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USC Computer Science Technical Reports, no. 910 (2009)
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USC Computer Science Technical Reports, no. 910 (2009)
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Neighborhoodcentric congestion control for
multihop wireless mesh networks
Sumit Rangwala, Apoorva Jindal, Member, IEEE, KiYoung Jang, Konstantinos Psounis, Senior Member, IEEE,
and Ramesh Govindan
Abstract—Complex interference in static multihop wireless
mesh networks can adversely affect transport protocol perfor
mance. Since TCP does not explicitly account for this, starvation
and unfairness can result from the use of TCP over such
networks. In this paper, we explore mechanisms for achieving
fair and efficient congestion control for multihop wireless mesh
networks. First, we design an AIMDbased ratecontrol proto
col called Wireless Control Protocol (WCP) which recognizes
that wireless congestion is a neighborhood phenomenon, not
a nodelocal one, and appropriately reacts to such congestion.
Second, we design a distributed rate controller that estimates
the available capacity within each neighborhood, and divides
this capacity to contending flows, a scheme we call Wireless
Control Protocol with Capacity estimation (WCPCap). Using
analysis, simulations, and real deployments, we find that our
designs yield rates that are both fair and efficient. WCP assigns
rates inversely proportional to the number of bottlenecks a flow
passes through while remaining extremely easy to implement.
And, an idealized version of WCPCap is maxmin fair, whereas
a practical implementation of the scheme achieves rates within
15% of the maxmin optimal rates, while still being distributed
and amenable to real implementation.
Index Terms—Congestion Control, Multihop, Mesh, Wireless,
WCP, WCPCap.
I. INTRODUCTION
Static multihop wireless mesh networks, constructed using
offtheshelf omnidirectional 802.11 radios, promise flexible
edge connectivity to the Internet, enabling lowcost community
networking in densely populated urban settings [2]. They
can also be rapidly deployed to provide a communications
backbone where none exists, such as in a disaster recovery
scenario.
However, their widespread adoption has been limited by
significant technical challenges. Finding highquality routing
paths was an early challenge addressed by the research
community [14]. However, that alone is not sufficient to
ensure good performance in mesh networks, where transport
protocols like TCP can perform poorly because of complex
interference among neighboring nodes.(We formally define a
wireless neighborhood in Section IIIA) In particular, TCP
does not explicitly account for the fact that congestion in
a mesh network is a neighborhood phenomenon. Consider
the topology of Figure 1, in which links connect nodes
which can exchange packets with each other, perhaps with
Sumit Rangwala, KiYoung Jang, and Ramesh Govindan are with the
Department of Computer Science, University of Southern California, Los
Angeles, CA, 90089.
Apoorva Jindal and Konstantinos Psounis are with the Department of Electri
cal Engineering, University of Southern California, Los Angeles, CA, 90089.
Email: {srangwal, apoorvaj, kjang, kpsounis, ramesh}@usc.edu.
asymmetric reception rates. In this topology, it is easy to show
in simulation and actual experiments that the TCP connection
in the middle is almost completely starved (gets extremely low
throughput), since it reacts more aggressively to congestion
than the two outer flows. As an aside, we note that research
on TCP for lasthop wireless networks [7], [8] does not address
this problem.
1 2 3 4 5 6 8 7 8 9 Fig. 1. Stack topol
ogy
0.4 0.5 0.6 0.7 0.8 0.9 1 Rate of Middle Flow (Mbps) Capacity Region with Optimal
Scheduling Achievable Rate Region with
802.11 0 0.1 0.2 0.3 0.4 0 0.2 0.4 0.6 0.8 1 Rate of Middle Flow (Mbps) Rate of Outer Flows (Mbps) WCPCap Optimal WCP TCP Fig. 2. The achievable rate region
To understand the properties of a desirable solution to this
problem, consider Figure 2. The yaxis plots the rate achieved
by the middle flow, and the xaxis for the outer two flows (by
symmetry, these flows will achieve approximately the same
rate for any scheme) of Figure 1. Now, with a perfect MAC
scheduler that has the same overhead as 802.11, it is intuitively
clear that the rates achievable lie on or below the straight line
shown in the figure (since an optimal scheduler would either
schedule the two outer flows simultaneously or the flow in the
middle). With 802.11, there is some loss of throughput due
to contention, and the corresponding achievablerate region
bounds the rates achievable by the flows on this topology
(in Section IVA, we describe a methodology to compute the
achievablerate region). TCP achieves rates that lie at one
corner of this plot. We contend that, for this topology, a
desirable solution is one that gets us close to the maxmin fair
rate allocation point, which corresponds to the intersection of
the 45
◦
line and the 802.11 achievablerate curve.
In this paper, we explore mechanisms for achieving such
a solution in wireless mesh networks. Three considerations
inform our choice of mechanisms. First, we do not make
any changes to the widelyused 802.11 MAC. It may well
be that such changes can improve the performance of our
mechanisms, but we have deliberately limited the scope of
our work to enable a clearer understanding of congestion
control. Second, our approach is cleanslate. We conduct
our explorations in the context of a ratebased protocol that
incorporates some of TCP’s essential features (such as ECN,
and SACK), yet allows us to explore more natural implementa
tions of the mechanisms for improving fairness and efficiency
that we study in this paper. However, our work makes no
value judgement on whether a cleanslate transport protocol
is necessary for mesh networks; it may be possible to retrofit
our mechanisms into TCP. Finally, we restrict our explorations
to plausibly implementable mechanisms, in contrast to other
work that has explored theoretical methods for optimizing
(separately or jointly) scheduling and rate assignment in
wireless networks [17], [34].
Contributions. We make two contributions in this paper. First,
we design an AIMDbased ratecontrol protocol called WCP
which explicitly reacts to congestion within a wireless neigh
borhood (Section IIIA). Specifically, we correctly identify the
precise set of nodes within the vicinity of a congested node that
needs to reduce its rates under the assumption that interference
range equals transmission range.
