The Network as a Storage Device: Dynamic Routing with Bounded Buffers

Abstract

We study dynamic routing in store-and-forward packet networks where each network link has bounded buffer capacity for receiving incoming packets and is capable of transmitting a fixed number of packets per unit of time. At any moment in time, packets are injected at various network nodes with each packet specifying its destination node. The goal is to maximize the throughput, defined as the number of packets delivered to their destinations.

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 $\tilde{O}(\sqrt{n})$-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 $\tilde{\Theta}(n^{2/3})$ while no greedy algorithm can achieve a ratio better than $\Omega(\sqrt{n})$. Finally, for an arbitrary network with m edges, we show that NTG is $\tilde{\Theta}(m)$-competitive, improving upon an earlier bound of O(mn) [1].