OPTIMIZING FLOW-RATES IN A QUEUING NETWORK WITH SIDE CONSTRAINTS

In this paper, modified versions of the classical deterministic maximu m flow and minimum cost network flow problems are presented in a stoch astic queueing environment. In the maximum flow network model, the thr oughput rate in the network is maximized such that for each are of the network the resulting probability of finding congestion along that ar e in excess of a desirable threshold does not exceed an acceptable val ue. In the minimum cost network flow model, the minimum cost routing o f a flow of given magnitude is determined under the same type of const raints on the arcs. After proper transformations, these models are sol ved by Ford and Fulkerson's labeling algorithm and out-of-kilter algor ithm, respectively.