Semi-open Jackson Network
A Semi-open Jackson network has features of both open and closed networks: it follows the descriptions of the open model with the exception that the total number in the network is limited to a maximum of K jobs at any time.
It turns out that the semiopen model can be reduced to a closed network with K jobs and J + 1 nodes. The additional node, indexed as node 0, represents the external world. Its service rate is defined as if and . This captures the blocking of the external arrivals when the buffer is full.
Set and, then they are solutions to the set of equations:
It is same as the one described in for a J + 1 closed work.
Read more about this topic: Jackson's Theorem (queueing Theory)
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