Optimal Control for Generalized Network-Flow Problems

TL;DR

This paper introduces the Universal Max-Weight (UMW) policy, an online algorithm that achieves throughput optimality for diverse network flow types, reducing delay compared to traditional methods in wireless networks.

Contribution

The paper presents the first throughput-optimal, versatile policy for generalized network flow problems, combining stochastic Lyapunov and adversarial queueing theories.

Findings

UMW policy is throughput-optimal for various traffic types.

UMW reduces delay compared to Back-Pressure policy.

Specialized to unicast, UMW yields cycle-free routing and scheduling.

Abstract

We consider the problem of throughput-optimal packet dissemination, in the presence of an arbitrary mix of unicast, broadcast, multicast and anycast traffic, in a general wireless network. We propose an online dynamic policy, called Universal Max-Weight (UMW), which solves the above problem efficiently. To the best of our knowledge, UMW is the first throughput-optimal algorithm of such versatility in the context of generalized network flow problems. Conceptually, the UMW policy is derived by relaxing the precedence constraints associated with multi-hop routing, and then solving a min-cost routing and max-weight scheduling problem on a virtual network of queues. When specialized to the unicast setting, the UMW policy yields a throughput-optimal cycle-free routing and link scheduling policy. This is in contrast to the well-known throughput-optimal Back- Pressure (BP) policy which allows for packet cycling, resulting in excessive latency. Extensive simulation results show that the proposed UMW policy incurs a substantially smaller delay as compared to the BP policy. The proof of throughput-optimality of the UMW policy combines ideas from stochastic Lyapunov theory with a sample path argument from adversarial queueing theory and may be of independent theoretical interest.