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For example, Baccelli and Hong [7] consider a window flow control model where the initial population is non-unique. , rij) and the other with n^ = ( n f , . . , n^).

This system is max-plus linear even though the machines do not operate according to FCFS and there are several types of customers. However, it should be clear from the model that the fact that this system is max-plus linear stems from the particular combination of priority service discipline and classes of customers (parts). 3 Blocking Schemes We have already considered blocking after service of manufacturing type. Another frequently used blocking scheme is blocking before service, that is, an item is only processed if a place is available at the next station.

We now consider the arrival process at j more closely. Let the A;*'' item departing from j be constituted out of the items which triggered the {ai{j^ k)Y'^ departure from i G A{j, k). If the item was initially present at j , set aj{j, fc) = 0 and A{j,k) = {j]. 30) and we call ai{j, k) the arrival index. If the network is open, we set ai(0, k) = e for all i and all k, which is tantamount to assuming that the source does not have to wait for arrivals. {aj{k),Xj{c[j,k))) = aj{k) ^'=^ ®Xj{c{j,k)) 0 Xi{ai{j,k))®Xj{c{j,k)).

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