Question

Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of 12 jobs/hour. The process time of the workstation is exponentially distributed with a mean of 4 minutes. The expected number of jobs at the workstation at any given point of time is _____ [round off to the nearest integer]

• A. 4

Answer 1

The correct option is A 4
$\lambda =12\text{per hour,}\frac{1}{\mu }=4min/Jobs,\mu =15Jobs/hr$

$\rho =\frac{12}{15}=\frac{4}{5}$

$L_s=\frac{\rho }{1-\rho }=\frac{\frac{4}{5}}{1-\frac{4}{5}}=\frac{\frac{4}{5}}{\frac{1}{5}}$

$=\frac{4}{5}\times \frac{5}{1}=4Jobs$