Online Packet-Routing in Grids with Bounded Buffers

TL;DR

This paper introduces new deterministic and randomized online algorithms for packet routing in grid networks with bounded buffers, achieving improved competitive ratios and handling various buffer and link capacities.

Contribution

It provides the first $O( ext{polylog } n)$ competitive deterministic algorithm for uni-directional grids and improves the randomized ratio to $O( ext{log } n)$ for lines.

Findings

Deterministic algorithm with $O( ext{log}^{O(1)} n)$ competitive ratio.

Randomized algorithm with $O( ext{log } n)$ expected competitive ratio.

Applicable to various buffer sizes and link capacities, including unit capacities.

Abstract

We present deterministic and randomized algorithms for the problem of online packet routing in grids in the competitive network throughput model \cite{AKOR}. In this model the network has nodes with bounded buffers and bounded link capacities. The goal in this model is to maximize the throughput, i.e., the number of delivered packets. Our deterministic algorithm is the first online algorithm with an $O\left(\log^{O(1)}(n)\right)$ competitive ratio for uni-directional grids (where $n$ denotes the size of the network). The deterministic online algorithm is centralized and handles packets with deadlines. This algorithm is applicable to various ranges of values of buffer sizes and communication link capacities. In particular, it holds for buffer size and communication link capacity in the range $[3 \ldots \log n]$. Our randomized algorithm achieves an expected competitive ratio of $O(\log n)$ for the uni-directional line. This algorithm is applicable to a wide range of buffer sizes and communication link capacities. In particular, it holds also for unit size buffers and unit capacity links. This algorithm improves the best previous $O(\log^2 n)$-competitive ratio of Azar and Zachut \cite{AZ}.