Changhee Joo

Understanding the capacity region of the Greedy maximal scheduling algorithm in multihop wireless networks

In this paper, we characterize the performance of an important class of scheduling schemes, called greedy maximal scheduling (GMS), for multihop wireless networks. While a lower bound on the throughput performance of GMS has been well known, empirical observations suggest that it is quite loose and that the performance of GMS is often close to optimal. In this paper, we provide a number of new analytic results characterizing the performance limits of GMS. We first provide an equivalent characterization of the efficiency ratio of GMS through a topological property called the local-pooling factor of the network graph. We then develop an iterative procedure to estimate the local-pooling factor under a large class of network topologies and interference models. We use these results to study the worst-case efficiency ratio of GMS on two classes of network topologies. We show how these results can be applied to tree networks to prove that GMS achieves the full capacity region in tree networks under the K-hop interference model. Then, we show that the worst-case efficiency ratio of GMS in geometric unit-disk graphs is between 1/6 and 1/3.

Understanding the Capacity Region of the Greedy Maximal Scheduling Algorithm in Multi-Hop Wireless Networks

In this paper, we characterize the performance of an important class of scheduling schemes, called greedy maximal scheduling (GMS), for multihop wireless networks. While a lower bound on the throughput performance of GMS has been well known, empirical observations suggest that it is quite loose and that the performance of GMS is often close to optimal. In this paper, we provide a number of new analytic results characterizing the performance limits of GMS. We first provide an equivalent characterization of the efficiency ratio of GMS through a topological property called the local-pooling factor of the network graph. We then develop an iterative procedure to estimate the local-pooling factor under a large class of network topologies and interference models. We use these results to study the worst-case efficiency ratio of GMS on two classes of network topologies. We show how these results can be applied to tree networks to prove that GMS achieves the full capacity region in tree networks under the K -hop interference model. Then, we show that the worst-case efficiency ratio of GMS in geometric unit-disk graphs is between 1/6 and 1/3.

Performance of random access scheduling schemes in multi-hop wireless networks

The performance of scheduling schemes in multi-hop wireless networks has attracted significant attention in the recent literature. It is well known that optimal scheduling solutions require centralized information and lead to impractical implementations due to their enormous complexity (high-degree polynomial or NP-hard, depending on the interference scenario). Further, multi-hop networks typically require distributed algorithms that operate on local information. Thus, in this paper, we develop a constant-time distributed random access algorithm for scheduling in multi-hop wireless networks. An important feature of this scheme is that it is guaranteed to achieve a fraction (efficiency factor) of the optimal performance. We show that this scheme theoretically achieves a superior efficiency factor as well as numerically achieves a significant performance improvement over the state-of-the-art. Simulation results also confirm that the performance of this scheme is close to a greedy centralized scheme.

Performance of Random Access Scheduling Schemes in Multi-hop Wireless Networks

The performance of scheduling schemes in multi-hop wireless networks has attracted significant attention in the recent literature. It is well known that optimal scheduling solutions require centralized information and lead to impractical implementations due to their enormous complexity (high-degree polynomial or NP-hard, depending on the interference scenario). Further, multi-hop networks typically require distributed algorithms that operate on local information. Thus, in this paper, we develop a constant-time distributed random access algorithm for scheduling in multi-hop wireless networks. An important feature of this scheme is that it is guaranteed to achieve a fraction (efficiency factor) of the optimal performance. We show that this scheme theoretically achieves a superior efficiency factor as well as numerically achieves a significant performance improvement over the state-of-the-art. Simulation results also confirm that the performance of this scheme is close to a greedy centralized scheme.

Finite-horizon energy allocation and routing scheme in rechargeable sensor networks

In this paper, we investigate the problem of maximizing the throughput over a finite-horizon time period for a sensor network with energy replenishment. The finite-horizon problem is important and challenging because it necessitates optimizing metrics over the short term rather than metrics that are averaged over a long period of time. Unlike the infinite-horizon problem, the fact that inefficiencies cannot be made to vanish to infinitesimally small values, means that the finite-horizon problem requires more delicate control. The finite-horizon throughput optimization problem can be formulated as a convex optimization problem, but turns out to be highly complex. The complexity is brought about by the “time coupling property,” which implies that current decisions can influence future performance. To address this problem, we employ a three-step approach. First, we focus on the throughput maximization problem for a single node with renewable energy assuming that the replenishment rate profile for the entire finite-horizon period is known in advance. An energy allocation scheme that is equivalent to computing a shortest path in a simply-connected space is developed and proven to be optimal. We then relax the assumption that the future replenishment profile is known and develop an online algorithm. The online algorithm guarantees a fraction of the optimal throughput. Motivated by these results, we propose a low-complexity heuristic distributed scheme, called NetOnline, in a rechargeable sensor network. We prove that this heuristic scheme is optimal under homogeneous replenishment profiles. Further, in more general settings, we show via simulations that NetOnline significantly outperforms a state-of-the-art infinite-horizon based scheme, and for certain configurations using data collected from a testbed sensor network, it achieves empirical performance close to optimal.

