Capacity of Ad Hoc Wireless Networks

Capacity of Ad Hoc Wireless Networks Jinyang Li Charles Blake Douglas S. J. De Couto Hu Imm Lee Robert Morris M.I.T. Laboratory for Computer Science jinyang, cblake, decouto, hilee, rtm ¡ @lcs.mit.edu Abstract available to each single node’s applications is limited not only by the raw channel capacity, but also by the forwarding load imposed Early simulation experience with wireless ad hoc networks sug- by distant nodes. This effect could seriously limit the usefulness of gests that their capacity can be surprisingly low, due to the require- ad hoc routing. ment that nodes forward each others’ packets. The achievable capacity depends on network size, traffic patterns, and detailed local In this paper, we focus our analysis and simulations on static ad hoc radio interactions. This paper examines these factors alone and networks. Note that in most mobility scenarios, nodes do not move in combination, using simulation and analysis from first principles. significant distances during packet transit times. Thus, for capacity Our results include both specific constants and general scaling rela- analysis, we can view mobile networks as effectively static. tionships helpful in understanding the limitations of wireless ad hoc networks. The following simplification of an analysis by Gupta and Kumar [8] estimates the per node capacity to be expected in an ad hoc network. We examine interactions of the 802.11 MAC and ad hoc forward- Radios that are sufficiently distant can transmit concurrently; the ing and the effect on capacity for several simple configurations and total amount of data that can be simultaneously transmitted for one traffic patterns. While 802.11 discovers reasonably good sched- hop increases linearly with the total area of the ad hoc network. ules, we nonetheless observe capacities markedly less than optimal If node density is constant, this means that the total one-hop ca- for very simple chain and lattice networks with very regular traffic £ pacity is O ¢ n , where n is the total number of nodes. However, as patterns. We validate some simulation results with experiments. the network grows larger, the number of hops between each source and destination may also grow larger, depending on communica- We also show that the traffic pattern determines whether an ad hoc tion patterns. One might expect the average path length to grow network’s per node capacity will scale to large networks. In partic- with the spatial diameter of the network, or equivalently the square ular, we show that for total capacity to scale up with network size £ root of the area, or O ¢¥¤ n . With this assumption, the total end-to- the average distance between source and destination nodes must ¤ ¦ £ end capacity is roughly O ¢ n n , and the end-to-end throughput remain small as the network grows. Non-local traffic patterns in available to each node is which this average distance grows with the network size result in a rapid decrease of per node capacity. Thus the question “Are large 1 O § (1) ¤ ad hoc networks feasible?” reduces to a question about the likely n ¨ locality of communication in such networks. Gupta and Kumar also demonstrated the existence of a global ¤ ¦ £ scheduling scheme achieving © ¢ 1 n log n for a uniform random 1. Introduction network with random traffic pattern. Ad hoc wireless networks promise convenient infrastructure-free It is not encouraging that the throughput available to each node ap- communication. We expect the total capacity of such networks to proaches zero as the number of nodes increases. Furthermore, this grow with the area they cover, due to spatial re-use of the spectrum: simple analysis omits the constant factors which determine whether nodes sufficiently far apart can transmit concurrently. However, any particular networks will have a useful per node throughput. ad hoc routing requires that nodes cooperate to forward each others’ packets through the network. This means that the throughput A common observation in analyses of ad hoc routing protocols [2, This research was supported by grants from NTT Corporation un- 10, 4] is that capacity is the limiting factor; that is, the symptom der the NTT-MIT collaboration. of failure under stress is congestion losses. A high volume of routing queries or updates, caused by mobility or a large number of nodes, causes congestion; the result is not just dropped data packets, but also lost routing information and consequent mis-routing of data. Evaluations of ad hoc protocols tend to use very low data rates in order to avoid running out of capacity. For example, Das et al. [4] observe that in a simulated network of 100 nodes, each with a 2 Mbps radio, the throughput available to each node is on the order of a few kilobits per second. They report that their network has an area large enough that 