We study some aspects of the instability of the last-in-first-out (LIFO) scheduling protocol in under-loaded packet-switched networks under the Adversarial Queueing Theory model [Borodin et al., Journal of the ACM, 48(1):13--38,2001] which allows to consider worse-case scenarios in the study of network traffic.
Using a typical strategy in the literature, we improve a known lower bound for the instability of LIFO. The strategy for obtaining such an improvement consist in extending the topology of the original network for which the previous lower bound was shown. Moreover, we show that every additional application of this technique leads to a further (although every time smaller) improvement of the lower bound for instability. However, the number of improvements that this strategy can achieve is limited. Not even when extending the topology infinitely is possible to obtain a lower bound for the instability of LIFO lower than 0.61804.