Optimizing Sectorized Wireless Networks: Model, Analysis, and Algorithm

Future wireless networks need to support the increasing demands for high data rates and improved coverage. One promising solution is sectorization, where an infrastructure node (e.g., a base station) is equipped with multiple sectors employing directional communication. Although the concept of sectorization is not new, it is critical to fully understand the potential of sectorized networks, such as the rate gain achieved when multiple sectors can be simultaneously activated. In this paper, we focus on sectorized wireless networks, where sectorized infrastructure nodes with beam-steering capabilities form a multi-hop mesh network for data forwarding and routing. We present a sectorized node model and characterize the capacity region of these sectorized networks. We define the flow extension ratio and the corresponding sectorization gain, which quantitatively measure the performance gain introduced by node sectorization as a function of the network flow. Our objective is to find the optimal sectorization of each node that achieves the maximum flow extension ratio, and thus the sectorization gain. Towards this goal, we formulate the corresponding optimization problem and develop an efficient distributed algorithm that obtains the node sectorization under a given network flow with an approximation ratio of 2/3. Through extensive simulations, we evaluate the sectorization gain and the performance of the proposed algorithm in various network scenarios with varying network flows. The simulation results show that the approximate sectorization gain increases sublinearly as a function of the number of sectors per node

Energy Efficient Scheduling and Routing via Randomized Rounding

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed scalable processors in a fully heterogeneous setting. For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.Comment: 27 page

Controlled Matching Game for Resource Allocation and User Association in WLANs

In multi-rate IEEE 802.11 WLANs, the traditional user association based on the strongest received signal and the well known anomaly of the MAC protocol can lead to overloaded Access Points (APs), and poor or heterogeneous performance. Our goal is to propose an alternative game-theoretic approach for association. We model the joint resource allocation and user association as a matching game with complementarities and peer effects consisting of selfish players solely interested in their individual throughputs. Using recent game-theoretic results we first show that various resource sharing protocols actually fall in the scope of the set of stability-inducing resource allocation schemes. The game makes an extensive use of the Nash bargaining and some of its related properties that allow to control the incentives of the players. We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as its MAC anomaly. The mechanism can be implemented as a virtual connectivity management layer to achieve efficient APs-user associations without modification of the MAC layer

Speed-scaling with no Preemptions

We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be minimized. We adopt the speed-scaling mechanism first introduced in [Yao et al., FOCS 1995] according to which the power dissipated is a convex function of the processor's speed. Intuitively, the higher is the speed of a processor, the higher is the energy consumption. For the single-processor case, we improve the best known approximation algorithm by providing a $(1+\epsilon)^{\alpha}\tilde{B}_{\alpha}$-approximation algorithm, where $\tilde{B}_{\alpha}$ is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratio $\tilde{B}_{\alpha}((1+\epsilon)(1+\frac{w_{\max}}{w_{\min}}))^{\alpha}$ improving the best known result by a factor of $(\frac{5}{2})^{\alpha-1}(\frac{w_{\max}}{w_{\min}})^{\alpha}$. Notice that our result holds for the fully heterogeneous environment while the previous known result holds only in the more restricted case of parallel processors with identical power functions

A Heavy Traffic Approximation for Queues with Restricted Customer-Server Matchings

We consider a queuing system with n customer classes and m servers. For each class i there is only a subset S(i) of servers that are able to process customer' i requests and they do that using a first-come-first-serve discipline. For this system, we are primarily interested in computing Pij , the steady-state fraction of class-i customers that are served by server j. We also look at stability conditions and standard performance measures like waiting times and queue lengths. Under the assumption that the system is heavy loaded, we approximate Pij as well as the other performance measures. Computational experiments are used to show the quality of our approximations.Operations Management Working Papers Serie