After the Revolution, and after the Worker's Paradise of each according to his ability, each according to his need been established, eventually the instruments of government, or ruling class, would wither away entirely, as the system would be smoothly functioning, and they would no longer be needed.

If you haven't read the Communist Manifesto, do so, mindful that Marx and Engalls writing in the mid 1800's were referring to what should happen to Great Britain alone after her industrialization, not about Russia or China (or any other state that put communism into practice) before their industrialization.  Communist Theory and Communist Practice -- well, I'll leave you to ponder those.

Marx final vision was that the workers, the creators of value, would take over the means of production, presently owned by the Capitalists, and would create a communist/socialist utopia where goods would be distributed according to their famous dictim:  "From each according to his ability; to each according to his needs."

I have no idea what should happen next.  There is historical evidence that the Pilgrims originally started out as a socialist colony, but reverted to a Capitalist system when the original experiment didn't work.  There have been many other attempts at social utopias, and most of them have also failed.  Perhaps Marx did not factor in human greed and laziness, but I feel that the next step is a return to some form of capitalism that encourages growth and competition while maintaining a clearly defined and limited social net for those who need the assistance.

George Orwell's "Animal Farm" shares pretty much the same vision.  Eventually someone attempts to seize power/control, and these individuals eventually take over for the Capitalists (Mr. Jones) that they threw out.  If you haven't read it yet, I'd do so at your earliest convenience.