1
Signaling these nodes can be implemented using a
lightweight congestion sharing mechanism. More interest
ingly, we find that congestion sharing alone is not enough,
and that, to achieve fairness, sources also need to clock their
rate adaptations at the timescale of the highest RTTs of flows
going through the congested region. This can be implemented
using a local mechanism for RTT sharing. Figure 2 shows that,
for the topology of Figure 1, WCP avoids starving the middle
flow (we discuss methodology and more detailed experimental
results in Sections IV and V).
Our second contribution is the design of a distributed rate
controller that estimates the available capacity within each
neighborhood, and apportions this capacity to contending
flows. This scheme, which we call WCPCap (Section IIIB),
has the property that it uses local information and can plausibly
be implemented in a distributed fashion. Techniques that
perform congestion control by estimating capacity in wired
networks have been proposed before, e.g., [29], but wireless
capacity estimation is significantly harder. WCPCap is the first
attempt in that direction that does not rely on heuristics, but
instead uses a precise analytical methodology to accurately
estimate the available capacity.
Using analysis, simulations, and real deployments, we find
that our designs yield rates that are both fair and efficient.
Analogous to TCP, WCP assigns rates inversely proportional
to the number of bottlenecks, which, in our case, is the number
of congested neighorhoods (defined in Section IIIB) a flow
passes through, while an idealized version of WCPCap is
maxmin fair, and a practical implementation of the scheme
allocates to each flow a rate within 15% of the rate allocated
to it by the maxmin fair rate allocation. WCP achieves con
sistently good performance in the topologies we study while
being extremely easy to implement. In fact, our experiments
using five flows in a 14node testbed show that, while TCP
starves one or two of these flows in each run, WCP assigns fair
rates to all the flows. Finally, in addition to good throughput
1
We explore the impact of relaxing this assumption on our protocol’s
performance in Section IVC.
performance, WCPCap exhibits low endtoend delay and fast
convergence.
II. RELATED WORK
Extensive research has been done to understand the short
coming and to improve the performance of TCP in wireless
networks [10], [21], [23], [30], [35], [46], [50], [52]. We
briefly discuss broad classes of research pertinent to our work
while referring interested reader to [36] for a more compre
hensive survey of congestion control in wireless networks.
Early work on improving TCP performance in wireless
networks focused on distinguishing between packet loss due
to wireless corruption from loss due to congestion, in the
context of lasthop wireless [7], [8] or wireless widearea
networks [44]. More recent work, however, has addressed
congestion control for mobile adhoc wireless networks. One
class of work concentrates on improving TCP’s throughput
by freezing TCP’s congestion control algorithm during link
failure induced losses, especially during route changes [10],
[23], [30], [35], [52]. However, unlike WCP, these proposals
do not explicitly recognize and account for congestion within
a neighborhood. As a result, they would exhibit the same
shortcomings of TCP as discussed in Section I.
Another class of work related to WCP address TCP perfor
mance issues for adhoc networks with no linkfailure induced
losses using congestion metrics that includes average number
of backoffs on a link [13], average number of retransmis
sions at the MAC layer [21] and the sum of the queuing
and transmission delay at each intermediate node [46]. Even
though these schemes do not recognize the need of congestion
detection and signaling over a neighborhood, their congestion
metric implicitly takes some degree of neighborhood conges
tion into account. However, congestion in wireless networks
exhibits strong location dependency [50], i.e., different nodes
in a congested neighborhood locally perceive different degrees
of congestion. In the above schemes, flows traversing different
nodes in a single congested neighborhood would receive
varying levels of congestion notification. In contrast, WCP
explicitly shares congestion within a neighborhood, ensuring
that each flow in a single congested neighborhood gets its fair
share of the bottleneck bandwidth.
Three other pieces of work, however, have recognized the
importance of explicitly detecting and signaling congestion
over a neighborhood. NRED [50] identifies a set of flows
which share channel capacity with flows passing through a
congested node. But, it identifies only a subset of the contend
ing flows: it misses flows that traverse two hop neighbors of
a node without traversing its one hop neighbors (for example,
the flow traversing 7→ 9 in Fig. 3, Section III). Moreover,
the mechanism to regulate the traffic rates on these flows is
quite a bit more complex than ours (it involves estimating a
neighborhood queue size, and using RED [20]style marking
on packets in this queue). Finally, unlike WCP, NRED requires
RTS/CTS, is intimately tied to a particular queue management
technique (RED), might require special hardware for channel
monitoring, and has not been tested in a real implementation.
EWCCP [47] correctly identifies the set of flows that share
channel capacity with flows passing through a congested node.
EWCCP is designed to be proportionallyfair, and its design as
well as its proof of correctness assumes that the achievable rate
region of 802.11 is convex. As Figure 2 shows, however, this is
not necessarily true. Moreover, EWCCP [47] has also not been
tested in a real implementation. Finally, COMUT [28] and our
own work IFRC [42] propose rate control schemes designed
for manytoone communication. These designs take advantage
of the treestructured topology and manytoone traffic pattern
and cannot be trivially extended for general, manytomany
traffic settings.
As a final note, our AIMDbased scheme WCP borrows
heavily from TCP’s essential features such as ECN, SACK,
and roundtrip time estimation [18], [25], and uses some well
established approaches from the active queue management
literature [20], [32] to detect congestion at a node.
An alternative to AIMDbased schemes are schemes in
which intermediate routers send explicit and precise feedback
to the sources. XCP [29] and RCP [16] are examples of
such schemes for wired networks. Such schemes cannot be
directly extended to multihop wireless networks, since the
available capacity at a wireless link depends on the link
rates at the neighboring edges, and ignoring this dependence
will overestimate the available capacity and lead to perfor
mance degradation [38] and eventually to instability. Prior
schemes for wireless networks that involve sending precise
rate feedback to the sources use heuristics based on indirect
quantities like queue sizes and the number of link layer
retransmissions [4], [45] to limit capacity overestimation. If,
instead, one can directly estimate the exact capacity of a link
as a function of the link rates at the neighboring edges using a
distributed algorithm, then an accurate XCPlike scheme can
be implemented for wireless multihop networks.
