Poster : Adaptive Topology Control for Wireless Ad-hoc Networks

Topology control in ad-hoc networks is the problem of adjusting the transmission power at network nodes in order to achieve the optimal topology that maximizes network performance. Recently, using effective topology control to optimize energy usage in the network has come into focus in the research community[1, 2]. The common thesis arrived at by existing works is that the transmission range used by mobile nodes should be the minimum required to keep the network connected. We refer to such a topology as the minimally connected topology in the rest of the paper. We argue in this work that the minimally connected topology does not always provide the optimal performance in typical ad-hoc networks. We show that in contrast, for typical ad-hoc networks with a few hundred nodes distributed over a few square miles area, the optimal topology is a function of the traffic load. 1. BASIS FOR THE MYTH The reasons for the presumed optimality of the minimally connected topology can be explained as follows. When the transmission range is decreased, the average hop-count for the paths traversed by flows increases linearly. However, the transmission power per hop decreases super linearly (given that the path loss exponent typically ranges from 2 to 4). Hence, the overall energy consumption in the network for the same amount of data transferred is minimized in a minimally connected topology. Furthermore, when the transmission range in a network is decreased, the average hopcount of flows in the network increases, which in turn increases the total number of one-hop flows (mini-flows) in the network increases, thus increasing the aggregate induced load in the network (We distinguish the basic load offered by the sources of the flows from the induced load that is the basic load multiplied by the average number of hops traversed by flows.). However, a decrease in the transmission range also increases the spatial re-use in the network, thus increasing the network capacity. It can be shown that, This work was funded in part by NSF grants ANI-0117840 and ECS-0225497, Yamacraw, and the Georgia Tech Broad-band Institute Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. MobiHoc’03, June 1–3, 2003, Annapolis, Maryland, USA. Copyright 2003 ACM 1-58113-684-6/03/0006 . $5.00. with a decrease in transmission range, while hop-count increases linearly, the spatial re-use in fact increases quadratically since the inhibition area of a transmission is proportional to the square of the transmission range. Hence, any increase in the aggregate induced load in the network is easily offset by the higher spatial re-use in the network, thus leaving the throughput unaffected for the same basic load in the network. 2. EXPOSING THE MYTH While a minimally connected topology is indeed optimal for generic ad-hoc networks, in this paper we show that for typical ad-hoc networks consisting of a few hundred nodes distributed in a few square-miles region, this is not true. Essentially, in such environments, the spatial re-use in the network does not scale as well as the hop-count when the transmission range is decreased. Thus, when the transmission range is minimized, the induced load in the network increases without a correspondingly equal increase in the capacity of the network. Due to this anomaly, the basic load in the network gains significance in terms of determining the efficacy of a particular network topology. For instance, if the basic load is low enough such that the induced load in a minimally connected topology is below the network capacity, optimal performance will still be achieved when the transmission range is minimized to achieve such a topology. However, if the basic load is high enough to cause the induced load to exceed the network capacity, due to the network operating under overloaded conditions, the observed throughput can fall drastically. 2.1 Experiments and Observations We use ns2 based simulations to study the throughput per unit energy performance of an 100 nodes, 1000m×1000m grid ad-hoc network under different load conditions and different transmission ranges using a CBR/UDP/DSR/CSMA/CA protocol stack. In Figure 1 (a), we observe the non optimality of the minimally connected topology for higher loads. It can be observed that (i) for the lightly loaded scenario, the maximum per-flow throughput is achieved at a transmission range of 300m; (ii) for the moderately loaded scenario, the maximum per-flow throughput is achieved at a transmission range of approximately 600m, and (iii) for the heavily loaded scenario, the utilization is poor and the maximum throughput is achieved approximately at 500m. This illustrates that for a given topology, the optimal transmission range (in terms of throughput) is variable, and is a function of the load.