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This paper addresses routing in networks with both delay-sensitive (class 1) and delay-insensitive (class 0) traffic where the class 1 traffic is to be delivered with bounded delay and the delay of class 0 traffic is to be minimized subject to this constraint. This delay-constrained routing, with constraints on the overall mean delay of class 1 traffic, is shown to be NP-hard with an M/M/1 link model...