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The backpressure algorithm has been widely used as a distributed solution tothe problem of joint rate control and routing in multi-hop data networks. Bycontrolling a parameter $V$ in the algorithm, the backpressure algorithm canachieve an arbitrarily small utility optimality gap. However, this in turnbrings in a large queue length at each node and hence causes large networkdelay. This phenomenon is known as the fundamental utility-delay tradeoff. Thebest known utility-delay tradeoff for general networks is $[O(1/V), O(V)]$ andis attained by a backpressure algorithm based on a drift-plus-penaltytechnique. This may suggest that to achieve an arbitrarily small utilityoptimality gap, the existing backpressure algorithms necessarily yield anarbitrarily large queue length. However, this paper proposes a new backpressurealgorithm that has a vanishing utility optimality gap, so utility converges toexact optimality as the algorithm keeps running, while queue lengths arebounded throughout by a finite constant. The technique uses backpressure anddrift concepts with a new method for convex programming.

A New Backpressure Algorithm for Joint Rate Control and Routing with Vanishing Utility Optimality Gaps and Finite Queue Lengths