Achieving Proportional Fairness Using Local Information in Aloha Networks

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. , "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.

Optimal multicast throughput in random access networks of general topology

“…(1). Note that for a transmitting node n and receiving node d, the weight w nmd and throughput µ nmd may take different values depending on the multicast tree (or multicast flow) of interest, i.e., links (n, D nm , d) and (n, D nl , d), m = l, are distinct, with w nmd = w nld .…”

“…Due to the large weights w nmd associated with the multicast flows emanating from node 5, node 5 is assigned a large access probability with p 5 > 0.9. As a result, the value of the link throughput µ nmd is smallest for links (3, 2, 5), (8,1,5), and (8, 1, 7), where node 5 is either a receiver or causes interference. The value of the link throughput µ nmd is largest for links on the edge of the network, which do not suffer interference.…”

“…The weighted proportional fairness problem is max µ I (n,Dnm,d) w nmd log µ nmd (1) where µ nmd is the throughput obtained by receiver d on tree (n, D nm ), i.e. the number of packets successfully received by receiver d on tree (n, D nm ) per unit time, and µ I = {µ nmd } is the vector of µ nmd for all links in the network.…”

“…Previous work has considered optimal throughput allocation for unicast transmission in random access. In works by Kar et al [1] and Gupta and Stolyar [2], the access probabilities are assigned in order to optimize a weighted proportional fairness objective function of the single-hop throughput. The access probabilities in this case can be computed using only the link weights in the local neighborhood (2-hop neighbors).…”

End-to-End and Mac-Layer Fair Rate Assignment in Interference Limited Wireless Access Networks

“…The literature on mac-layer fairness is rich (see [14], [17], [16], [9], [10], [7]). While [14], [17], [16], [9], [10]) address the fairness issues at the mac layer over a single-hop network, [9] extends this to multi-hop scenario ignoring flow-based end-to-end fairness. Our paper complements these works as it concretizes the relationship between mac-layer fairness and end-to-end fairness.…”