Purchasing requests arrive $toan$ agent $at$ a rate $of$ six per day. The time between arrivals $is$ exponentially distributed. The agent typically requires $1$ hour $to$ process a request. The processing time $is$ also exponentially distributed. Assuming $8-$hour working days:

$a.$ What $is$ the cycle time $(the$ average time that a request spends $in$ the process$)?$

$b.$ What $is$ the WIP inventory $(the$ average number $of$ requests $in$ the process$)?$

$c.$ How often $is$ the WIP entirely replaced with a new set $of$ requests?

Little's Law: $L=W,L_q=W_q$

$MM1$ system

$=\frac{}{}$

$P_0=1-$

$P_n={}^n(1-)$

$L=\frac{}{1-}$

$L_q=\frac{{}^2}{1-}=L-$

$P(nk)={}^k$