We provide an improved bound for the expectation of the stationary delay under the maximum weight scheduling (MWS) policy in one-hop wireless networks. In the model, the interference of the links is characterized by an interference graph G=(V, E). For a vector μ ϵ R|V|+, let χf(G, μ) be the weighted fractional coloring number for the graph G under the weight vector μ. For an arrival rate vector λ in the capacity region, we define a quantity ε(λ)to be the unique value satisfying the condition χf(G, λ+ε(λ)e) = 1, where e = (1, 1,..., 1)T. We show that the stationary delay is upper-bounded by B(2(Σi=1|V|λi) ε(λ)), where B is a constant depending on the arrival process. We show that the new bound is the tightest single-parameter bound obtainable with an often-used analytical framework. Generalizing the above, we also provide the tightest bounds for all MWS-w policies.

We provide bounds for the expectations of the stationary delay and the sum of the stationary queue sizes under the approximate maximum weight scheduling (MWS) policy and under the longest-queue-first (LQF) policy in one-hop wireless networks. For MWS, our results improves the previously provided bounds; for LQF, the results are new. In the derivation of the new bounds, a connection with certain graph theory quantities has been established. We also derive bounds for the sum of the second moments of the stationary queue sizes, which are also bounds for the sum of the queue-size variances. The method is general and it can be used to derive bounds for the sum of even higher moments of the stationary queue sizes. However, for the approximate MWS policy, the bounds for the second or higher moments are only valid when the average arrival rate vector is confined to a subset of the capacity region that depends on the order of the moment.

Efficient link scheduling in a wireless network is challenging. Typical optimal algorithms require solving an NP-hard subproblem. To meet the challenge, one stream of research focuses on finding simpler suboptimal algorithms that have low complexity but high efficiency in practice. In this paper, we study the performance guarantee of one such scheduling algorithm, the longest-queue-first (LQF) algorithm. It is known that the LQF algorithm achieves the full capacity region,$\Lambda $, when the interference graph satisfies the so-called local pooling condition. For a general graph$G$, LQF achieves (i.e., stabilizes) a part of the capacity region,$\sigma ^{\ast }(G) \Lambda $, where$\sigma ^{\ast }(G)$is the overall local pooling factor of the interference graph$G$and$\sigma ^{\ast }(G) \leq 1$. It has been shown later that LQF achieves a larger rate region,$\Sigma ^{\ast }(G) \Lambda $, where$\Sigma ^{\ast }(G)$is a diagonal matrix. The contribution of this paper is to describe three new achievable rate regions, which are larger than the previously known regions. In particular, the new regions include all the extreme points of the capacity region and are not convex in general. We also discover a counterintuitive phenomenon in which increasing the arrival rate may sometime help to stabilize the network. This phenomenon can be well explained using the theory developed in this paper.

One of the major challenges in wireless networking is how to optimize the link scheduling decisions under interference constraints. Recently, a few algorithms have been introduced to address the problem. However, solving the problem to optimality for general wireless interference models is known to be NP-hard. The research community is currently focusing on finding simpler suboptimal scheduling algorithms and on characterizing the algorithm performance. In this paper, we address the performance of a specific scheduling policy called Longest Queue First (LQF), which has gained significant recognition lately due to its simplicity and high efficiency in empirical studies. There has been a sequence of studies characterizing the guaranteed performance of the LQF schedule, culminating at the construction of the σ-local pooling concept by Joo In this paper, we refine the notion of σ -local pooling and use the refinement to capture a larger region of guaranteed performance.

The paper studies the complexity of the wireless scheduling problem under interference constraints. We first relate the definition of the capacity region to the weighted fractional coloring problem. Then, the scheduling-for-stability problem under deterministic arrivals is studied in light of this relationship. We emphasize the requirement that the scheduling algorithm uses a tractable amount of processing and storage resources. Two classes of algorithms are defined and a complexity result is derived for the intersection of the two classes. We also exhibit an algorithm that can achieve the storage requirement by relaxing the processing requirement. The results are used to examine interesting sections of the capacity region. Finally, we relate the new interpretation and theory about the capacity region to the notion of set ¿-local pooling.

One of the major challenges in wireless networking is how to optimize the link scheduling decisions under interference constraints. Recently, a few algorithms have been introduced to address the problem. However, solving the problem to optimality for general wireless interference models is known to be NP-hard. The research community is currently focusing on finding simpler, sub-optimal scheduling algorithms and on characterizing the algorithm performance. In this paper, we address the performance of a specific scheduling policy called Longest Queue First (LQF), which has gained significant recognition lately due to its simplicity and high efficiency in empirical studies. There has been a sequence of studies characterizing the guaranteed performance of the LQF schedule, culminating at the construction of the σ-local pooling concept by Joo et al. [10]. In this paper, we refine the notion of σ-local pooling and use the refinement to capture a larger region of guaranteed performance.