This tutorial paper overviews recent developments in optimization based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multi-hop wireless networks. Towards this end, we show that a clean-slate optimization based approach to the multi-hop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.

We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different re-ceiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropriately chosen queue-length based policies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queue-length-based scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queue-length stability.

Abstract — We develop a dynamic control strategy for minimizing energy expenditure in a time varying wireless network with adaptive transmission rates. The algorithm operates without knowledge of traffic rates or channel statistics, and yields average power that is arbitrarily close to the minimum possible value achieved by an algorithm optimized with complete knowledge of future events. Proximity to this optimal solution is shown to be inversely proportional to network delay. We then present a similar algorithm that solves the related problem of maximizing network throughput subject to peak and average power constraints. The techniques used in this paper are novel and establish a foundation for stochastic network optimization.

In multi-hop wireless networks, designing distributed scheduling algorithms to achieve the maximal throughput is a challenging problem because of the complex interference constraints among different links. Traditional maximal-weight (MW) scheduling, although throughput-optimal, is difficult to implement in distributed networks; whereas a distributed greedy protocol similar to IEEE 802.11 does not guarantee the maximal throughput. In this paper, we introduce an adaptive CSMA scheduling algorithm that can achieve the maximal throughput distributedly under some assumptions. Major advantages of the algorithm include: (1) It applies to a very general interference model; (2) It is simple, distributed and asynchronous. Furthermore, we combine the algorithm with endto-end flow control to achieve the optimal utility and fairness of competing flows. The effectiveness of the algorithm is verified by simulations. Finally, we consider some implementation issues in the setting of 802.11 networks.

We consider the problem of throughput-optimal scheduling in wireless networks subject to interference constraints. We model the interference using a family of K-hop interference models. We define a K-hop interference model as one for which no two links within K hops can successfully transmit at the same time (Note that IEEE 802.11 DCF corresponds to a 2-hop interference model.). For a given K, a throughput-optimal scheduler needs to solve a maximum weighted matching problem subject to the K-hop interference constraints. For K = 1, the resulting problem is the classical Maximum Weighted Matching problem, that can be solved in polynomial time. However, we show that for K> 1, the resulting problems are NP-Hard and cannot be approximated within a factor that grows polynomially with the number of nodes. Interestingly, we show that for specific kinds of graphs, that can be used to model the underlying connectivity graph of a wide range of wireless networks, the resulting problems admit polynomial time approximation schemes. We also show that a simple greedy matching algorithm provides a constant factor approximation to the scheduling problem for all K in this case. We then show that under a setting with single-hop traffic and no rate control, the maximal scheduling policy considered in recent related works can achieve a constant fraction of the capacity region for networks whose connectivity graph can be represented using one of the above classes of graphs. These results are encouraging as they suggest that one can develop distributed algorithms to achieve near optimal throughput in case of a wide range of wireless networks.

In this work, we describe and analyze a joint scheduling, routing and congestion control mecha-nism for wireless networks, that asymptotically guarantees stability of the buffers and fair allocation of the network resources. The queue lengths serve as common information to different layers of the network protocol stack. Our main contribution is to prove the asymptotic optimality of a primal-dual congestion controller, which is known to model different versions of TCP well.

This paper proposes a new class of simple, distributed algorithms for scheduling in wireless networks. The algorithms generate new schedules in a distributed manner via simple local changes to existing schedules. The class is parameterized by integers k ≥ 1. We show that algorithm k of our class achieves k/(k +2) of the capacity region, for every k ≥ 1. The algorithms have small and constant worst-case overheads: in particular, algorithm k generates a new schedule using (a) time less than 4k + 2 round-trip times between neighboring nodes in the network, and (b) at most three control transmissions by any given node, for any k. The control signals are explicitly specified, and face the same interference effects as normal data transmissions. Our class of distributed wireless scheduling algorithms are the first ones guaranteed to achieve any fixed fraction of the capacity region while using small and constant overheads that do not scale with network size. The parameter k explicitly captures the tradeoff between control overhead and scheduler throughput performance and provides a tuning knob protocol designers can use to harness this trade-off in practice. 1.

Abstract — We consider the problem of distributed scheduling in wireless networks. We present two different algorithms whose performance is arbitrarily close to that of maximal schedules, but which require low complexity due to the fact that they do not necessarily attempt to find maximal schedules. The first algorithm requires each link to collect local queue-length information in its neighborhood, and its complexity is independent of the size and topology of the network. The second algorithm is presented for the node-exclusive interference model, does not require nodes to collect queue-length information even in their local neighborhoods, and its complexity depends only on the maximum node degree in the network. I.

Abstract—We develop opportunistic scheduling policies for cognitive radio networks that maximize the throughput utility of the secondary (unlicensed) users subject to maximum collision constraints with the primary (licensed) users. We consider a cognitive network with static primary users and potentially mobile secondary users. We use the technique of Lyapunov Optimization to design an online flow control, scheduling and resource allocation algorithm that meets the desired objectives and provides explicit performance guarantees.

We establish, for multiple multicast sessions with intra-session network coding, the capacity region of input rates for which the network remains stable in ergodically time-varying networks. Building on the back-pressure approach introduced by Tassiulas et al., we present dynamic algorithms for multicast routing, network coding, rate control, power allocation, and scheduling that achieves stability for rates within the capacity region. Decisions on routing, network coding, and scheduling between different sessions at a node are made locally at each node based on virtual queues for different sinks. For correlated sources, the sinks locally determine and control transmission rates across the sources. The proposed approach yields a completely distributed algorithm for wired networks. In the wireless case, scheduling and power control among different transmitters are centralized while routing, network coding, and scheduling between different sessions at a given node are distributed. 1