1 A Distributed Algorithm for Optimal Throughput and Fairness in Wireless Networks with a General Interference Model Libin Jiang and Jean Walrand EECS Department, University of California at Berkeley {ljiang,wlr}@eecs.berkeley.edu Abstract—In multi-hop wireless networks, earlier research on joint scheduling and congestion control has suggested that MAC- layer scheduling is the bottleneck. Distributed scheduling for maximal throughput is difficult since the conflicting relationship between different links is complex. Existing works on maximal- throughput scheduling usually assumes synchronized time slots, and in each slot, a maximal-weighted “independent set” needs to be found or approximated. However, this is hard to implement in distributed networks. On the other hand, a distributed greedy protocol similar to IEEE 802.11 can only achieve a fraction of the throughput region. In this paper, we introduce an adaptive CSMA algorithm, which can achieve the maximal throughput distributedly under some assumptions. The intuitive idea is that each link should adjust its aggressiveness of transmission based on its backlog. Furthermore, we combine the algorithm with end- to-end flow control to achieve fairness among competing flows. The effectiveness of the algorithm is verified by simulations. We show that the proposed CSMA scheduling is a modular MAC- layer algorithm and demonstrate its combination with optimal routing and optimal channel selection. Finally, we considered some implementation issues in the setting of 802.11 networks. Index Terms—Cross-layer optimization, joint scheduling and congestion control, maximal throughput, CSMA I. I NTRODUCTION In multi-hop wireless networks, it is important to efficiently utilize the network resources and provide fairness to competing data flows. This needs cooperation of different network layers. Transport layer needs to inject the right amount of traffic into the network based on the congestion level. And MAC layer needs to serve the traffic efficiently to achieve high throughput. Through a utility optimization framework [1], this problem can be naturally decomposed into rate control at the transport layer and scheduling at the MAC layer. It turns out that MAC-layer scheduling is the bottleneck of the algorithm [1]. In particular, it is not easy to achieve the maximal throughput through distributed scheduling, which in turn prevents full utilization of the wireless network. Scheduling is challenging since the conflicting relationship between different links can be complicated. Existing works on maximal-throughput scheduling usually assume synchronized time slots for transmission. [2] shows that Maximal-weight (MW) scheduling is throughput-optimal (that is, it can support any incoming rates within the capacity region). This has been applied to achieve 100% throughput in input-queued switches [3]. However, finding the maximal-weighted “Independent Set” (“IS”) 1 in each time slot is NP-complete in general, and is hard even for centralized algorithms. [4] introduces a throughput-optimal randomized algorithm. Although it has low complexity in computation, a global comparison between the weights of two Independent Sets is needed in each slot. This introduces communication overhead when applied to a distributed wireless network. A few recent works proposed throughput-optimal algorithms for specific interference models. For example, [5] proposed a polynomial-complexity algorithm for the “two-hop interfer- ence model” 2 . Modiano et al. [6] introduced a gossip algorithm for the “node-exclusive model” 3 . Both of them are related to the randomized algorithm [4]. The extensions to more general interference models, as discussed in [5] and [6], usually involves extra challenges. [7] introduced an algorithm that can approach the throughput capacity (with increasing overhead) for the node-exclusive model. On the other hand, by using a distributed greedy protocol similar to IEEE 802.11, reference [10] shows that only a frac- tion of the throughput region can be achieved (after ignoring collisions), depending on the specific network topology and interference relationships. Reference [11] studied the impact of such imperfect scheduling on utility maximization in wireless networks. In this paper, we introduce an adaptive CSMA (Carrier Sensing Multiple Access) algorithm for a general interference model. We show that if packet collisions are ignored (as in the above references), the algorithm can achieve maximal through- put, if the adaptation is slow enough 4 . Since the algorithm utilizes the carrier-sensing capability, it may not be directly comparable to the throughput-optimal algorithms mentioned above. However, it does have a few distinct features: • Each node only uses its local information (e.g., its back- log). No explicit communication or control messages are required among the nodes. 1 An IS is a set of links that can transmit at the same time without conflicting. The “weight” of an IS is the summation of the queue lengths of all transmitting links in this IS. 2 In the two-hop interference model, a transmission over a link (n; m) is successful iff none the one-hop neighbors of n and m is in any conversation at the time. 3 In this model, a transmission over a link (n; m) is successful iff neither n nor m is in another conversation at the time. 4 However, the algorithm works well with a wide range of step sizes in our simulations. Submitted for Publication, June 18, 2008