Joint congestion control and distributed scheduling for throughput guarantees in wireless networks

We consider the problem of throughput-optimal cross-layer design of wireless networks. We propose a joint congestion control and scheduling algorithm that achieves a fraction 1/dI(G) of the capacity region, where dI(G) depends on certain structural properties of the underlying connectivity graph G of the wireless network and also on the type of interference constraints. For a wide range of wireless networks, dI(G) can be upper bounded by a constant, independent of the number of nodes in the network. The scheduling element of our algorithm is the maximal scheduling policy. Although maximal scheduling policy has been considered in many of the previous works, the difficulties that arise in implementing it in a distributed fashion in the presence of interference have not been dealt with previously. In this paper, we propose two novel randomized distributed algorithms for implementing the maximal scheduling policy under the 1-hop and 2-hop interference models.

Delay-based back-pressure scheduling in multihop wireless networks

Scheduling is a critical and challenging resource allocation mechanism for multihop wireless networks. It is well known that scheduling schemes that favor links with larger queue length can achieve high throughput performance. However, these queue-length-based schemes could potentially suffer from large (even infinite) packet delays due to the well-known last packet problem, whereby packets belonging to some flows may be excessively delayed due to lack of subsequent packet arrivals. Delay-based schemes have the potential to resolve this last packet problem by scheduling the link based on the delay the packet has encountered. However, characterizing throughput optimality of these delay-based schemes has largely been an open problem in multihop wireless networks (except in limited cases where the traffic is single-hop.) In this paper, we investigate delay-based scheduling schemes for multihop traffic scenarios with fixed routes. We develop a scheduling scheme based on a new delay metric and show that the proposed scheme achieves optimal throughput performance. Furthermore, we conduct simulations to support our analytical results and show that the delay-based scheduler successfully removes excessive packet delays, while it achieves the same throughput region as the queue-length-based scheme.

Longest-queue-first scheduling under SINR interference model

We investigate the performance of longest-queue-first (LQF) scheduling (i.e., greedy maximal scheduling) for wireless networks under the SINR interference model. This interference model takes network geometry and the cumulative interference effect into account, which, therefore, capture the wireless interference more precisely than binary interference models. By employing the ρ-local pooling technique, we show that LQF scheduling achieves zero throughput in the worst case. We then propose a novel technique to localize interference which enables us to decentralize the LQF scheduling while preventing it from having vanishing throughput in all network topologies. We characterize the maximum throughput region under interference localization and present a distributed LQF scheduling algorithm. Finally, we present numerical results to illustrate the usefulness and to validate the theory developed in the paper.

Delay Performance of Scheduling with Data Aggregation in Wireless Sensor Networks

In-network aggregation has become a promising technique for improving the energy efficiency of wireless sensor networks. Aggregating data at various nodes in the network results in a reduction in the amount of bits transmitted over the network, and hence, saves energy. In this paper, we focus on another important aspect of aggregation, i.e., delay performance. In conjunction with link scheduling, in-network aggregation can reduce the delay by lessening the demands for wireless resources and thus expediting data transmissions. We formulate the problem that minimizes the sum delay of sensed data, and analyze the performance of optimal scheduling with in-network aggregation in tree networks under the node-exclusive interference model. We provide a system wide lower bound on the delay and use it as a benchmark for evaluating different scheduling policies. We numerically evaluate the performance of myopic and non-myopic scheduling policies, where myopic one considers only the current system state for a scheduling decision while non-myopic one simulates future system states. We show that the one-step non-myopic policies can substantially improve the delay performance. In particular, the proposed non-myopic greedy scheduling achieves a good tradeoff between performance and implementability.

Performance limits of greedy maximal matching in multi-hop wireless networks

In this paper, we characterize the performance limits of an important class of scheduling schemes, called greedy maximal matching (GMM), for multi-hop wireless networks. For simplicity, we focus on the well-established node-exclusive interference model, although many of the stated results can be readily extended to more general interference models. The study of the performance of GMM is intriguing because although a lower bound on its performance is well known, empirical observations suggest that this bound is quite loose, and that the performance of GMM is often close to optimal. In fact, recent results have shown that GMM achieves optimal performance under certain conditions. In this paper, we provide new analytic results that characterize the performance of GMM through the topological properties of the underlying graphs. To that end, we generalize a recently developed topological notion called the local pooling condition to a far weaker condition called the sigma-local pooling. We then define the local-pooling factor on a graph, as the supremum of all sigma such that the graph satisfies sigma-local pooling. We show that for a given graph, the efficiency ratio of GMM (i.e., the worst-case ratio of the throughput of GMM to that of the optimal) is equal to its local-pooling factor. Further, we provide results on how to estimate the local-pooling factor for arbitrary graphs and show that the efficiency ratio of GMM is no smaller than d*/(2d*-1) in a network topology of maximum node-degree d*. We also identify a specific network topology for which the efficiency ratio of GMM is strictly less than 1.