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
Early simulation experience with wireless ad hoc networks sug-
gests that their capacity can be surprisingly low, due to the require-
ment that nodes forward each others’ packets. The achievable ca-
pacity depends on network size, traffic patterns, and detailed local
radio interactions. This paper examines these factors alone and
in combination, using simulation and analysis from first principles.
Our results include both specific constants and general scaling rela-
tionships helpful in understanding the limitations of wireless ad hoc
networks.
We examine interactions of the 802.11 MAC and ad hoc forward-
ing and the effect on capacity for several simple configurations and
traffic patterns. While 802.11 discovers reasonably good sched-
ules, we nonetheless observe capacities markedly less than optimal
for very simple chain and lattice networks with very regular traffic
patterns. We validate some simulation results with experiments.
We also show that the traffic pattern determines whether an ad hoc
network’s per node capacity will scale to large networks. In partic-
ular, we show that for total capacity to scale up with network size
the average distance between source and destination nodes must
remain small as the network grows. Non-local traffic patterns in
which this average distance grows with the network size result in a
rapid decrease of per node capacity. Thus the question “Are large
ad hoc networks feasible?” reduces to a question about the likely
locality of communication in such networks.
1. Introduction
Ad hoc wireless networks promise convenient infrastructure-free
communication. We expect the total capacity of such networks to
grow with the area they cover, due to spatial re-use of the spectrum:
nodes sufficiently far apart can transmit concurrently. However,
ad hoc routing requires that nodes cooperate to forward each oth-
ers’ packets through the network. This means that the throughput
This research was supported by grants from NTT Corporation un-
der the NTT-MIT collaboration.
available to each single node’s applications is limited not only by
the raw channel capacity, but also by the forwarding load imposed
by distant nodes. This effect could seriously limit the usefulness of
ad hoc routing.
In this paper, we focus our analysis and simulations on static ad hoc
networks. Note that in most mobility scenarios, nodes do not move
significant distances during packet transit times. Thus, for capacity
analysis, we can view mobile networks as effectively static.
The following simplification of an analysis by Gupta and Kumar [8]
estimates the per node capacity to be expected in an ad hoc network.
Radios that are sufficiently distant can transmit concurrently; the
total amount of data that can be simultaneously transmitted for one
hop increases linearly with the total area of the ad hoc network.
If node density is constant, this means that the total one-hop ca-
pacity is O
n
, where n is the total number of nodes. However, as
the network grows larger, the number of hops between each source
and destination may also grow larger, depending on communica-
tion patterns. One might expect the average path length to grow
with the spatial diameter of the network, or equivalently the square
root of the area, or O
n
. With this assumption, the total end-to-
end capacity is roughly O
n
n
, and the end-to-end throughput
available to each node is
O
1
n
(1)
Gupta and Kumar also demonstrated the existence of a global
scheduling scheme achieving
1
n logn
for a uniform random
network with random traffic pattern.
It is not encouraging that the throughput available to each node ap-
proaches zero as the number of nodes increases. Furthermore, this
simple analysis omits the constant factors which determine whether
any particular networks will have a useful per node throughput.
A common observation in analyses of ad hoc routing protocols [2,
10, 4] is that capacity is the limiting factor; that is, the symptom
of failure under stress is congestion losses. A high volume of rout-
ing queries or updates, caused by mobility or a large number of
nodes, causes congestion; the result is not just dropped data pack-
ets, 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 concur-
rently without interfering; this means that the per node throughput
actually available was about 50 times smaller than the apparent ca-
pacity
. The loads used in other ad hoc routing studies are consonant
with this; for example, both Karp and Kung [9] and Broch et al. [2]
limit the total offered load to about 60 Kbps despite using 2 Mbps
radios. The interaction of ad hoc routing and capacity suggests that
any evaluation of an ad hoc network requires an understanding of
network capacity.
While the above discussion suggests that ad hoc networks are fun-
damentally non-scalable, it may not reflect reality. The studies cited
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
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-
cal communication predominates, path lengths could remain nearly
constant as the network grows, leading to constant per node avail-
able throughput.