In 802.11scheduled multihop networks, the complex in
terference among nodes makes it very hard to estimate the
capacity of a link. Results have been known either for multi
hop networks that use perfect MAC schedulers [26], or for
singlehop 802.11scheduled networks under saturation traffic
conditions [9]. We have recently developed an analytical
methodology which characterizes the achievable rate region
of 802.11scheduled multihop networks [27]. Our second
scheme, WCPCap, uses this prior work of ours to find the
supportable perflow rate in a neighborhood. Further, it uses
a novel, decentralized mechanism that relies on message
exchanges within local neighborhoods only, to calculate the
endtoend flow rates.
Related to WCPCap are interesting line of works that either
explore theoretical methods for jointly optimizing scheduling
and rate assignment in wireless networks [17], [34] or reply
on a nonstandardize MAC [51]. Unlike this body of work, we
restrict the scheduler to be 802.11. Explicit rate assignments
for 802.11scheduled MAC always use a centralized computa
tion [33], [43], while our work explores distributed ratecontrol
mechanisms. While optimized rate assignment through a dis
tributed realization of backpressure techniques [48] have been
proposed, it still requires every node in the network to maintain
separate queues for each possible network destination. More
recent practical studies of the problem have not been able
to relax this requirement [5], [49]. Horizon [41], another
distributed realization of backpressure techniques, addresses
the challenge of load balancing in multihop networks with
multipath routing, and unlike WCP and WCPCap, does not
study congestion control.
Finally, there has been a growing interest in industry [6] and
academia [31] in using multiple radios per node, in an effort
to mitigate or nullify the complex interference found in multi
hop wireless networks. This line of work is orthogonal to our
efforts. We believe that in dense deployments our work will
be relevant even if multiple radios are used, since the large
number of channels required to completely avoid interference,
as well as the complexity associated with their scheduling,
would be prohibitively expensive.
III. DESIGN
In this section, we first discuss the design and implementa
tion of WCP, an AIMDbased ratecontrol protocol that incor
porates many of the features of TCP, but differs significantly in
its congestion control algorithms. We then describe WCPCap
which incorporates wireless capacity estimation in order to
assign fair and efficient rates to flows.
A. WCP
WCP is a ratebased congestion control protocol for static
multihop wireless mesh networks which use the 802.11 MAC.
In this section, we assume that the link rates of all the links are
equal and autorate adaptation is turned off. In Section IVC,
we discuss the impact of relaxing this assumption on our
design. In WCP, for every flow, the source maintains a rate
r which represents the long term sending rate for the flow.
WCP is AIMDbased, so that the source additively increases
r on every ACK reception and multiplicatively decreases r
upon receiving a congestion notification from routers (in
termediate forwarding nodes). Routers signal congestion by
setting a congestion bit in the packet header of ongoing
packets. Unlike existing congestion control techniques, WCP
has novel algorithms for detecting and signaling congestion
at the intermediate routers, as well as for adapting rates at
sources in response to congestion signals.
6 7 9 8 5 2 4 1 3 10 Fig. 3. Congestion neighborhood
Congestion in Multihop Wireless Networks. The central
observation underlying the design of WCP is that the nature
of congestion in a wireless network is qualitatively different
from that in a wired network. In a wireless network, since
neighboring nodes share the wireless channel, the available
transmission capacity at a node can depend on traffic between
its neighbors.
More precisely, congestion in wireless networks is defined
not with respect to a node, but with respect to transmissions
from a node to its neighbor. In what follows, we use the term
link to denote a onehop senderreceiver pair. (We use the
terms sender and receiver to denote onehop transmissions,
and source and destination to denote the endpoints of a flow).
Thus, in Figure 3, we say that a transmission from 5 to 6 is
along the link 5→ 6. Consider the following example. When
5 is transmitting to node 6 it shares the wireless channel
with any transmission from node 7, say a transmission from
node 7 to node 9, as that transmission can collide with a
transmission from node 5 to node 6. However, when node
5 is transmitting to node 2 it does not share capacity with,
for example, a transmission from node 7 to node 9. Thus,
congestion in wireless networks is defined not with respect to
a node i, but with respect to a link i→ j.
What, then, are the set of links (L
i→ j
) that share capacity
with a given link (i→ j)? Consider link 5→ 6 in Figure 3.
Clearly, all outgoing links from node 5 and node 6 share
capacity with link 5→ 6. Moreover, every outgoing link from
a onehop neighbor of node 5 shares capacity with link 5→ 6
because any transmission from a neighbor of 5, say node 2, can
be sensed by node 5 and would prevent node 5 from capturing
the channel while node 2 is transmitting. Additionally, any
incoming link to any neighbor of node 5, say 1→ 2, also shares
capacity with link 5→ 6 as the linklayer acknowledgement
from node 2 to node 1 would also prevent node 5 from
capturing the channel for transmission. Similarly, any outgoing
link from a neighbor of node 6 shares capacity with link
5→ 6 as any transmission along the outgoing link of neighbor
of 6 can collide with transmission along 5→ 6. Finally, any
incoming link into a neighbor of node 6, say 8→ 7, also shares
capacity with 5→ 6 as the linklayer acknowledgement from
node 7 to node 8 can collide with transmissions along 5→ 6.
Thus, L
i→ j
, for a mesh network using an 802.11 MAC is
defined as:
the set of all incoming and outgoing links of i, j, all
neighbors of i, and all neighbors of j.
Note that L
i→ j
includes i→ j. Moreover, this relationship is
symmetric. If a link i→ j belongs to L
k→l
, k→ l also belongs
to L
i→ j
. Furthermore, this definition is valid even when RTS
CTS is used. However, there is an important limitation in our
definition. If a node is outside another node’s transmission
range, but within its interference range, WCP cannot account
for the reduction in channel capacity as a result of the latter’s
transmissions.
Congestion Detection and Sharing. In WCP, one key idea
is congestion sharing: if link i→ j is congested, it shares this
information with all links in L
i→ j
. Packets traversing those
links (as well as link i→ j itself) are marked with an explicit
congestion notification, so that sources can appropriately adapt
the rates of the corresponding flows. We now describe how
routers detect congestion, and how they share their congestion
state.
