If one have a continuous review $($S$1,$S$)$ inventory system

with constant lead time

and Poisson demand with arrival rate $\backslash$lambda $.$

$1.$ If a customer is lost if stock on hand is zero, when the customer arrives.

What is the maximum possible number of outstanding orders?

$2.$ If a customer is backordered if stock on hand is zero, when the customer arrives.

What is the maximum possible number of outstanding orders?

$3.$ If a customer is lost if stock on hand is zero, when the customer arrives.

Given that P$\_$i$=($P$($IL$=$i$)$ is known for all i$,$

what is the average number of lost customers per unit of time?