This paper makes two contributions to the understanding of prac-
tical ad hoc network scalability. At a detailed level, it examines
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 pat-
terns on the form of Equation 1, and determines some conditions
under which per node capacity is likely to scale to large networks.
These results are likely to be useful both in understanding simula-
tion studies of ad hoc network performance and in the deployment
of real ad hoc networks.
2. 802.11 Background
This paper assumes use of the IEEE 802.11 [3] Distributed Co-
ordination Function, the access method used in ad hoc mode. To
reduce collisions caused by hidden terminals [1] in the network,
802.11 uses a four-way RTS/CTS/Data/Ack exchange. In brief, a
node that wishes to send a data packet first sends an RTS (request
to send) packet to the destination. If the destination believes the
network is idle, it responds with a CTS (clear to send). The sender
then transmits the data packet, and waits for an ACK (acknowl-
edgment) from the receiver. If a node overhears an RTS or CTS, it
knows the medium will be busy for some time, and avoids initiating
new transmissions or sending any CTS packets.
802.11 RTS and CTS packets include the amount of time the
medium will be busy for the remainder of the exchange. Each node
uses these times to update its “network allocation vector” (NAV).
The NAV value indicates the amount of time remaining before the
network will become available. Upon successful receipt of an RTS
frame not addressed to itself, a node updates its NAV to the max-
imum of the time carried in the RTS frame and its current NAV
value. Upon receiving an RTS addressed to itself, a node returns
a CTS frame only if its NAV value is zero, otherwise no CTS is
sent. Hence, a sender will see no CTS if its RTS packet has col-
lided with another transmission at the receiver, or if the receiver’s
NAV indicates that the network is not available. A node times out
and re-sends the RTS if it receives no CTS.
802.11 doubles its backoff window each time a timeout occurs; it
resets the backoff to a minimum value after a packet is transmitted
successfully or is dropped after reaching maximum retry limit.
0
0.5
1
1.5
2
0 10 20 30 40 50
Mbps
Number of Nodes
64 byte packets
500 byte packets
1500 byte packets
Figure 1: Total network throughput achieved as a function of
the number of competing nodes. All nodes are within each oth-
ers’ radio ranges, and all nodes send as fast as 802.11 allows.
3. MAC Interactions
This section presents simulations of scenarios that illustrate the de-
tailed interaction between ad hoc forwarding and the 802.11 MAC.
The section starts with simple scenarios and works towards com-
plex situations that are more likely to be seen.
The simulator used is the ns [5] simulator with the CMU wire-
less extensions [7] whose parameters are tuned to model the Lucent
Wavelan card at a 2 Mbps data rate.
Note that one node can interfere with packet reception at another
node even when they are too far apart for successful transmission.
At long enough distances the interference becomes negligible. In
the simulator, the effective transmission range is 250 meters, and
the interfering range is about 550 meters.
Most of the simulations involve stations separated by 200 meters,
just under the transmission range. This separation is likely to yield
close to the maximum capacity possible, since with higher node
density the capacity must be divided up among more nodes.
All simulated data packets are preceded by an RTS/CTS exchange,
regardless of size. Each data point is an average of 5 runs lasting
300 seconds of simulated time. Nodes are stationary.
3.1 Single Cell Capacity
As a baseline for comparison with more complex situations, Fig-
ure 1 shows the simulated total capacity of a single cell (200m by
200m) network as the number of nodes increases. Each node is a
packet source, sending as fast as 802.11 allows, each packet to a
randomly selected destination. The 2-node scenario has the highest
capacity, since it has the minimum contention.
Figure 1 also shows that the RTS/CTS/ACK exchange adds signif-
icant overhead. An RTS packet is 40 bytes, CTS and ACK packets
are 39 bytes, and the MAC header of a data packet is 47 bytes long.
1 2 5
6
43
Figure 2: MAC interference among a chain of nodes. The
solid-line circle denotes a node’s valid transmission range. The
dotted-line circle denotes a node’s interference range. Node 4’s
transmission will corrupt node 1’s transmissions at node 2.
Thus the data throughput is at most
1500
1500
40
39
47
2
1
8 Mbps
with 1500-byte data packets. When various inter-frame timings are
also accounted for this limit is reduced to 1.7 Mbps.
