We consider dynamic routing and power allocation for a wireless network with time varying channels. The network consists of power constrained nodes which transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (# ij ) that the system can stably support---where (# ij ) represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed which stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an ad-hoc wireless network where channel variations are due to user mobility, and compare its performance with the Grossglauser-Tse relay model developed in [13].

In this paper, we study the problem of joint routing, link scheduling and power control to support high data rates for broadband wireless multi-hop networks. We first address the problem of finding an optimal link scheduling and power control policy that minimizes the total average transmission power in the wireless multi-hop network, subject to given constraints regarding the minimum average data rate per link, as well as peak transmission power constraints per node. Multi-access signal interference is explicitly modeled. We use a duality approach whereby, as a byproduct of finding the optimal policy, we find the sensitivity of the minimal total average power with respect to the average data rate for each link. Since the minimal total average power is a convex function of the required minimum average data rates, shortest path algorithms with the link weights set to the link sensitivities can be used to guide the search for a globally optimum routing. We present a few simple examples that show our algorithm can find policies that support data rates that are not possible with conventional approaches. Moreover, we find that optimum allocations do not necessarily route traffic over minimum energy paths.

In this paper we study a model for ad-hoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that -- in comparison to the cost known on Unit Disk Graphs -- the complexity results in this model contain the additional factor 1/d². We prove that in Quasi Unit Disk Graphs flooding is an asymptotically message-optimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.

Abstract — We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from contention for channel access. We present two algorithms that are not only distributed spatially, but more interestingly, they decompose vertically into two protocol layers where TCP and MAC jointly solve the system problem. The first is a primal algorithm where the MAC layer at the links generates congestion (contention) prices based on local aggregate source rates, and TCP sources adjust their rates based on the aggregate prices in their paths. The second is a dual subgradient algorithm where the MAC sub-algorithm is implemented through scheduling linklayer flows according to the congestion prices of the links. Global convergence properties of these algorithms are proved. This is a preliminary step towards a systematic approach to jointly design TCP congestion control algorithms and MAC algorithms, not only to improve performance, but more importantly, to make their interaction more transparent.

Abstract — We define and study the scheduling complexity in wireless networks, which expresses the theoretically achievable efficiency of MAC layer protocols. Given a set of communication requests in arbitrary networks, the scheduling complexity describes the amount of time required to successfully schedule all requests. The most basic and important network structure in wireless networks being connectivity, we study the scheduling complexity of connectivity, i.e., the minimal amount of time required until a connected structure can be scheduled. In this paper, we prove that the scheduling complexity of connectivity grows only polylogarithmically in the number of nodes. Specifically, we present a novel scheduling algorithm that successfully schedules a strongly connected set of links in time O(log 4 n) even in arbitrary worst-case networks. On the other hand, we prove that standard MAC layer or scheduling protocols can perform much worse. Particularly, any protocol that either employs uniform or linear (a node’s transmit power is proportional to the minimum power required to reach its intended receiver) power assignment has a Ω(n) scheduling complexity in the worst case, even for simple communication requests. In contrast, our polylogarithmic scheduling algorithm allows many concurrent transmission by using an explicitly formulated non-linear power assignment scheme. Our results show that even in large-scale worst-case networks, there is no theoretical scalability problem when it comes to scheduling transmission requests, thus giving an interesting complement to the more pessimistic bounds for the capacity in wireless networks. All results are based on the physical model of communication, which takes into account that the signal-tonoise plus interference ratio (SINR) at a receiver must be above a certain threshold if the transmission is to be received correctly. I.

To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical Signal-to-Interference-plus-Noise-Ratio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time. For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worst-case networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure. Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graph-based interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links.

Ultra-Wide Band (UWB) is an emerging wireless physical layer technology that uses a very large bandwidth. We are interested in finding the design objectives of the medium access (MAC, namely, power control and scheduling) and routing protocols of a multi-hop, best-effort, UWB network. Our objective is to maximize flow rates (more precisely, log-utility of flow rates) given node power constraints. The specificity of UWB is expressed by the linear dependence between rate and signal-to-noise ratio at the receiver. It is known that, in wireless networks, different routing strategies can imply differences in MAC protocol design. Hence we search for the jointly optimal routing, scheduling and power control.

Efficient use of energy while providing an adequate level of connection to individual sessions is of paramount importance in multi-hop wireless networks. Energy efficiency and connection quality depend on mechanisms that span several communication layers due to the existing co-channel interference among competing flows that must reuse the limited radio spectrum. Although independent consideration of these layers simplifies the system design, it is often insufficient for wireless networks when the overall system performance is examined carefully. The multi-hop wireless extensions and the need for routing users' sessions from source to the destination only intensify this point of view. In this work, we present a framework for cross-layer design towards energy-efficient communication. Our approach is characterized by a synergy between the physical and the medium access control (MAC) layers with a view towards inclusion of higher layers as well. More specifically, we address the joint problem of power control and scheduling with the objective of minimizing the total transmit power subject to the end-to-end quality of service (QoS) guarantees for sessions in terms of their bandwidth and bit error rate guarantees. Bearing to the NP-hardness of this combinatorial optimization problem, we propose our heuristic solutions that follow greedy approaches.

We consider the joint optimal design of the physical, medium access control (MAC), and routing layers to maximize the lifetime of energy-constrained wireless sensor networks. The problem of computing lifetime-optimal routing flow, link schedule, and link transmission powers for all active time slots is formulated as a non-linear optimization problem. We first restrict the link schedules to the class of interference-free time division multiple access (TDMA) schedules. In this special case, we formulate the optimization problem as a mixed integerconvex program, which can be solved using standard techniques. Moreover, when the slots lengths are variable, the optimization problem is convex and can be solved efficiently and exactly using interior point methods. For general non-orthogonal link schedules, we propose an iterative algorithm that alternates between adaptive link scheduling and computation of optimal link rates and transmission powers for a fixed link schedule. The performance of this algorithm is compared to other design approaches for several network topologies. The results illustrate the advantages of load balancing, multihop routing, frequency reuse, and interference mitigation in increasing the lifetime of energy-constrained networks. We also briefly discuss computational approaches to extend this algorithm to large networks.

With increasing interest in energy constrained multi-hop wireless networks [2], a fundamental problem is one of determining energy efficient communication strategies over these multi-hop networks. The simplest problem is one where a given source node wants to communicate with a given destination, with a given rate over a multi-hop wireless network, using minimum power. Here the power refers to the total amount of power consumed over the entire network in order to achieve this rate between the source and the destination. There are three decisions that have to be made (jointly) in order to minimize the power requirement. • The path(s) that...