We investigate packet routing games in which network users selfishly route themselves through a network over discrete time, aiming to reach the destination as quickly as possible. Conflicts due to limited capacities are resolved by the first-in, first-out (FIFO) principle. Building upon the line of research on packet routing games initiated by Werth et al. [21], we derive the first non-trivial bounds for packet routing games with FIFO. Specifically, we show that the price of anarchy is at most 2 for the important and well-motivated class of uniformly fastest route equilibria introduced by Scarsini et al. [16] on any linear multigraph. We complement our results with a series of instances on linear multigraphs, where the price of stability converges to at least \(\frac{e}{e-1}\) . Furthermore, our instances provide a lower bound for the price of anarchy of continuous Nash flows over time on linear multigraphs which establishes the first lower bound of \(\frac{e}{e-1}\) on a graph class where the monotonicity conjecture is proven by Correa et al. [5].