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Queueing networks are typically subject to demultiplexing operations, whereby network nodes split flows into multiple sub-flows. The demultiplexing operation captures relevant network aspects such as packet loss or multi-path routing. In this paper we propose a novel approach to analyze queueing networks with demultiplexing. The basic idea is to represent a network node implementing a demultiplexing operation on an output flow as an equivalent system for which the corresponding input flow is logically demultiplexed according to the demultiplexing operation at the output. In this way, the service given to one of the demultiplexed sub-flows at the output can be expressed in terms of a leftover service curve, and consequently performance bounds can be derived using the network calculus methodology. Using numerical illustrations, we show that the obtained bounds improve upon existing bounds, especially in the case of the rather small sub-flows.