Congestion detection in WCP is deliberately simple. A
router detects congestion on its outgoing link using a simple
thresholding scheme. It maintains an exponentially weighted
moving average (EWMA) of the queue size, q
avg
i→ j
, for every
outgoing link i→ j as
q
avg
i→ j
=(1− w
q
)∗ q
avg
i→ j
+ w
q
∗ q
inst
i→ j
where q
inst
i→ j
is the instantaneous queue size for link i→ j and
w
q
is the EWMA weight. A link is congested when its average
queue size is greater than a congestion threshold K. Various
other congestion detection techniques have been explored in
wireless networks: channel utilization [50], average number of
retransmissions [22], mean time to recover loss [40], among
others. We choose queue size as a measure of congestion for
two reasons: it has been shown to work sufficiently well in
wireless networks [24], [42]; and is a more natural choice
for detecting congestion per link compared to, say, channel
utilization which measures the level of traffic around a node.
Also, more sophisticated queue management schemes are
possible (e.g., RED or A VQ), but they are beyond the scope
of this paper.
When a router i detects that i→ j is congested, it needs
to share this information with nodes at the transmitting ends
of links in L
i→ j
(henceforth referred to as nodes in L
i→ j
).
This is achieved by piggybacking congestion information on
each outgoing packets which neighbors snoop. Specifically,
each node maintains the congestion state of all its outgoing
and incoming links. Nodes can locally determine (from queue
size) the congestion state of their outgoing links. For nodes
to obtain congestion state on their incoming links, every node
during an outgoing packet transmission along a link includes
congestion state of that link in the outgoing packet. In addition,
every node also includes the following information in each
outgoing packet: a bit indicating if any outgoing or incoming
link from the node is congested and the identity of the link
(sender and receiver of the link); and a bit indicating if any
outgoing or incoming link from any of the node’s neighbors
is congested and the identity of the link. This latter bit is
calculated from information obtained by snooping the former
bit from neighbors and requires no additional information
exchange. In the event of more than one link being congested
at a node, it is sufficient for the node to select (and inform
its neighbors) of only one of these links. Information shared
in this manner is sufficient for any node in L
i→ j
to receive
congestion notification when link i→ j is congested
Finally, when a node in L
i→ j
detects that link i→ j is
congested, it marks all outgoing packets on that link with an
explicit congestion indicator (a single bit).
Rate Adaptation. In WCP sources perform rate adaptation.
While the principles behind our AIMD rate adaptation algo
rithms are relatively standard, our contribution is to correctly
determine the timescales at which these operations are per
formed. The novel aspect of our contribution is that these
timescales are determined by the RTTs of flows traversing a
congested neighborhood; without our innovations (described
below), flows do not get a fair share of the channel, and
sometimes react too aggressively to congestion.
A source S in WCP maintains a rate r
f
for every flow
f originating at S. It linearly increases the rate r
f
every t
ai
seconds, where t
ai
is the control interval for additive increase:
r
f
= r
f
+ α
where α is a constant. The choice of t
ai
is an important design
parameter in WCP. In the above equation the rate of change
of r
f
, dr
f
/dt is α/t
ai
. Intuitively, for stable operation, dr
f
/dt
should be dependent on feedback delay of the network. Using
the weighted average roundtrip time of flow f , rtt
avg
f
, of the
flow seems an obvious choice for t
ai
as it satisfies the above
requirement. But consider three flows 1→ 3, 4→ 6, and 7→ 9
in Figure 1. Packets of flow 1→ 3 share the wireless channel
with nodes 1 through 6 while packets from flow 4→ 6 share
wireless channel with all the nodes in the figure. As the rate of
all the flows in the network increases, flow 4→ 6 experiences
more contention as compared to flow 1→ 3 and the average
RTT of flow 4→ 6 increases much faster than the average
RTT of flow 1→ 3. Thus, even if these flows were to begin
with the same rate, their rates would diverge with the choice of
t
ai
= rtt
avg
f
. This happens because a fair allocation of capacity
using a AIMD scheme requires similar dr
f
/dt for all the flows
sharing the capacity [12].
To enable fairness, WCP introduces the notion of a shared
RTT. Denote by rtt
avg
i→ j
the average RTT of all the flows
traversing the link i→ j (the average RTT of each flow is
computed by the source, and included in the packet header)
i.e.,
rtt
avg
i→ j
=
∑
∀ f∈F
i→ j
rtt
avg
f
F
i→ j

where F
i→ j
is the set of flows traversing link i→ j. For each
link i→ j, node i computes the shared RTT, rtt
Smax avg
i→ j
, as the
maximum RTT among all links in L
i→ j
i.e.,
rtt
Smax avg
i→ j
= max
∀k→l∈L
i→ j
(rtt
avg
k→l
)
In words, this quantity measures the largest average flow RTT
across the set of links that i→ j shares the channel with.
Why this particular choice of timescale? Previous work has
shown that the average RTT of flows is a reasonable control
interval for making congestion control decisions [29]. Our
definition conservatively chooses the largest control interval
in the neighborhood.
For all flows traversing link i→ j, the router includes
rtt
Smax avg
i→ j
in every packet header only if it exceeds the current
value of that field in the header. The source uses this value for
t
ai
: thus, t
ai
is the largest shared RTT across all the links that
the flow traverses. This ensures that the value of the control
interval t
ai
for a flow is no less than the highest RTT of any
flow with which it shares a wireless neighborhood. Intuitively,
with this choice of the control interval, all flows in the Stack
topology will increase their rates at the same timescale.
Upon receiving a packet with a congestion notification bit
set, a source reduces the rate r
f
by half and waits for the
control interval for multiplicative decrease t
md
before reacting
again to any congestion notification from the routers. t
md
must
be long enough so that the source has had time to observe
the effect of its rate reduction. Moreover, for fairness, flows
that traverse the congested region
2
must all react at roughly
the same timescale. To ensure this, WCP also computes a
quantity for each link that we term the shared instantaneous
RTT, denoted by rtt
Smax inst
i→ j
. This is computed in exactly the
same way as the shared RTT, described above, except that
the instantaneous RTT is used, rather than the average RTT.
The former is a more accurate indicator of the current level
of congestion in the network and is a more conservative
choice of the timescale required to observe the effect of a
rate change. As before, routers insert this shared instantaneous
RTT into the packet header only if it exceeds the current
value. Sources set t
md
to be the value of this field in the
packet header that triggered the multiplicative decrease. If a
flow traverses multiple congested regions, its multiplicative
decreases are clocked by the neighborhood with the largest
shared instantaneous RTT.
