Twelve Reasons not to Route over Many Short Hops Martin Haenggi Department of Electrical Engineering University of Notre Dame Notre Dame, IN 46556, USA E-mail: mhaenggi@nd.edu Abstract— For multihop wireless networks, a fundamental question is whether it is advantageous to route over many short hops (short-hop routing) or over a smaller number of longer hops (long-hop routing). Short-hop routing gained a lot of support, and its proponents mainly produce two arguments: reduced energy consumption and less interference. Both arguments stem from an oversimplified analysis that is based on inaccurate channel models and neglects delay, end-to-end relability, bias power consumption, the impact of channel coding, mobility, and routing overhead. In this paper, we shed more light on these issues by listing twelve reasons why short-hop routing is not as beneficial as it seems to be. The conclusion is that for many networks, long-hop routing is in every aspect a very competitive strategy. I. I NTRODUCTION For certain wireless networks, such as ad hoc and sensor networks, a fundamental question is whether it is advantageous to route over many short hops (short-hop routing or, in the extreme case, nearest-neighbor routing) or over a smaller number of longer hops (long-hop routing). Recently, this debate extended to multihop extensions of WLANs [1] and multihop cellular networks [2]. Short-hop routing gained a lot of support, and its proponents mainly produce the following two arguments: 1. Energy consumption. If a long hop of distance d is divided into n hops of distance d/n, the energy benefit is often assumed to be n α-1 , where α is the path loss exponent. 2. Capacity. The shorter the hops, the higher the transport capacity in an interference-limited network [3]. The first argument stems from an oversimplified analysis of the energy consumption and neglects important issues such as delay, end-to-end reliability, and bias power consumption. The second argument is only valid as long as the connectivity of the network is guaranteed; it was derived for an increasingly dense network that takes advantage of the singularity of the attenuation d -α at d =0, which may lead to the unrealis- tic situation that the received power exceeds the transmitter power; and it neglects delay, too. In this paper, we shed more light on these issues by listing twelve reasons why short-hop routing is not as beneficial as it seems to be. Some of the reasons have been mentioned in other work, but this is, to the best of our knowledge, the first comprehensive collection. Often, a disk model 1 is used for the analysis of wireless networks, where a transmission is either 100% successful or fails completely, depending on whether the distance is smaller or larger than the so-called transmission radius. More realistic is the threshold model 2 , where a certain signal-to- noise-and-interference ratio (SINR) is needed for successful transmission. Still, for AWGN channels, the threshold model yields 0% or 100% probability and should therefore be used with great care. To get accurate results, reception probabilities should be based on bit, block, and packet errors rates, taking into account the error correction capabilities of the channel code. We will demonstrate that by discarding the disk model and directly focusing on SINR levels, many advantages of long- hop routing become apparent. II. NETWORK AND LINK MODEL Part of our discussion applies to many types and classes of networks and wireless channels. However, to be concrete, we often focus on networks with random node distribution and Rayleigh fading channels. A. Node Distribution and Generic Routing The analytical results are derived for networks whose nodes constitute a Poisson point process in the plane. Note that for infinite networks, the Poisson point process corresponds to a uniform distribution [4], [5], and for large networks, the two distributions are equivalent for all practical purposes. Many different routing algorithms exist for ad hoc networks [6], [7], but common to all of them is the fact that at each hop, progress shall be made towards the destination. This generic routing strategy is illustrated in Fig. 1. If the nearest neighbor within a certain sector of the source-destination axis is chosen as the next relay, this is certainly an instance of short-hop routing. If many nearby neighbors are skipped and a node 1 Also called protocol model [3]. 2 Also denoted as physical model [3].