3.2 Capacity of a Chain of Nodes
In an ad hoc network, packets travel along a chain of intermediate
nodes toward the destinations. The successive packets of a single
greedy connection interfere with each other as they move down the
chain, forcing contention in the MAC protocol. This subsection
examines the realizable capacity of a single chain of nodes where
packets originate at the first node and are forwarded to the last node
in the chain.
The following analysis shows that an ideal MAC protocol could
achieve a chain utilization as high as
1
3
. Consider the network
shown in Figure 2, where node 1 is the source and 6 is the sink.
Assume for the moment that the radios of nodes that are not neigh-
bors do not interfere with each other. Nodes 1 and 2 cannot transmit
at the same time because node 2 cannot receive and transmit simul-
taneously. Nodes 1 and 3 cannot transmit at the same time because
node 2 cannot correctly hear 1 if 3 is sending. Nodes 1 and 4 can,
with the above assumption, send at the same time. This leads to a
channel utilization of
1
3
.
However, if one assumes that radios can interfere with each other
beyond the range at which they can communicate successfully, the
situation is worse. For example, 802.11 nodes in the ns simulator
can correctly receive packets from 250 meters away, but can inter-
fere at 550 meters. Hence, in Figure 2, node 4’s packet transmis-
sions will interfere with RTS packets sent from 1 to 2, preventing 2
from correctly receiving node 1’s RTS transmissions or sending the
corresponding CTS. Therefore, we expect the maximum utilization
of a chain of ad hoc nodes in the ns simulator to be
1
4
.
Figure 3 shows simulation results for a single chain. For this set
of simulations, each node is 200 meters away from its immediate
neighbors. Node 1 is the source of data traffic and the last node in
the chain is the traffic sink. Node 1 sends data as fast as its MAC
allows. A chain of only two nodes achieves a throughput of about
1.7 Mbps for 1500-byte packets, rather than 2 Mbps, due to the
overhead of headers, RTS, CTS, and ACK packets.
0
0.5
1
1.5
2
0 2 4 6 8 10
Chain Throughput (Mbps)
Chain Length (Number of Nodes)
64 byte packets
500 byte packets
1500 byte packets
Figure 3: Throughput achieved along a chain of nodes, as a
function of the chain length. The nodes are 200 meters apart.
The first node originates packets as fast as 802.11 allows, to be
forwarded along the chain to the last node. The throughputs
for chains of 20 and 50 nodes are the same as for 10 nodes.
As the chains get longer, they approach a utilization of 0.25 Mbps
for 1500-byte packets, or
1
7
of the maximum of 1.7 Mbps. This is
substantially less than the predicted
1
4
.
To shed light on the discrepancy between
1
4
and
1
7
, we conducted
a set of simulations in which the source (node 1) sent 1500-byte
packets at various controlled rates. Figure 4 shows the results. The
maximum throughput is achieved at 0.41 Mbps, which is very close
to 1
7
1
4
0
425 Mbps. However, as the offered load increases
(even a little) beyond this optimum, the chain throughput drops
sharply. This shows that the 802.11 MAC is capable of sending
at the optimal rate, but does not discover the optimum schedule of
transmissions on its own.
802.11 fails to achieve the optimum chain schedule because an
802.11 node’s ability to send is affected by the amount of compe-
tition it experiences. For example, node 3 in a 7-node chain expe-
riences interference from 5 other nodes, while node 1 is interfered
with by three other nodes. This means that node 1 could actu-
ally inject more packets into the chain than the subsequent nodes
can forward, as detailed in Figure 5. These packets are eventually
dropped at nodes 2 and 3. The time node 1 spends sending those
extra packets decreases delivered throughput since it prevents trans-
missions from subsequent nodes. This unfairness was also noted by
Nandagopal et al. [12]; their proposed solution, which tries to give
each single-hop flow equal capacity allocation, might raise the ef-
ficiency of ad hoc chain forwarding configurations.
In addition to allocatingbandwidth unevenly, 802.11 backoff works
badly with ad hoc forwarding. Consider the case when node 4 is
in the middle of transmitting a data packet to node 5 and node 1
attempts to initiate transmission to 2 (see Figure 2). Because of
two-hop interference, node 1’s RTS packet will be corrupted by
node 4’s transmission and node 2 will not respond with a CTS.