Similar to congestion sharing, computation of rtt
Smax avg
i→ j
(rtt
Smax inst
i→ j
) requires sharing “link RTTs”, rtt
avg
i→ j
(rtt
inst
i→ j
),
among all nodes in L
i→ j
requiring significant overhead. How
ever, its definition permits a natural optimization. Similar to
congestion sharing discussed above, every node includes in
each outgoing packet only the maximum of rtt
avg
i→ j
(rtt
inst
i→ j
) over
all incoming and outgoing links of the node and the maximum
of rtt
avg
i→ j
(rtt
inst
i→ j
) over all incoming and outgoing links of all
the neighbors of the node. This allows for a lowoverhead
distributed calculation of shared RTT over all the nodes in
L
i→ j
.
Finally, we describe how the source uses the value r
f
.
WCP aims to assign fair goodputs. Naively sending packets at
the rate r
f
assigns fair throughputs, but packet losses due to
channel error or interference can result in unequal goodputs.
Instead, WCP sends packets at a rate r
f
/p, when p is the
empirically observed packet loss rate over the connection.
Intuitively, this goodput correction heuristic sends more pack
ets for flows traversing lossy paths, equalizing flow good
puts. Other ratebased protocols [39] use more sophisticated
loss rate computation techniques to perform similar goodput
correction. As we show in Section IV, our approach works
extremely well for WCP. In that section, we also quantify the
impact of turning off this “correction”.
Implementation. We could have retrofitted congestion and
RTT sharing in TCP. But, the complexity of current TCP
implementations, and the fact that TCP performs error re
covery, congestion control and flow control using a single
windowbased mechanism, made this retrofit conceptually
more complex. Given that our goal was to understand the
issues underlying congestion in mesh networks, incremental
deployability was not paramount. So, at the cost of some
additional packet header overhead, we decided to explore a
cleanslate approach. Our implementation uses a ratebased
protocol for congestion control (as described above), but
uses an implementation of TCP SACK for error recovery, a
windowbased flow control mechanism exactly like TCP, and
the same RTO estimation as in TCP. In a later section, we
show that our implementation does not bias the results in any
2
We use the terms congested region and congested neighborhood inter
changeably in this paper.
way: if we remove our sharing innovations from WCP, its
performance is comparable to TCP.
B. WCPCap
An alternative to WCP is a protocol in which the network
sends explicit and precise feedback to the sources. In order to
do this, it is important to be able to estimate the available
capacity within a neighborhood, a nontrivial task. In this
section, we describe WCPCap, a protocol that provides explicit
feedback (in much the same way that XCP [29] and RCP [16]
do for wired networks). An important goal in designing
WCPCap is to explore the feasibility of capacity estimation
using only local information, thereby making it amenable to
distributed implementation.
Determining the Achievable LinkRate Region. At the core
of WCPCap is a technique to determine whether a given set of
rates is achievable in an 802.11 network; using this technique,
WCPCap estimates the available capacity and distributes this
fairly among relevant flows. This technique is presented in
detail in our prior work [27]. For completeness, we describe
the main idea of the analytical methodology here, assuming
IEEE 802.11 scheduling with RTS/CTS in the network.
The precise goal of the technique is as follows. Given a
link i→ j, and a set of candidate aggregate rates r
l→m
over
links l→ m belonging to L
i→ j
(link i→ j belongs to this set),
we seek a decision procedure that will enable us to determine
if these rates are achievable. The decision process assumes
that the channel loss rates (losses not due to collisions) of
links in L
i→ j
, and the interference graph between links in
L
i→ j
are known. Channel losses are assumed to be independent
Bernoulli random variables. The interference model neglects
some physical layer phenomena like the capture effect [11]
(where a receiver can correctly decode data despite of in
terference), situations where transmitters send data despite of
interference and carrier sensing, and situations where remote
links in isolation do not interfere with the link under study, but
their aggregate effect may cause loses on the link [15]. The
interested reader is referred to [27] for a detailed description
of all the assumptions, an extensive evaluation of their effect
on the accuracy of the model, and a discussion on how to
remove them.
The decision process first determines, for each link, the
expected service time in terms of (a) the collision probability
at the receiver and (b) the idle time perceived by the transmitter
of that link. Given these service times, the given set of link
rates is achievable only if
∑
e∈O
v
λ
e
E[S
e
]≤ U,∀v∈ V
where V is the set of all nodes, O
v
is the set of outgoing
links from a node v∈ V , λ
e
is the packet arrival rate at link
e, E[S
e
] is the expected service time of a packet at link e,
and the utilization factor U is a fraction between 0 and 1 and
reflects the desired utilization of the channel. In practice, U is
usually set to less than 1 to keep the system stable. Otherwise,
small nonidealities can drive the network beyond the capacity
region.
The key challenge then, is to determine the collision and
the idle time probabilities, made difficult because these values
for a link depend on the rates at its neighboring links, which,
in turn, depend on the rates at their neighboring links and so
on. We use the following procedure: the subgraph formed
by the set of links in L
i→ j
is decomposed into a number
of twolink topologies and the collision and idle probabilities
for each twolink topology is derived. The net probability is
found by appropriately combining the individual probabilities
from each twolink topology. Combining these probabilities
is quite complicated due to the interdependence among links.
For brevity, we will omit the analytical formulas and their
complete derivations. The interested reader is referred to [27]
for details.
Estimating Available Bandwidth. WCPCap uses the achiev
able rate computation technique to estimate achievable band
width and give precise rate feedback to sources. Conceptually,
each router maintains, for each outgoing link i→ j, a rate R
i→ j
which denotes the maximum rate allowable for a flow passing
through the link. However, a flow traversing i→ j is actually
only allowed to transmit at the minimum (denoted R
min
i→ j
) of
all rates R
k→l
such that k→ l belongs to L
i→ j
(intuitively, at
the most constraining rate over all links that share channel
capacity with i→ j). The rate feedback is carried in the
packet header. When a packet traverses i→ j, the router sets
the feedback field to R
min
i→ j
if R
min
i→ j
is lower than the current
value of the field. This feedback rate is eventually delivered
to the source in an endtoend acknowledgement packet, and
the source uses this value to set its rate. Thus the source
sets its rate to the smallest allowable rate in the wireless
neighborhoods that it traverses.
