Conference Paper

# LIFO-Backpressure achieves near optimal utility-delay tradeoff

Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA
DOI: 10.1109/WIOPT.2011.5930067 Conference: Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), 2011 International Symposium on
Source: IEEE Xplore

ABSTRACT There has been considerable recent work developing a new 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 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 general stochastic network optimization problems and general 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 good match between theory and practice.

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• "V * N ) be a vector of Lagrange multipliers , which solves the dual problem (9) with parameter V . The following theorem from [9] describes a steady state property of the drift-plus-penalty algorithm: "
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ABSTRACT: One practical open problem is the development of a distributed algorithm that achieves near-optimal utility using only a finite (and small) buffer size for queues in a stochastic network. This paper studies utility maximization (or cost minimization) in a finite-buffer regime and considers the corresponding delay and reliability (or rate of packet drops) tradeoff. A floating-queue algorithm allows the stochastic network optimization framework to be implemented with finite buffers at the cost of packet drops. Further, the buffer size requirement is significantly smaller than previous works in this area. With a finite buffer size of $B$ packets, the proposed algorithm achieves within $O(e^{-B})$ of the optimal utility while maintaining average per-hop delay of $O(B)$ and an average per-hop drop rate of $O(e^{-B})$ in steady state. From an implementation perspective, the floating-queue algorithm requires little modification of the well-known Drift-Plus-Penalty policy (including MaxWeight and Backpressure policies). As a result, the floating-queue algorithm inherits the distributed and low complexity nature of these policies.
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• "Finally, some recent ideas [6] [7] could be incorporated in an orthogonal way to improve analogously the delay performance of all policies, but this is beyond the scope of this paper. Here, we take holistic approaches in designing efficient delay-aware backpressure algorithms, which are both practical – have low computational overhead and are robust to topology changes. "
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• "There have been recent works trying to obtain improved utility-delay tradeoff for stochastic systems. For instance, [16], [17], and [18] propose algorithms that can achieve the [O(), O([log(1//)] 2 )] tradeoff. However, all the above algorithms require a convergence time of Θ(1//). "
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