a discrete$-$event simulation model of the ICT elevators. However, we did not construct an analytical

model for this system $($thank goodness!$).($a$)(3$ marks$)$ Draw a simple Markov chain to represent the

various states and state transitions for the humans. As a hint, your diagram should have at least $3$ states,

but no more than $12$ states. State any assumptions.

b: Draw a simple Markov chain to represent the various states and state transitions for a single elevator.

As a hint, your diagram should have at least $5$ states, but no more than $20$ states. State any assumptions.

c: Suppose that you want to determine the steady$-$state probability pi that the $($single$)$ elevator is on

floor i$.$ With reference to your diagram in $($b$)$ above, what additional information would be required in

order to solve for the steady$-$state probabilities, and what would be the $($logical$)$ steps for doing so$?$

$($Note that you do NOT need to solve the Markov chain to determine the steady$-$state probabilities; you

merely need to indicate HOW one would go about solving it$,$ by listing the main steps involved.$)$