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I request your help in order to know, how can i configure this problem as a continuous markov chain, need to define the main variable, the states, transition rates, and the matrix.

I thought that it could be relationed with the status of the machines, because if the machine 1 is working or blocked the machine 2 will be working, blocking or idle, and machine 3 may be working or idle too. That is my only approach about the issue

Another approach is, Thus (w,b,w) will be a state where the first machine is working, the second machine is blocked and third machine is working. In this state, what are possible events: the last machine can finish, in which case the part machine 2 will move to machine 3, and machine 2 will be come idle, machine 3 will start working on this part, machine 1 will continue working. Thus the new state will be (w,i,w). Thus the transition rate from (w,b,w) to (w,i,w) will be mu_3.

Right now i have not any further aproximations about the way to configure this chain, thats why i kindly request your help,

kindly regards

Pablo Rodríguez Bogotá Colombia

[I]An automobile part needs three machining operations performed in a given sequence. These operations are performed by three machines. The part is fed to the first machine, where the machining operation takes an Exp. 1/ amount of time. After the operation is complete, the part moves to machine 2, where the machining operation takes Exp. 2/ amount of time. It then moves to machine 3, where the operation takes Exp. 3/ amount of time. There is no storage room between the two machines, and hence if machine 2 is working, the part from machine 1 cannot be removed even if the operation at machine 1 is complete. We say that machine 1 is blocked in such a case. There is an ample supply of unprocessed parts available so that machine 1 can always process a new part when a completed part moves to machine 2. [/I]

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closed as off-topic by Did, John Doe, polfosol, José Carlos Santos, Tom-Tom Apr 10 '18 at 20:24

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  • $\begingroup$ the approach given is that, Thus (w,b,w) will be a state where the first machine is working, the second machine is blocked and third machine is working. In this state, what are possible events: the last machine can finish, in which case the part machine 2 will move to machine 3, and machine 2 will be come idle, machine 3 will start working on this part, machine 1 will continue working. Thus the new state will be (w,i,w). Thus the transition rate from (w,b,w) to (w,i,w) will be mu_3. $\endgroup$ – Pablo Rodríguez Apr 10 '18 at 20:07