R
i→ j
for each link is updated every k· rtt
Smax avg
i→ j
, where
rtt
Smax avg
i→ j
is the shared RTT defined in Section IIIA and k is
a parameter which tradesoff the response time to dynamics for
lower overhead. The duration between two successive updates
of R
i→ j
is referred to as an epoch. During each epoch,
transmitter i measures x
i→ j
, the actual data rate over link i→ j
and n
i→ j
, the number of flows traversing link i→ j. Using x
k→l
and n
k→l
for all k→ l in L
i→ j
transmitter i computes the new
value of R
i→ j
(denoted by R
new
i→ j
) to be used in the next time
epoch, and broadcasts x
i→ j
, n
i→ j
, and R
new
i→ j
to all nodes in
L
i→ j
. (If the measured x
i→ j
in the previous epoch equals zero
at a link i→ j, it does not broadcast its current value of R
new
i→ j
.
Thus links which become inactive due to network dynamics
will not contribute in determining the largest achievable flow
rate in a neighborhood.)
We now describe how R
new
i→ j
is determined (Figure 4).
Note that the transmitter i has x
k→l
and n
k→l
for all links
k→ l in L
i→ j
. It uses this information, and the methodology
described above, to determine the maximum value of δ
such that the rate vector ~ x shown in Figure 4 is achievable.
(δ can have a negative value if the current rates in the
neighborhood are not achievable.) Then, node i sets R
new
i→ j
to
R
i→ j
+ ρδ− βq
inst
i→ j
/rtt
Smax avg
i→ j
if δ is positive, else R
new
i→ j
is
set to R
i→ j
+ δ− βq
inst
i→ j
/rtt
Smax avg
i→ j
. We use a scaling factor
ρ while increasing the rate to avoid big jumps, analogous to
similar scaling factors in XCP and RCP. On the other hand,
we remain conservative while decreasing the rate. q
inst
i→ j
denotes
the instantaneous queue at link i→ j, rtt
Smax avg
i→ j
is the shared
RTT defined in Section IIIA, and β is a scaling parameter.
To ensure that the rate goes down when the queue builds up,
we subtract a fraction of the bandwidth required to drain the
queue within one shared RTT (q
inst
i→ j
/rtt
Smax avg
i→ j
). Each node
independently computes R
k→l
for its links. These computations
do not need to be synchronized, and nodes use the most recent
information from their neighbors for the computation.
Next, we describe how the value of the parameter U (the
maximum allowed utilization per queue) is determined. The
analysis described at the start of this section to derive the
achievable rate region does not incorporate losses at higher
layers (that is, it incorporates only channel losses and colli
sions), and hence, assumes infinite buffer sizes and infinite
MAC retransmit limits. Assuming no losses, operating very
close to the capacity region will result in large delays and
huge queues. However, in practice both the buffer sizes and
MAC retransmit limits are finite. Hence, these huge queues
can result in significant losses. Additionally, note that the
procedure presented in [27] assumes global knowledge, while
the information exchange in WCPCap is only between neigh
bors. Hence, the computation itself is approximate which can
potentially lead to an overestimation of available capacity. For
these two reasons, we operate the network well within the
capacity region; the parameter U controls how far the network
is from the boundary of the capacity region. How close to
the boundary of the capacity region can we operate without
overflowing buffers and without overestimating available ca
pacity depends on the topology at hand. Hence, the value of
U depends on the topology. Choosing a conservative value for
U is inefficient as it leads to a low channel utilization in most
topologies. So we use the following algorithm to set the value
of U. If q
avg
i→ j
(the average queue size) is greater than 1, the
value of U is reduced; and if q
avg
i→ j
remains less than 1 for 5
iterations of the algorithm described in Figure 4, the value of
U is increased. Binary search is used to converge to the correct
value of U. For example, in the Stack topology (Figure 1), this
approach yields a value of U = 0.85.
The computational overhead of the WCPCap algorithm is
very low. To determine R
new
i→ j
, we perform a binary search
to find the maximum value of δ such that the rate vector
~ x is achievable. Each iteration decomposes L
i→ j
into two
link topologies, computes collision and idle probabilities for
each twolink topology, and combines the results. Overall, the
algorithm requires a logarithmic number of iterations whose
complexity is polynomial inL
i→ j
. In practical topologies the
cardinality of L
i→ j
is small. For example, in our experiments
(run on 3.06GHz Linux boxes) determining R
new
i→ j
takes as
much time as it takes to send a data packet. Since each epoch
consists of about 30 data packet transmissions and a single
R
new
i→ j
computation, the computational overhead per epoch is
very low.
Finally, we note that, if naively designed, WCPCap can
impose significant communication overhead. For each link
i→ j, the following information needs to be transmitted to
all nodes in L
i→ j
once every epoch: the maximum RTT
Every k· rtt
Smax_avg
i→ j
sec
Find max δ such that
~ x←
x
k→l
+ n
k→l
δ for k→ l∈ L
i→ j
is achievable
R
new
i→ j
←
(
R
i→ j
+ ρδ− βq
inst
i→ j
/rtt
Smax_avg
i→ j
δ > 0
R
i→ j
+ δ− βq
inst
i→ j
/rtt
Smax_avg
i→ j
δ≤ 0
Broadcast R
new
i→ j
, x
i→ j
and n
i→ j
to all links in L
i→ j
Fig. 4. Pseudocode for rate controller at link i→ j
across the flows passing through the link, the actual data rate
at the link, the number of flows passing through the link
and R
i→ j
. Assuming one byte to represent each variable, the
overhead is equal to 4L
i→ j
bytes. For practical topologies,
where neighborhood sizes are expected to be less than 20, this
overhead consumes less than 15% of the actual throughput.
However, the overhead does increase linearly with L
i→ j
. There
are ways to optimize this, by quantizing the information or
reducing the frequency of updates, but we have left these
to future work. Instead, in our simulations, we assume that
all the relevant information is available at each node without
cost, since our goal has been to understand whether available
bandwidth estimation using only local information is plausibly
implementable in wireless networks.
