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.

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.

This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models.

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.

Abstract — We consider a multi-hop wireless network shared by many users. For an interference model that only constrains a node to either transmit or receive at a time, but not both, we propose an architecture for fair resource allocation that consists of a distributed scheduling algorithm operating in conjunction with an asynchronous congestion control algorithm. We show that the proposed joint congestion control and scheduling algorithm supports at least one-third of the throughput supportable by any other algorithm, including centralized algorithms. I.

We study efficient link scheduling for a multihop wireless network to maximize its throughput. Efficient link scheduling can greatly reduce the interference effect of close-by transmissions. Unlike the previous studies that often assume a unit disk graph model, we assume that different terminals could have different transmission ranges and different interference ranges. In our model, it is also possible that a communication link may not exist due to barriers or is not used by a predetermined routing protocol, while the transmission of a node always result interference to all non-intended receivers within its interference range. Using a mathematical formulation, we develop synchronized TDMA link schedulings that optimize the networking throughput. Specifically, by assuming known link capacities and link traffic loads, we study link scheduling under the RTS/CTS interference model and the protocol interference model with fixed transmission power. For both models, we present both efficient centralized and distributed algorithms that use time slots within a constant factor of the optimum. We also present efficient distributed algorithms whose performances are still comparable with optimum, but with much less communications. Our theoretical results are corroborated by extensive simulation studies.

We present a framework for the provision of deterministic end-toend bandwidth guarantees in wireless ad hoc networks. Guided by a set of local feasibility conditions, multi-hop sessions are dynamically offered allocations, further translated to link demands. Using a distributed Time Division Multiple Access (TDMA) protocol nodes adapt to the demand changes on their adjacent links by local, conflict-free slot reassignments. As soon as the demand changes stabilize, the nodes must incrementally converge to a TDMA schedule that realizes the global link (and session) demand allocation. We first derive sufficient local feasibility conditions for certain topology classes and show that trees can be maximally utilized. We then introduce a converging distributed link scheduling algorithm that exploits the logical tree structure that arises in several ad hoc network applications. Decoupling bandwidth allocation to multi-hop sessions from link scheduling allows support of various end-to-end Quality of Service (QoS) objectives. We focus on the max-min fairness (MMF) objective and design an end-to-end asynchronous distributed algorithm for the computation of the session MMF rates. Once the end-to-end algorithm converges, the link scheduling algorithm converges to a TDMA schedule that realizes these rates. We demonstrate the applicability of this framework through an implementation over an existing wireless technology. This implementation is free of restrictive assumptions of previous TDMA approaches: it does not require any a-priori knowledge on the number of nodes in the network nor even network-wide slot synchronization.

Abstract — We study joint end-to-end congestion control and per-link medium access control (MAC) in ad-hoc networks. We use a network utility maximization formulation, in which by adjusting the types of utility functions, we can accommodate multiclass services as well as exploit the tradeoff between efficiency and fairness of resource allocation. Despite the inherent difficulties of non-convexity and non-separability of the optimization problem, we show that, with readily-verifiable sufficient conditions, we can develop a distributed algorithm that converges to the globally and jointly optimal rate allocation and persistence probabilities. Index Terms — Congestion control, medium access control, adhoc wireless network, network utility maximization, optimization. I. INTRODUCTION AND RELATED WORK SINCE the publication of the seminal paper [1], the network utility maximization (NUM) framework has found

Abstract — This paper designs medium access control (MAC) protocols for wireless networks through the network utility maximization (NUM) framework. A network-wide utility maximization problem is formulated, using a collision/persistenceprobabilistic model and aligning selfish utility with total social welfare. By adjusting the parameters in the utility objective functions of the NUM problem, we can also control the tradeoff between efficiency and fairness of radio resource allocation. We develop two distributed algorithms to solve the utility-optimal random-access control problem, which lead to random access protocols that have slightly more message passing overhead than the current exponential-backoff protocols, but significant potential for efficiency and fairness improvement. We provide readily-verifiable sufficient conditions under which convergence of the proposed algorithms to a global optimality of network utility can be guaranteed, and numerical experiments that illustrate the value of the NUM approach to the complexityperformance tradeoff in MAC design. Index Terms — Wireless network, medium access control (MAC), mathematical programming/optimization, network utility maximization, network control by pricing.

Abstract—The current framework of network utility maximization for rate allocation and its price-based algorithms assumes that each link provides a fixed-size transmission “pipe ” and each user’s utility is a function of transmission rate only. These assumptions break down in many practical systems, where, by adapting the physical layer channel coding or transmission diversity, different tradeoffs between rate and reliability can be achieved. In network utility maximization problems formulated in this paper, the utility for each user depends on both transmission rate and signal quality, with an intrinsic tradeoff between the two. Each link may also provide a higher (or lower) rate on the transmission “pipes ” by allowing a higher (or lower) decoding error probability. Despite nonseparability and nonconvexity of these optimization problems, we propose new price-based distributed algorithms and prove their convergence to the globally optimal rate-reliability tradeoff under