Multirate Anypath Routing in Wireless Mesh Networks

arXiv:0809.1681v1 [cs.NI] 9 Sep 2008 Multirate Anypath Routing in Wireless Mesh Networks Rafael Laufer and Leonard Kleinrock Computer Science Department University of California at Los Angeles August 29, 2008 Technical Report UCLA-CSD-TR080025 Abstract—In this paper, we present a new routing paradigm that generalizes opportunistic routing in wireless mesh networks. In multirate anypath routing, each node uses both a set of next hops and a selected transmission rate to reach a destination. Using this rate, a packet is broadcast to the nodes in the set and one of them forwards the packet on to the destination. To date, there is no theory capable of jointly optimizing both the set of next hops and the transmission rate used by each node. We bridge this gap by introducing a polynomial-time algorithm to this problem and provide the proof of its optimality. The proposed algorithm runs in the same running time as regular shortest-path algorithms and is therefore suitable for deployment in link-state routing protocols. We conducted experiments in a 802.11b testbed network, and our results show that multirate anypath routing performs on average 80% and up to 6.4 times better than anypath routing with a fixed rate of 11 Mbps. If the rate is fixed at 1 Mbps instead, performance improves by up to one order of magnitude. I. INTRODUCTION The high loss rate and dynamic quality of links make routing in wireless mesh networks extremely challenging [1], [2]. Anypath routing1 has been recently proposed as a way to circumvent these shortcomings by using multiple next hops for each destination [4]–[7]. Each packet is broadcast to a forwarding set composed of several neighbors, and the packet must be retransmitted only if none of the neighbors in the set receive it. Therefore, while the link to a given neighbor is down or performing poorly, another nearby neighbor may receive the packet and forward it on. This is in contrast to single-path routing where only one neighbor is assigned as the next hop for each destination. In this case, if the link to this neighbor is not performing well, a packet may be lost even though other neighbors may have overheard it. Existing work on anypath routing has focused on wireless networks that use a single transmission rate. This approach, albeit straightforward, presents two major drawbacks. First, using a single rate over the entire network underutilizes available bandwidth resources. Some links may perform well at a higher rate, while others may only work at a lower rate. Secondly and most importantly, the network may become disconnected at a higher bit rate. We provide experimental measurements from a 802.11b testbed which show that this phenomenon is not uncommon in practice. The key problem is 1We use the term anypath rather than opportunistic routing, since oppor- tunistic routing is an overloaded term also used for opportunistic contacts [3]. that higher transmission rates have a shorter radio range, which reduces network density and connectivity. As the bit rate in- creases, links becomes lossier and the network eventually gets disconnected. Therefore, in order to guarantee connectivity, single-rate anypath routing must be limited to low rates. In multirate anypath routing, these problems do not exist; however, we face additional challenges. First, we must find not only the forwarding set, but also the transmission rate at each hop that jointly minimizes its cost to a destination. Secondly, loss probabilities usually increase with higher trans- mission rates, so a higher bit rate does not always improve throughput. Finally, higher rates have a shorter radio range and therefore we have a different connectivity graph for each rate. Lower rates have more neighbors available for inclusion in the forwarding set (i.e., more spatial diversity) and less hops between nodes. Higher rates have less spatial diversity and longer routes. Finding the optimal operation point in this tradeoff is the focus of this paper. We thus address the problem of finding both a forwarding set and a transmission rate for every node, such that the overall cost of every node to a particular destination is minimized. We call this the shortest multirate anypath problem. To our knowledge, this is still an open problem [4], [5], [8] and we believe our algorithm is the first solution for it. We introduce a polynomial-time algorithm to the shortest multirate anypath problem and present a proof of its optimality. Our solution generalizes Dijkstra’s algorithm for the multirate anypath case and is applicable to link-state routing protocols. One would expect that the running time of such an algorithm is longer than a shortest-path algorithm. However, we show that it has the same running time as the corresponding shortest- path algorithm, being suitable for implementation at current wireless routers. We also introduce a novel routing metric that generalizes the expected transmission time (ETT) metric [9] for multirate anypath routing

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