 25 minutes. If the cycle's arrival is approximately Poisson with an average rate of 12 for 8 hour days. What is the expected number of cycles in the system ?

• A. $\frac{25}{9}$
• B. $\frac{5}{3}$
• C. $\frac{2}{3}$
• D. $\frac{8}{3}$

Answer 1

The correct option is B $\frac{5}{3}$

$\text{Arrival rate,}\lambda =\frac{12}{8\times 60}=\frac{1}{40}\text{cycles/min}$

$\text{Service rate,}\mu =\frac{1}{25}\text{cycles/min}$

$\text{Now, number of cycles in system}$

$L_s=\frac{\lambda }{\mu -\lambda }=\frac{\frac{1}{40}}{\left(\frac{1}{25}\right)-\left(\frac{1}{40}\right)}$

$L_s=\frac{25}{15}=\frac{5}{3}$