This has to be done in Python. Thank you so much.

Implement a simulation of this Markov chain and plot a trajectory on the time interval $[0,60]

S=(0,1,2,3,4)

It is time for students to register for classes, and a line is forming at the registrars office for those who need assistance. It takes the registrar an exponentially distributed amount of time to service each student, at the rate of one student every 5 minutes. Students arrive at the office and get in line according to a Poisson process at the rate of one student every 4 minutes. Line size is capped at 4 people. If an arriving student finds that there are already 4 people in line, then they try again later. As soon as there is at least one person in line, the registrar starts assisting the first available student. The arrival times of the students are independent of the registrars service time.