The question of providing throughput guarantees through distributed scheduling, which has remained an open problem for some time, is addressed in this paper. It is shown that a simple distributed scheduling strategy, maximal scheduling, attains a guaranteed fraction of the maximum throughput region in arbitrary wireless networks. The guaranteed fraction depends on the "interference degree" of the network, which is the maximum number of transmitter-receiver pairs that interfere with any given transmitter-receiver pair in the network and do not interfere with each other. Depending on the nature of communication, the transmission powers and the propagation models, the guaranteed fraction can be lower-bounded by the maximum link degrees in the underlying topology, or even by constants that are independent of the topology. The guarantees are tight in that they cannot be improved any further with maximal scheduling. The results can be generalized to end-to-end multihop sessions. Finally, enhancements to maximal scheduling that can guarantee fairness of rate allocation among different sessions, are discussed. KeywordsFairness guarantees, maximal scheduling, throughput guarantees, wireless networks This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. Abstract-The question of providing throughput guarantees through distributed scheduling, which has remained an open problem for some time, is addressed in this paper. It is shown that a simple distributed scheduling strategy, maximal scheduling, attains a guaranteed fraction of the maximum throughput region in arbitrary wireless networks. The guaranteed fraction depends on the "interference degree" of the network, which is the maximum number of transmitter-receiver pairs that interfere with any given transmitter-receiver pair in the network and do not interfere with each other. Depending on the nature of communication, the transmission powers and the propagation models, the guaranteed fraction can be lower-bounded by the maximum link degrees in the underlying topology, or even by constants that are independent of the topology. The guarantees are tight in that they cannot be improved any further with maximal scheduling. The results can be generalized to end-to-end multihop sessions. Finally, enhancements to maximal scheduling that can guarantee fairness of rate allocation among different sessions, are discussed.

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We address the problem of attaining proportionally fair rates using Aloha protocols at the medium access layer. We consider a wireless network where all nodes need not be in transmission ranges of each other. We show how the attempt probabilities in Aloha protocols should be set so that the achieved rates are globally proportionally fair. For both slotted and unslotted Aloha,we argue that each node can compute its optimal attempt probability just by knowing some minimal information about the network topology in its two-hop radius. , "Robust control of nonlinear systems by estimating time variant uncertainties," IEEE Trans. Automat. Contr., vol. 47, pp. 115-121, Jan. 2002. [14] , Control Lett., vol. 24, pp. 351-359, 1995. [20] J. Tsinias, "Observer design for nonlinear systems," Syst. Control Lett., vol. 42, pp. 233-244, 1989. Keywords Achieving Proportional Fairness Using Local Information in Aloha NetworksKoushik Kar, Saswati Sarkar, and Leandros Tassiulas Abstract-We address the problem of attaining proportionally fair rates using Aloha protocols at the medium access layer. We consider a wireless network where all nodes need not be in transmission ranges of each other. We show how the attempt probabilities in Aloha protocols should be set so that the achieved rates are globally proportionally fair. For both slotted and unslotted Aloha, we argue that each node can compute its optimal attempt probability just by knowing some minimal information about the network topology in its two-hop radius.

Multirate multicasting, where the receivers of a multicast group can receive service at different rates, is an efficient mode of data delivery for many real-time applications. In this paper, we address the problem of achieving rates that maximize the total receiver utility for multirate multicast sessions. This problem not only takes into account the heterogeneity in user requirements, but also provides a unified framework for diverse fairness objectives. We propose two algorithms and prove that they converge to the optimal rates for this problem. The algorithms are distributed and scalable, and do not require the network to know the receiver utilities. We discuss how these algorithms can be implemented in a real network, and also demonstrate their convergence through simulation experiments.

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