Consider a single$-$server workstation that processes two types of jobs, type $1$ and type $2.$ Each job type arrives according

to a Poisson process with corresponding rates ra$1=6$ hr$1$ and ra$2=9$ hr$1$ Use the result from part $($i$)$ to argue that this workstation

can be modeled as an M$/$G$/1$ queue. Let r$.$v$.$ Te denote the effective

processing time for this queueing station, and determine the mean te$,$

the variance $\backslash$sigma

$2$

e and the squared coefficient of variation c

$2$

e

for this r$.$v$.$

iii. $(5$ pts$)$ Use your results from part $($ii$)$ to show that the operation of

this workstation is stable.

$.$

These two arrival processes are independent from each other, and jobs are

processed according to a first$-$come$-$first$-$serve policy. The processing times

of the two job types are normally distributed with the corresponding distributions being N$1(5$min, $4$min$2$

$)$ and N$2(3$min, $1$min$2$

$).$