In this paper, we study cross-layer design for congestion control in multihop wireless networks. In previous work, we have developed an optimal cross-layer congestion control scheme that jointly computes both the rate allocation and the stabilizing schedule that controls the resources at the underlying layers. However, the scheduling component in this optimal crosslayer congestion control scheme has to solve a complex global optimization problem at each time, and is hence too computationally expensive for online implementation. In this paper, we study how the performance of cross-layer congestion control will be impacted if the network can only use an imperfect (and potentially distributed) scheduling component that is easier to implement. We study both the case when the number of users in the system is fixed and the case with dynamic arrivals and departures of the users, and we establish performance bounds of cross-layer congestion control with imperfect scheduling. Compared with a layered approach that does not design congestion control and scheduling together, our cross-layer approach has provably better performance bounds, and substantially outperforms the layered approach. The insights drawn from our analyses also enable us to design a fully distributed cross-layer congestion control and scheduling algorithm for a restrictive interference model.

Abstract — We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capacity. The strategy is decoupled into separate algorithms for flow control, routing, and resource allocation, and allows each user to make decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimal operating point achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network. Analysis is performed at the packet level and considers the full effects of queueing.

We consider the problem of optimal scheduling and routing in an ad-hoc wireless network with multiple traffic streams and time varying channel reliability. Each packet transmission can be overheard by a subset of receiver nodes, with a transmission success probability that may vary from receiver to receiver and may also vary with time. We develop a simple backpressure routing algorithm that maximizes network throughput and expends an average power that can be pushed arbitrarily close to the minimum average power required for network stability, with a corresponding tradeoff in network delay. The algorithm can be implemented in a distributed manner using only local link error probability information, and supports a “blind transmission” mode (where error probabilities are not required) in special cases when the power metric is neglected and when there is only a single destination for all traffic streams.

We consider a slotted system with N queues, and i.i.d. Bernoulli arrivals at each queue during each slot. Each queue is associated with a channel that changes between "on" and "off" states according to i.i.d. Bernoulli processes. We assume that the system has K identical transmitters ("servers"). Each server, during each slot, can transmit up to C packets from each queue associated with an "on" channel. We show that a policy that assigns the servers to the longest queues whose channel is "on" minimizes the total queue size, as well as a broad class of other performance criteria. We provide several extensions, as well as some qualitative results for the limiting case where N is very large. Finally, we consider a "fluid" model under which fractional packets can be served, and subject to a constraint that at most C packets can be served in total from all of the N queues. We show that when K = N , there is an optimal policy which serves the queues so that the resulting vector of queue lengths is "Most Balanced."

We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sum-rate optimal point on the boundary of the multiple-access channel capacity region is the unique Nash Equilibrium of the corresponding water-filling game. This result sheds a new light on the opportunistic communication principle and argues for the fairness of the sum-rate optimal point, at least from a game theoretic perspective. The base-station is then introduced as a player interested in maximizing a weighted sum of the individual rates. We propose a Stackelberg formulation in which the base-station is the designated game leader. In this set-up, the base-station announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. We show that this formulation allows for achieving all the corner points of the capacity region, in addition to the sum-rate optimal point. On the negative side, we prove the non-existence of a base-station strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, we present a repeated game approach which achieves the capacity region of the fading multiple access channel. Finally, we extend our study to vector channels highlighting interesting differences between this scenario and the scalar channel case. 1

We study the stability and the capacity problems in packetized wireless networks. Communication medium is modelled using probability density functions that determine the packet reception probabilities. The model subsumes several previous models as spe-cial cases, and it is suitable for networks with time-varying topology and channels. Our main result is a characterization of the stability and the capacity regions using network flows. We also introduce a class of control policies sufficient to achieve every rate inside these regions. In the second part of the paper, we apply the proposed policies and the flow analysis to regular networks. We obtain closed-form expressions for the capacity of Manhattan networks (two-dimensional grid) and ring networks (circular array of nodes). We analyze the performance loss due to suboptimal medium access and routing. We also investigate the impact of link fading, link state information, and variable connectivity on achievable rates in Manhattan networks.

Abstract—For fading broadcast channels (BC), a throughput optimal scheduling policy called queue proportional scheduling (QPS) is presented via geometric programming (GP). QPS finds a data rate vector such that the expected rate vector over all fading states is proportional to the current queue state vector and is on the boundary of the ergodic capacity region of a fading BC. Utilizing the degradedness of BC for each fading state, QPS is formulated as a geometric program that can be solved with efficient algorithms. The GP formulation of QPS is also extended to orthogonal frequency-division multiplexing (OFDM) systems in a fading BC. The throughput optimality of QPS is proved, and it is shown that QPS can arbitrarily scale the ratio of each user’s average queueing delay. Throughput, delay, and fairness properties of QPS are numerically evaluated in a fading BC and compared with other scheduling policies such as the well-known maximum weight matching scheduling (MWMS). Simulation results for Poisson packet arrivals and exponentially distributed packet lengths demonstrate that compared with MWMS, QPS provides a significant decrease in average queueing delay and has more desirable fairness properties. Index Terms—Broadcast channels (BC), channel capacity, convex optimization, cross-layer resource allocation, fairness, geometric programming (GP), orthogonal frequency-division multiplexing (OFDM), queueing analysis, queueing delay, scheduling. I.

Abstract—Most of the current communication networks, including the Internet, are packet switched networks. One of the main reasons behind the success of packet switched networks is the possibility of performance gain due to multiplexing of network bandwidth. The multiplexing gain crucially depends on the size of the buffers available at the nodes of the network to store packets at the congested links. However, most of the previous work assumes the availability of infinite buffer-size. In this paper, we study the effect of finite buffer-size on the performance of networks of interacting queues. In particular, we study the throughput of flow-controlled loss-less networks with finite buffers. The main result of this paper is the characterization of a dynamic scheduling policy that achieves the maximal throughput with a minimal finite buffer at the internal nodes of the network under memory-less (e.g., Bernoulli IID) exogenous arrival process. However, this ideal performance policy is rather complex and, hence, difficult to implement. This leads us to the design of a simpler and possibly implementable policy. We obtain a natural trade-off between throughput and buffer-size for such implementable policy. Finally, we apply our results to packet switches with buffered crossbar architecture. Index Terms—Queuing theory, flow-controlled networks, scheduling, packet switching, buffered crossbars. 1

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 σ-local pooling. We then define the local-pooling factor on a graph, as the supremum of all σ such that the graph satisfies σ-local pooling. We show that for a given graph, the efficiency ratio of GMM (i.e., the 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 specific network topologies for which the efficiency ratio of GMM is strictly less than 1. I.

Abstract — 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 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. I.