Optimal Control for Generalized Network-Flow Problems

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.