7 transmissions may proceed concurrently without interfering; this means that the per node throughput actually available was about 50 times smaller than the apparent ca- 2 64 byte packets pacity . The loads used in other ad hoc routing studies are consonant 500 byte packets with this; for example, both Karp and Kung [9] and Broch et al. [2] 1500 byte packets limit the total offered load to about 60 Kbps despite using 2 Mbps radios. The interaction of ad hoc routing and capacity suggests that 1.5 any evaluation of an ad hoc network requires an understanding of network capacity. While the above discussion suggests that ad hoc networks are fun- 1 damentally non-scalable, it may not reflect reality. The studies cited Mbps above assume a random communication pattern: each pair of nodes is equally likely to communicate, so that packet path lengths grow along with the physical diameter of the network. This assumption 0.5 is probably reasonable for small networks. However, users in large networks may communicate mostly with physically nearby nodes: their neighbors in the same lecture hall of a university, or on the same floor of a building, or in the same company in a city. If lo- 0 cal communication predominates, path lengths could remain nearly 0 10 20 30 40 50 constant as the network grows, leading to constant per node avail- Number of Nodes able throughput. Figure 1: Total network throughput achieved as a function of This paper makes two contributions to the understanding of prac- the number of competing nodes. All nodes are within each oth- tical ad hoc network scalability. At a detailed level, it examines ers’ radio ranges, and all nodes send as fast as 802.11 allows. the interaction between ad hoc forwarding and the 802.11 medium access protocol in order to estimate the constants in Equation 1. At a system level, it examines the impact of communication patterns on the form of Equation 1, and determines some conditions 3. MAC Interactions under which per node capacity is likely to scale to large networks. This section presents simulations of scenarios that illustrate the de- These results are likely to be useful both in understanding simula- tailed interaction between ad hoc forwarding and the 802.11 MAC. tion studies of ad hoc network performance and in the deployment The section starts with simple scenarios and works towards com- of real ad hoc networks. plex situations that are more likely to be seen. 2. 802.11 Background The simulator used is the ns [5] simulator with the CMU wireless extensions [7] whose parameters are tuned to model the Lucent This paper assumes use of the IEEE 802.11 [3] Distributed Co- Wavelan card at a 2 Mbps data rate. ordination Function, the access method used in ad hoc mode. To reduce collisions caused by hidden terminals [1] in the network, Note that one node can interfere with packet reception at another 802.11 uses a four-way RTS/CTS/Data/Ack exchange. In brief, a node even when they are too far apart for successful transmission. node that wishes to send a data packet first sends an RTS (request At long enough distances the interference becomes negligible. In to send) packet to the destination. If the destination believes the the simulator, the effective transmission range is 250 meters, and network is idle, it responds with a CTS (clear to send). The sender the interfering range is about 550 meters. then transmits the data packet, and waits for an ACK (acknowl- edgment) from the receiver. If a node overhears an RTS or CTS, it Most of the simulations involve stations separated by 200 meters, knows the medium will be busy for some time, and avoids initiating just under the transmission range. This separation is likely to yield new transmissions or sending any CTS packets. close to the maximum capacity possible, since with higher node density the capacity must be divided up among more nodes. 802.11 RTS and CTS packets include the amount of time the medium will be busy for the remainder of the exchange. Each node All simulated data packets are preceded by an RTS/CTS exchange, uses these times to update its “network allocation vector” (NAV). regardless of size. Each data point is an average of 5 runs lasting The NAV value indicates the amount of time remaining before the 300 seconds of simulated time. Nodes are stationary. network will become available. Upon successful receipt of an RTS frame not addressed to itself, a node updates its NAV to the max- 3.1 Single Cell Capacity imum of the time carried in the RTS frame and its current NAV value. Upon receiving an RTS addressed to itself, a node returns As a baseline for comparison with more complex situations, Fig- a CTS frame only if its NAV value is zero, otherwise no CTS is ure 1 shows the simulated total capacity of a single cell (200m by sent.

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