Question $3)$ Consider an automated guided$-$vehicle system with two stations and two vehicles. A load request arrives every hour and is transported by one of the vehicles. It takes a vehicle $10$ minutes to load and unload the unit and $15$ minutes to move to the other station. The vehicle stays at the station where the load is delivered and waits until it is needed. Note that the load requests arrive far enough apart that they always find the vehicles empty and waiting at the stations. There is a $70\%$ chance that the arriving load request is at station $1$ destined for station $2.$ The remaining loads arrive at station $2$ destined for station $1.($It is sometimes necessary for a vehicle to travel empty to pick up the load.$)$ Represent the state of the system as seen by the $k^{th}$ arriving load as $V_k=(N{1}_k,N{2}_k)$ where $N{1}_k$ is the number of vehicles found at station $1$ and $N{2}_k$ is the number of vehicles found at station $2.$ Note that $\{V_k,k=0,1,$dots$\}$ is a discrete$-$time Markov chain.