Properties. To understand the design rationale of the WCPCap
algorithm, we characterize the fairness properties of an ideal
ized WCPCap algorithm. The idealized WCPCap algorithm
assumes that all control message broadcasts are exchanged
instantaneously and without loss, and each node has complete
information about the entire network instead of just its neigh
borhood. Specifically, each node is aware of the data rate at
each link in the network and the global network topology.
The last assumption is needed because residual capacity at
a link depends on the global topology and not merely the
local neighborhood topology [27]. Hence WCPCap obtains
an approximate value of the residual capacity while idealized
WCPCap will obtain an exact value of the residual capacity.
We prove fairness properties for idealized WCPCap here, and
evaluate how the nonidealities impact the performance of
WCPCap through simulations in Section IV.
We will prove that the rates assigned by idealized WCP
Cap converge to the maxmin rate allocation. The proof is
constructed using two lemmas. The first lemma looks at the
properties of the maxmin allocation in wireless multihop
networks while the second lemma studies the rates assigned
by idealized WCPCap. Before presenting the lemmas, we
define three concepts which will be extensively used in the
proofs. At the maxmin allocation, let the links whose queues
are fully utilized (arrival rate = service rate) be referred to
as congested links, and the neighborhood of congested links
be referred to as congested neighborhoods. Note that each
flow may pass through several congested neighborhoods. We
define the most congested neighborhood a flow passes through
to be the neighborhood which gets congested at the lowest
throughput amongst the congested neighborhoods that flow
traverses. Thus, there is a unique most congested neighborhood
associated with each flow. The throughput achieved by a flow
is dictated by the most congested neighborhood it passes
through.
Lemma 1: A rate allocation which assigns the largest
achievable equal rate to the flows which share the most
congested neighborhood is the maxmin rate allocation.
Proof: Let there be n flows passing through the congested
neighborhood C
R
. Additionally, let k of these n flows have
C
R
as the most congested neighborhood they pass through.
Consider the following rate allocation. Fix the rate of the other
n− k flows as dictated by the most congested neighborhood
they pass through, and then assign the maximum possible
equal rate to the k flows. Label this rate r
eq
. Then, by definition
of the most congested neighborhood a flow passes through, the
other n− k flows have a rate smaller than r
eq
.
Let i→ j denote the congested link in the congested neigh
borhood C
R
. (That is, link i→ j is fully utilized.) Increasing
the rate of any of the k flows will either increase the busy
probability or the collision probability at link i→ j, making
its queue unstable [27]. To keep the rate allocation feasible,
the rates of one of the other flows (which have either smaller
or equal rates) will have to be reduced. Hence, by definition,
allocating the maximum possible equal rate to the k flows
sharing the same most congested neighborhood is the max
min rate allocation.
Let f
1
and f
2
be two flows which share the most congested
neighborhood they traverse. The next lemma relates the rates
allocated to f
1
and f
2
by idealized WCPCap.
Lemma 2: The rates allocated by idealized WCPCap to f
1
and f
2
converge to the largest achievable equal rate.
Proof: By design, f
1
and f
2
are allocated equal rates by
idealized WCPCap. So, to prove this lemma, we will prove
that this equal rate converges to the largest achievable equal
rate. We first assume that the rate of flows f
1
and f
2
is
initialized to 0. WCPCap calculates the maximum rate increase
per flow which keeps the system stable. (Since, by assumption,
idealized WCPCap calculates the exact residual capacity at
each link, the flowrate updates will not cause any linkrate
to exceed its capacity,and hence, the flow rates will always
increase.) This maximum rate increase is labelled δ. Then,
the rate allocated to f
1
and f
2
is increased by ρδ. Since
the system remains within the stable region, the queue size
remains negligible. Hence, within
log(1−θ)
log(1−ρ)
iterations of the
algorithm, the rate allocated to f
1
and f
2
is more than θ < 1
of the largest achievable equal rate. Thus, the rates allocated
by idealized WCPCap converge to the largest achievable equal
rate.
Finally, now we comment on convergence of the algorithm
if the rate of flows f
1
and f
2
is initialized to a nonzero value.
Then, if the initialization is to a value such that the arrival rate
on the bottleneck link is less than its service rate, by the same
argument as before, within
log(1−θ)
log(1−ρ)
iterations of the algorithm,
the rate allocated to f
1
and f
2
is more than θ < 1 of the largest
achievable equal rate. Now, if the initialization is to a value
such that the arrival rate on the bottleneck link exceeds its
service rate, in the next iteration, WCPCap will reduce the
rate of the flows to a value such that the arrival rate reduces
below the service rate as the reduction will not only be due
to a lower estimated capacity but also due to nonnegligible
queue sizes. After this first iteration, the same argument for
convergence applies.
Theorem 1: The rates assigned by idealized WCPCap con
verge to the maxmin rate allocation.
Proof: Since Lemma 2 holds for all flows which share
the most congested neighborhood they traverse, in conjuntion
with Lemma 1, it implies that the rates allocated by idealized
WCPCap converge to the maxmin rate allocation.
IV. SIMULATION RESULTS
In this section we evaluate the performance of WCP and
WCPCap in simulation, and in the next we report on results
from realworld experiments of WCP.
A. Methodology
We have implemented WCP and WCPCap using the Qualnet
simulator [3] version 3.9.5. Our WCP implementation closely
follows the description of the protocol in Section IIIA. Our
WCPCap implementation, on the other hand, does not simulate
the exchange of control messages at the end of each epoch;
rather, this control information is made available to the relevant
simulated nodes through a central repository. This ignores
the control message overhead in WCPCap, so our simulation
results overestimate WCPCap performance. This is consistent
with our goal, which has been to explore the feasibility of a
wireless capacity estimation technique.
All our simulations are conducted using an unmodified
802.11b MAC (DCF). We use default parameters for 802.11b
in Qualnet unless stated otherwise. Autorate adaption at the
MAC layer is turnedoff and the rate is fixed at 11Mbps. Most
of our simulations are conducted with zero channel losses
(we report on one set of simulations with nonzero channel
losses), although packet losses due to collisions do occur.
