Hardness of Low Delay Network Scheduling
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Author(s)
Shah, Devavrat
Tse, David N. C.
Tsitsiklis, John N.
Date Issued
December 2011
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Shah, Devavrat, David N. C. Tse, and John N. Tsitsiklis. “Hardness of Low Delay Network Scheduling.” IEEE Transactions on Information Theory 57.12 (2011): 7810–7817.
Version
Author's final manuscript
Abstract
We consider a communication network and study the problem of designing a high-throughput and low-delay scheduling policy that only requires a polynomial amount of computation at each time step. The well-known maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable performance in terms of throughput and delay but, for general networks, it can be computationally very expensive. A related randomized policy proposed by Tassiulas (1998) provides maximal throughput with only a small amount of computation per step, but seems to induce exponentially large average delay. These considerations raise some natural questions. Is it possible to design a policy with low complexity, high throughput, and low delay for a general network? Does Tassiulas' randomized policy result in low average delay? In this paper, we answer both of these questions negatively. We consider a wireless network operating under two alternative interference models: (a) a combinatorial model involving independent set constraints and (b) the standard SINR (signal to interference noise ratio) model. We show that unless NP ⊆ BPP (or P = NP for the case of determistic arrivals and deterministic policies), and even if the required throughput is a very small fraction of the network's capacity, there does not exist a low-delay policy whose computation per time step scales polynomially with the number of queues. In particular, the average delay of Tassiulas' randomized algorithm must grow super-polynomially. To establish our results, we employ a clever graph transformation introduced by Lund and Yannakakis (1994).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
https://doi.org/10.1109/tit.2011.2168897
