PLEASE HELP ME SOLVE THSI STEP BY STEP IN ARENA

$8-7$ A prototype of a new airport bag$-$screening system is currently being designed, as

in the following figure. Bags arrive to the system with interarrival times of EXPO$(0\mathrm{.}25)$

$($all times are in minutes$),$ and are loaded on a load conveyor $(75$ feet long$)$ and conveyed

to an initial scan area. At the initial scan area, the bags are dropped into a chute to wait

for the initial scan, which is of duration TRIA$(0\mathrm{.}1,0\mathrm{.}25,0\mathrm{.}35).$ Based on the results of

the scan, accepted bags $(81\%)$ are loaded on an out conveyor $(40$ feet long$)$ and con$-$

veyed to exit the system, whereas rejected bags are loaded on a secondary conveyor $(20$

feet long$)$ and conveyed to a secondary scan area. At the secondary scan area, the bags

are dropped into a chute to wait for a visual inspection, which takes TRIA$(0\mathrm{.}6,1\mathrm{.}2,1\mathrm{.}4).$

After the inspection, they are sent through a secondary scanner that is $10$ feet long. This

Chapter $8$

scan takes $1\mathrm{.}2$ minutes and only one bag can be in the scanner at a time. At the end of

the secondary scanner, the bags are examined by another inspector, taking EXPO$(0\mathrm{.}4).$

Based on the results of this secondary inspection, $10\%$ of the bags are sent to a reject

area for further inspection, accepted bags are loaded on a third conveyor $(20$ feet long$)$

and conveyed to exit the system. All conveyors are nonaccumulating with a velocity of

$40$ feet per minute. Each bag requires one foot of space on each of the conveyors. De$-$

velop a model of this system and run it for $2,000$ minutes. Use a resource$-$constrained

route to model the second scanner.

The current design calls for a chute capacity of $20$ at the initial scan area and a

total capacity of $25$ at the secondary scan area, not including the bag undergoing the

visual inspection. What percent of the time would you expect this capacity be exceeded?

$($Work this exercise with infinite chute capacities, and just watch the percent of time the

chute capacities contemplated above would be exceeded if they were put into effect.$)$

HINT: Add two time$-$persistent statistics to collect this information using logical expres$-$

sions that evaluate to zero if the number of bags is less than the capacity, and to one if

the capacity is exceeded.