Since node 1 does not know about node 4’s transmission, it will
back off and retry. Hence for the duration of node 4’s transmission
0
0.5
1
1.5
2
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65
Chain Throughput (Mbps)
Offered Load (Mbps)
Figure 4: Throughput delivered by an 8-node chain with differ-
ent send rates, using 1500-byte packets. The fact the peak rate
of 0.41 Mbps is not maintained shows the 802.11 MAC does not
schedule greedy senders optimally for ad hoc forwarding.
Node
1 2 3 4 5 6
Send rate 0.48 0.35 0.27 0.26 0.26 0.26
Wasted time (%) 5.4 3.3 3.1 1.5 0 0
Figure 5: Individual node send rates in Mbps, and percent of
total time spent in wasted backoff for a 7-node chain, with 1500-
byte packets. Note that the 802.11 MAC allows node 1 to send
much faster than nodes 2 or 3 can forward, resulting in lost
packets.
all transmission attempts from node 1 will fail, causing a dramatic
increase in its backoff window under 802.11’s binary exponential
backoff scheme. Therefore when node 4 is done with its transmis-
sion and has nothing more to send, node 1 may remain backed off
during a time in which it could be transmitting. Figure 5 shows
the percent of time spent in wasted backoff for each node along a
7-node chain. We consider a certain period of backoff to be wasted
when no node that might cause interference is transmitting. As we
can see, even though node 3 is receiving packets from node 2 at a
rate (0.35 Mbps) already much less than the optimum rate that can
be supported (0.425 Mbps), node 3 is unable to maintain the same
rate as node 2, while at the same time wasting time backing off.
To summarize, an ideal ad hoc forwarding chain should be able
to achieve
1
4
of the throughput that a single-hop transmission can
achieve. Simulation shows that the 802.11 MAC protocol manages
1
7
of the single-hop throughput.
3.3 Verification of Chain Results
As a rough check on the simulations presented above for ad hoc
chains, Figure 6 shows results measured on real hardware. The
hardware was configured to mimic the simulation parameters used
0
0.5
1
1.5
2
2 4 6 8 10
Chain Throughput (Mbps)
Chain Length (Number of Nodes)
64 byte packets
500 byte packets
1500 byte packets
Figure 6: Real hardware throughput achieved along a chain of
nodes, as a function of the chain length. Each node was placed
at the maximum distance from the previous that allowed low-
loss communications. Hardware parameters were set to mimic
the simulation parameters as much as possible.
Figure 7: Lattice network topologies, showing just horizontal
traffic on the left, and both horizontal and vertical on the right.
in Figure 3 as closely as possible. The radios involved are Cisco
340 (Aironet PC4800) cards operated in ad hoc mode at 2 Mbps.
Each node was placed as far from its predecessor as possible with-
out sacrificing low-loss communication. Only 6 nodes were avail-
able. The fact that Figure 6 matches Figure 3 fairly closelysuggests
that the simulations do not contain major errors; for example, the
average difference for the 1500-byte packet throughput is only 6
.
3.4 Capacity of a Regular Lattice Network
The previous analysis showed how the successive nodes in a single
forwarding chain interfere with each other. To gauge the effective-
ness of 802.11 channel allocation, we consider a lattice network.
Two types of traffic pattern will be discussed: horizontal traffic
flows moving from the left edge to the right edge and crossed hor-
izontal and vertical flows (see Figure 7). The regularity of the net-
work and traffic patterns allows estimation of nearly optimal global
scheduling schemes to compare with 802.11’s actual performance.
