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This paper considers the problem of finding the shortest path from the source node to the sink node in networks of queues in steady conditions. Some nodes in the network contain service stations with either one or infinite number of servers. The arrival process is assumed to be Poisson and also the arc lengths are assumed to be mutually independent random variables. The paper introduces a
method, which transforms each node that contains a service station to a stochastic arc corresponding to the waiting time in that node. The stochastic network is then transformed to a bicriteria network by computing the expected value and the variance of the waiting times and augmenting those to the new arc. Finally, by defining the proper utility function, dynamic programming is used to obtain the shortest path.