In this paper, we make some progress in understanding what is achievable on various network topologies. For line networks, Nearest-to-Go (NTG), a natural greedy algorithm, was shown to be O(n ^2/3)-competitive by Aiello et al [1]. We show that NTG is [(O)\tilde](Ön)\tilde{O}(\sqrt{n})-competitive, essentially matching an identical lower bound known on the performance of any greedy algorithm shown in [1]. We show that if we allow the online routing algorithm to make centralized decisions, there is indeed a randomized polylog(n)-competitive algorithm for line networks as well as rooted tree networks, where each packet is destined for the root of the tree. For grid graphs, we show that NTG has a performance ratio of [(Q)\tilde](n^2/3)\tilde{\Theta}(n^{2/3}) while no greedy algorithm can achieve a ratio better than W(Ön)\Omega(\sqrt{n}). Finally, for an arbitrary network with m edges, we show that NTG is [(Q)\tilde](m)\tilde{\Theta}(m)-competitive, improving upon an earlier bound of O(mn) [1].