How can i set this problem as a continuous markov chain?

[Pablorodn]

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

kindly regards

Pablo RodrÃ*guez Bogotá Colombia

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.

 

[Valkarie]

This problem can be configured as a continuous Markov chain with the main variable being the status of the machines (working, blocked, or idle). The states of the chain would be the combination of the statuses of each of the three machines. For example, WBI would indicate that machine 1 is working, machine 2 is blocked, and machine 3 is idle. The transition rates for the Markov chain would be determined by the Exponential distributions of the time needed to complete the machining operations for each respective machine. The transition matrix for the Markov chain would consist of the transition rates between the different states.