Near-Optimal Packet Scheduling in Multihop Networks with End-to-End Deadline Constraints

Abstract

Scheduling packets with end-to-end deadline constraints in multihop networks is an important problem that has been notoriously difficult to tackle. Recently, there has been progress on this problem in the worst-case traffic setting, with the objective of maximizing the number of packets delivered within their deadlines. Specifically, the proposed algorithms were shown to achieve Ω(1/log(L)) fraction of the optimal objective value if the minimum link capacity in the network is C min = Ω(log (L)), where L is the maximum length of a packet's route in the network (which is bounded by the packet's maximum deadline). However, such guarantees can be quite pessimistic due to the strict worst-case traffic assumption and may not accurately reflect real-world settings. In this work, we aim to address this limitation by exploring whether it is possible to design algorithms that achieve a constant fraction of the optimal value while relaxing the worst-case traffic assumption. We provide a positive answer by demonstrating that in stochastic traffic settings, such as i.i.d. packet arrivals, near-optimal, (1-ε)-approximation algorithms can be designed if C min = Ω((over (logL/ε) Ω 2 ). To the best of our knowledge, this is the first result that shows this problem can be solved near-optimally under nontrivial assumptions on traffic and link capacity.