[Paper Review] Throughput Optimal Decentralized Scheduling of Multi-Hop Networks with End-to-End Deadline Constraints: II Wireless Networks with Interference

Rahul Singh, P. Rajesh Kumar+1 more|arXiv (Cornell University)|Sep 6, 2017

Advanced Wireless Network Optimization23 references3 citations

TL;DR

This paper proposes a decentralized, throughput-optimal scheduling policy for multi-hop wireless networks with end-to-end deadline constraints, where link interference is modeled via a link interference graph. The policy achieves optimal timely throughput by making decisions based solely on local packet age and location, without requiring global network state knowledge, and scales linearly with network size, with asymptotic optimality under bandwidth constraints.

ABSTRACT

Consider a multihop wireless network serving multiple flows in which wireless link interference constraints are described by a link interference graph. For such a network, we design routing-scheduling policies that maximize the end-to-end timely throughput of the network. Timely throughput of a flow $f$ is defined as the average rate at which packets of flow $f$ reach their destination node $d_f$ within their deadline. Our policy has several surprising characteristics. Firstly, we show that the optimal routing-scheduling decision for an individual packet that is present at a wireless node $i\in V$ is solely a function of its location, and "age". Thus, a wireless node $i$ does not require the knowledge of the "global" network state in order to maximize the timely throughput. We notice that in comparison, under the backpressure routing policy, a node $i$ requires only the knowledge of its neighbours queue lengths in order to guarantee maximal stability, and hence is decentralized. The key difference arises due to the fact that in our set-up the packets loose their utility once their "age" has crossed their deadline, thus making the task of optimizing timely throughput much more challenging than that of ensuring network stability. Of course, due to this key difference, the decision process involved in maximizing the timely throughput is also much more complex than that involved in ensuring network-wide queue stabilization. In view of this, our results are somewhat surprising.

Motivation & Objective

• To design a decentralized scheduling policy that maximizes timely throughput in multi-hop wireless networks with end-to-end deadline constraints.
• To address the challenge of interference in wireless networks by modeling it via a link interference graph.
• To ensure that scheduling decisions depend only on local information—specifically, the age and location of packets—without requiring global network state knowledge.
• To achieve throughput optimality under both average and hard bandwidth constraints, with asymptotic optimality in the high-load regime.
• To develop online learning algorithms for unknown network parameters, ensuring convergence to the optimal policy.

Proposed method

• The policy uses a dual decomposition approach to derive link prices that reflect the probability of successful delivery within deadline, enabling age-based prioritization.
• Scheduling decisions are made based solely on the age of packets at each node and the local interference constraints, eliminating the need for global state exchange.
• The algorithm is decentralized: each node makes decisions using only its own queue state and the age of its backlogged packets.
• For unknown parameters, iterative online learning algorithms are derived that converge to the optimal policy.
• Under hard bandwidth constraints, the policy is truncated to ensure no more than K units of bandwidth are used per time slot, with asymptotic optimality proven as traffic scales to infinity.
• The approach extends prior work on stochastic networks to wireless interference models, using a link interference graph to model mutual interference between links sharing a node.

Experimental results

Research questions

• RQ1 Can a decentralized scheduling policy achieve throughput optimality in multi-hop wireless networks with end-to-end deadline constraints?
• RQ2 Is it possible to design a policy that makes optimal scheduling decisions using only local information—specifically, packet age and location—without requiring global network state?
• RQ3 How can timely throughput be maximized under both average and hard bandwidth constraints in interference-limited wireless networks?
• RQ4 What is the performance gap between the proposed policy and the optimal policy under increasing network load?
• RQ5 Can online learning algorithms be designed to converge to the optimal policy when network parameters are unknown?

Key findings

• The proposed policy achieves optimal timely throughput with a complexity that scales linearly with the number of links in the network.
• The policy is highly decentralized: each node only needs to know the age of its own packets and local interference constraints, not global network state.
• Even with a network scale of N=4, the normalized timely throughput converges quickly to the asymptotic value, suggesting that the theoretical sub-optimality bound of O(1/√N) may be pessimistic.
• The optimal policy significantly outperforms Q-CSMA with EDF-SP, especially in bandwidth allocation, due to its use of link prices that prioritize packets based on their delivery probability within deadline.
• For hard bandwidth constraints, the truncated policy achieves asymptotic optimality as the network load scales to infinity.
• The performance of the policy using the derived r* from Theorem 4 is near-optimal, with timely throughput close to the theoretical upper bound of 1.6 pkts/time-slot in the network of Fig. 3.