[Paper Review] Integrating Sub-6 GHz and Millimeter Wave to Combat Blockage: Delay-Optimal Scheduling

Guidan Yao, Morteza Hashemi+1 more|arXiv (Cornell University)|Jan 4, 2019

Millimeter-Wave Propagation and Modeling22 references5 citations

TL;DR

This paper proposes a delay-optimal scheduling policy that integrates sub-6 GHz and millimeter wave (mmWave) radios to combat blockage-induced outages. By modeling the system as a Markov Decision Process, it proves that a threshold-based policy—routing packets to mmWave only when queue length is below a critical threshold—minimizes both discounted and average delay, reducing average delay by up to 70% under heavy traffic compared to baseline policies.

ABSTRACT

Millimeter wave (mmWave) technologies have the potential to achieve very high data rates, but suffer from intermittent connectivity. In this paper, we provision an architecture to integrate sub-6 GHz and mmWave technologies, where we incorporate the sub-6 GHz interface as a fallback data transfer mechanism to combat blockage and intermittent connectivity of the mmWave communications. To this end, we investigate the problem of scheduling data packets across the mmWave and sub-6 GHz interfaces such that the average delay of system is minimized. This problem can be formulated as Markov Decision Process. We first investigate the problem of discounted delay minimization, and prove that the optimal policy is of the threshold-type, i.e., data packets should always be routed to the mmWave interface as long as the number of packets in the system is smaller than a threshold. Then, we show that the results of the discounted delay problem hold for the average delay problem as well. Through numerical results, we demonstrate that under heavy traffic, integrating sub-6 GHz with mmWave can reduce the average delay by up to 70%. Further, our scheduling policy substantially reduces the delay over the celebrated MaxWeight policy.

Motivation & Objective

• To address the challenge of intermittent mmWave connectivity due to blockage, especially from human bodies or obstacles.
• To investigate whether integrating a sub-6 GHz fallback link can reduce system delay in mmWave networks.
• To design a proactive scheduling policy that minimizes average delay across both sub-6 GHz and mmWave interfaces.
• To prove the optimality of a threshold-type policy for both discounted and average delay minimization.

Proposed method

• Formulates the scheduling problem as a Markov Decision Process (MDP) with state space defined by queue lengths in mmWave and sub-6 GHz interfaces.
• Uses value iteration to derive structural properties of the optimal policy, showing monotonicity and convexity in the cost-to-go function.
• Reduces the four-dimensional state space to a three-dimensional one by collapsing system states based on total queue occupancy.
• Proves that the optimal policy is of threshold-type: route to mmWave only if the mmWave queue length is below a critical threshold.
• Extends results from discounted delay minimization to average delay minimization using structural analysis and convergence arguments.
• Employs dynamic programming and recursive inequalities to verify the optimality of the threshold policy under various system conditions.

Experimental results

Research questions

• RQ1 Can integrating sub-6 GHz as a fallback link reduce system delay in mmWave networks suffering from blockage?
• RQ2 What is the optimal scheduling policy that minimizes average delay across sub-6 GHz and mmWave interfaces?
• RQ3 Is the optimal policy for discounted delay also optimal for average delay in this hybrid system?
• RQ4 Does the optimal policy exhibit a threshold structure based on queue length?
• RQ5 How does the proposed policy compare to the well-known MaxWeight policy in terms of delay performance?

Key findings

• The optimal scheduling policy for delay minimization is of threshold-type: packets should be routed to mmWave only when the mmWave queue length is below a specific threshold.
• The threshold policy is optimal not only for discounted delay but also for average delay, extending its practical relevance.
• Numerical results show that the proposed policy reduces average delay by up to 70% under heavy traffic compared to non-integrated or reactive schemes.
• The policy achieves similar throughput performance to the MaxWeight policy while significantly outperforming it in delay reduction.
• The cost difference between routing to mmWave versus sub-6 GHz increases with total system load, justifying the threshold policy at high traffic.
• The structural proof confirms that the optimal policy prioritizes mmWave when the system is lightly loaded, deferring to sub-6 GHz only when mmWave is congested or blocked.