Problem $4$

In this problem, you are asked to develop a Petri net model $($i$.$e$.,$ in PIPE$)$ for a fictitious railroad loop that has

six sectors $($i$.$e$.,$ Sector $1$ to $6$ as shown in the Figure $3$ below$)$ in it and three $(3)$ trains are running in the loop

$($clockwise$).$ Implement the model of the system with the following conditions. These constraints must satisfy at

all times.

Condition #$1$: All three trains initially are in Sector $6,$ i$.$e$.,$ Sector $6$ has a capacity of three $(3)$ trains.

Condition #$2$: Sector $6$ has a maintenance facility and a single train can be temporarily removed from

the sector.

Condition #$3$: Sectors $4$ and $5$ have a combined capacity of two $(2)$ trains, i$.$e$.,$ two trains can be in

these two sectors at the same time $($i$.$e$.,$ one in Sector $4$ and the other in Sector $5).$

Condition #$4$: Sector $1$ has two tracks. The two tracks in this sector can be used for two trains to

occupy the sector at the same time.

Condition #$5$: Sectors $2$ and $3$ have a combined capacity of one $(1)$ train, i$.$e$.,$ a total of at most one

train can be in these two sectors combined.

Figure $3$