LIFO-Backpressure Achieves Near-Optimal Utility-Delay Tradeoff

There has been considerable work developing a stochastic network utility maximization framework using Backpressure algorithms, also known as MaxWeight. A key open problem has been the development of utility-optimal algorithms that are also delay-efficient. In this paper, we show that the Backpressure algorithm, when combined with the last-in-first-out (LIFO) queueing discipline (called LIFO-Backpressure), is able to achieve a utility that is within
O
(1/
V
) of the optimal value, for any scalar
V
≥ 1, while maintaining an average delay of
O
([log(
V
)]
²
) for all but a tiny fraction of the network traffic. This result holds for a general class of problems with Markovian dynamics. Remarkably, the performance of LIFO-Backpressure can be achieved by simply changing the queueing discipline; it requires no other modifications of the original Backpressure algorithm. We validate the results through empirical measurements from a sensor network testbed, which show a good match between theory and practice. Because some packets may stay in the queues for a very long time under LIFO-Backpressure, we further develop the LIFO
^p
-Backpressure algorithm, which generalizes LIFO
^p
-Backpressure by allowing interleaving between first-in-first-out (FIFO) and LIFO. We show that LIFO
^p
Backpressure also achieves the same
O
(1/
V
) close-to-optimal utility performance and guarantees an average delay of
O
([log(
V
)]
²
) for the packets that are served during the LIFO period.