Consider the scenario in the left-hand half of Figure 7. Here a
lattice of nodes has parallel traffic flows moving from the left edge
to the right edge. Assume each node is 200 meters from its east,
0
0.05
0.1
0.15
0.2
0.25
0.3
0 20 40 60 80 100
Per Flow Throughput (Mbps)
Number of Nodes
64 byte packets
500 byte packets
1500 byte packets
Figure 8: Average per flow throughput in square lattice net-
works with horizontal data streams only, as a function of net-
work size. There are as many parallel chains as there are nodes
per chain. The X axis value is the total number of nodes. Each
node is separated from its four neighbors by 200 meters.
west, north, and south radio neighbors. To account for inter-flow
interference, when only every third chain is active, the active chains
are separated vertically by more than the 550 meter interference
limit. This implies that every third chain can operate without inter-
chain interference, potentially delivering the
1
4
of channel capacity
derived in Section 3.2. Thus each flow in the lattice network may
be expected to achieve a throughput of
1
12
of the channel capacity.
For 1500-byte packets, this is
1
12
1
7 Mbps, or 0.14 Mbps.
Figure 8 shows the per flow throughput for a variety of lattice sizes.
The number of chains is the same as the number of nodes in each
chain, producing square lattices. The total number of nodes is
shown on the X axis. As the network grows large, the per flow
throughput for 1500-byte packets settles at about 0.1 Mbps, some-
what less than our estimated value. The inefficiencies of 802.11
we have found in the chain scenarios are still present: nodes in the
beginning of the chain experience less contention and hence send
more packets that could handled by nodes in the later part of the
chain. There are also wasted backoff periods for the same reason
as explained in the chain scenario.
3.5 Cross Traffic in a Lattice
Now consider a slightly more general situation, in which both ver-
tical and horizontal flows are present, as in the right-hand diagram
in Figure 7. All traffic originates at the top and left edges of the
network, and is forwarded downward or rightward to the opposite
edges; the middle nodes do not originate any traffic.
In this case, we should not expect the overall capacity of the net-
work to decrease significantly. In theory we could impose a sched-
ule on the entire network in which all the vertical flows operate in
one time cycle, and all the horizontal flows in the next. This would
cause each flow to see half as much throughput as in the previous
section, but since there are twice as many flows, the overall network
throughput is the same. Of course, 802.11 may not schedule pack-
0
0.05
0.1
0.15
0.2
0.25
0.3
0 20 40 60 80 100
Per Flow Throughput (Mbps)
Number of Nodes
64 byte packets
500 byte packets
1500 byte packets
Figure 9: Average per flow throughput in square lattice net-
works with both horizontal and vertical data streams. This
configuration has twice as many chains of traffic sharing the
same network as Figure 8, which explains most of the differ-
ence between the two results.
ets this efficiently in practice. For example, the fact that each node
has a single queue means that a node may lose a chance to send a
packet vertically while the packet at the head of the queue is waiting
for contention in the horizontal direction. Figure 9 shows the aver-
age per flow throughput obtained by simulation, which is slightly
less than the predicted value of half of the per flow throughput for
lattice networks without cross traffic. We find that the average per-
centage of time spent in wasted backoff is 2
23
as opposed to
0
75
in the 8 by 8 lattice network without cross traffic. We con-
sider a backoff period to be wasteful if any packet in the queue
(not necessarily at the head) might be transmitted successfully dur-
ing that time. The increased wasted backoff reflects head-of-queue
blocking.
As an alternate analysis, the efficiency of the 802.11 MAC under
different topologies and traffic patterns can be evaluated by mea-
suring total one-hop network throughput. Figure 10 illustrates the
simulated total throughput obtained in various 2-dimensional net-
work configurations. The X axis indicates the physical area of the
network; the number of nodes is proportional to the area.
The
axis indicates the one-hop throughput of the network with
1500-byte packets. One-hop throughput measurements count all ra-
dio transmissions for data packets that successfully arrive at their fi-
nal destinations, including packets forwarded by intermediate nodes.
One-hop throughput is similiar in concept to the bit-meter/second
unit proposed in [8]. Figure 10 shows that one-hop throughput
scales roughly linearly with the area of network. The actual slope
of the curve depends on how effectively 802.11 schedules packet
transmissions. The points marked “horizontal” reflect the network
and traffic configuration described in the previous sub-section. The
points marked “horizontal and vertical” show that the addition of
vertical traffic decreases the total one-hop capacity. However, the
fact that it is just a slight constant factor decrease implies that
802.11 does find a reasonably efficient schedule for interleaving
the two directions.
