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In this paper we address the problem of finding end-to-end delay bounds for single leaky-bucket shaped flows subject to FIFO multiplexing in tandems of rate-latency nodes. More specifically, we focus on a methodology, called the Least Upper Delay Bound (LUDB) method, which is based on Network Calculus. The latter has already been used for computing delay bounds in tandems in which the paths of the flows are subject to particular restrictions. In this paper we generalize and extend it to tandems traversed by flows following arbitrary paths. We show that such methodology yields better bounds than those obtained through both per-node analysis and comparable methods proposed in the literature.