$4\mathrm{.}24$ At a facility for train maintenance, work is done on a number of separate parallel tracks.

On each of these tracks there is room for two trains on a front part and a back part. Trains

can leave the tracks only on the same side they enter the tracks. That is$,$ upon completion of

its maintenance a train may be locked in by another train that arrived later on the same track

but has not yet completed its maintenance. For each of the tracks there are two maintenance

crews, one for the train at the front part of the track and one for the train at the back. Trains

requesting maintenance arrive at the maintenance facility according to a Poisson process

with rate $.$ A train immediately receives maintenance when it finds a free place at one of

the tracks upon arrival; otherwise, the train waits until a maintenance place becomes free.

A newly arriving train is directed to a front part if both a front part and a back part are free.

The amount of time needed to serve a train has an exponential distribution with mean $\frac{1}{}.$

It is assumed that

$($a$)$ Formulate a continuous$-$time Markov time chain for the performance evaluation of

the maintenance track.

This problem is related to the Advanced Stochastic processes, so need answer from the expert who has this advanced stochastic processes background. Thank you