However, we adjusted the carrier sensing threshold to reduce
interference range to equal transmission range in order to
generate interesting topologies to study.
On this set of topologies (described below), we run bulk
transfer flows for 200 seconds for WCP, WCPCap, and TCP.
Our TCP uses SACK with ECN, but with Nagle’s algorithm
and the delayed ACK mechanism turned off; WCP implements
this feature set
3
. (We have also evaluated TCPReno on our
topologies. The results are qualitatively similar.) Congestion
detection for TCP uses the average queue size thresholding
technique discussed in Section IIIA. Other parameters used
during the runs are given in Table I. We discuss the choice
of parameter U later, but our choice of α is conservative,
ensuring small rate increases over the range of timescales we
see in our topologies. This choice of α also works in our real
world experiments, but more experimentation is necessary to
determine a robust choice of α. For each topology we show
results averaged over 10 runs.
We measure the goodput achieved by each flow in a given
topology by TCP, WCP, and WCPCap, and compare these
goodputs with the optimal maxmin rate allocations for each
topology. To compute these allocations, we observe that the
methodology in Section IIIB, with U = 1, can be applied to
a complete topology to characterize the achievable rate region
3
Parameter Value
Congestion Threshold(K) 4
EWMA Weight (w
q
) 0.02
Router Buffer size 64 packets
Packet Size 512 bytes
Additive Increase Factor (α) 0.1
Utilization Factor (U) 0.7
WCPCap epoch duration constant (k) 10
WCPCap scale factors (ρ and β) 0.3 and 0.1
TABLE I
PARAMETERS USED IN SIMULATIONS
for a collection of flows. Intuitively, we can view the service
times and arrival rates on links, together with flow conser
vation constraints, as implicitly defining the achievable rate
region for the topology [27]. (Essentially, this is how we derive
the achievable rate region in Figure 2. However, in this section
we assume the transport overhead to be equal to the overhead
of WCP while Figure 2 assumes the transport overhead to
the same as that of TCP.) The maxmin allocations can then
be found by searching along the boundary of the achievable
rate region. Note that the optimal allocation determined by
this methodology is achievable as has been verified by [27]
through extensive simulations. Using this methodology, we are
also able to identify the links in a given topology that tend to
be congested: we simply simulate the optimal maxmin rate
allocations, and identify congested links as those whose queues
are nearly fully utilized. Note that we use this information in
our intuitive discussion about the dynamics of each topology;
this information is obviously not used in any way by neither
WCP nor WCPCap.
To understand the performance of WCP and WCPCap, we
examine four topologies
4
, with associated flows, as shown in
Figures 1, 5, 6, and 7. Nodes connected by a solid line can
hear each others’ transmissions. (Since, in our simulations, we
equalize interference range and transmission range, only nodes
that can hear each others’ transmissions share channel capacity
with each other.) Arrows represent flows in the network.
Congested links (determined using the methodology described
above) are indicated with a symbol depicting a queue. Each
of these four topologies has qualitatively different congestion
characteristics, as we discuss below.
Stack (Figure 1) consists of a single congested region.
4→ 5 is the congested link, and all other links in the topology
belong to L
4→5
. Diamond (Figure 5) contains two intersecting
congested regions. 1→ 2 and 7→ 8 are both congested links.
L
1→2
includes all outgoing links from nodes 1 to 6 and L
7→8
includes all outgoing link from node 4 to 9. HalfDiamond
(Figure 6) contains two overlapping congested regions. 4→ 5
and 7→ 8 are congested, and L
7→8
is a subset of L
4→5
. Chain
Cross (Figure 7) contains two congested regions, with four
flows traversing one region, and two flows the other. 1→ 2 is
a congested link, but 6→ 7 does not belong to L
1→2
. 4→ 5
and 4→ 3 are also congested, and L
4→5
does include 6→ 7.
Finally, since WCP uses a ratebased implementation, it
is important to ensure that its baseline performance is com
4
parable to that of TCP. To validate this, we ran TCP and
WCP on a chain of 15 nodes. WCP gets 20% less throughput
on this topology; it is less aggressive than TCP. We also
disabled RTT and congestion sharing in WCP, and ran this
on all our topologies. In general, this strippeddown version
of WCP gets qualitatively the same performance as TCP. For
example, Figure 8 shows the goodputs achieved by each flow
for the Stack topology. As expected, WCP without congestion
and RTT sharing starves the middle flow, just as TCP does,
although to a lesser extent since its rate increases are less
aggressive than that of TCP.
B. Performance of WCP and WCPCap
We now discuss the performance of WCP and WCPCap for
each of our topologies. In what follows, we use the notation
f
i→ j
to denote a flow from node i to node j.
Stack (Figure 9). The optimal (maxmin) achievable rates
for this topology are 300 kbps for all the flows. TCP, as
described earlier, starves the middle flows ( f
4→6
). Intuitively,
in TCP, flows traversing links that experience more congestion
(4→ 5) react more aggressively to congestion, leading to lower
throughput. WCP identifies the single congestion region in this
topology (L
4→5
) and shares the rate equally among all the
flows assigning about 250 kbps to all the flows. WCPCap,
with a more precise rate feedback, assigns slightly higher
rates to all the flows and these allocated rates for each flow
is within 15% of the rate allocated to it by the maxmin fair
rate allocation. Intuitively, one would expect the performance
difference between WCPCap and WCP to be higher than what
it is, since the latter’s AIMD mechanism is more conservative
than one which can directly estimate capacity. However, as we
discuss below, we have decided to be conservative and set the
utilization factor U to 0.7, which is a value that guarantees
stability in every topology we have studied. Higher values of
U are possible depending on the topology and yield better
performance for WCPCap. Finally, from the plot it is evident
that for the parameter values discussed above, WCP is within
20% of the optimal achievable rate for this topology.
Diamond (Figure 10). The optimal achievable rates for this
topology are 325 kbps for all the flows. TCP starves flows
traversing the congested links in this topology. By contrast,
WCPCap, assigns 300 kbps to all the flows. Hence, it achieves
rates within 10% of the maxmin optimal rates. WCP,
however, assigns f
4→6
approximately half the rate assigned
to the other flows. This topology consists of two congested
regions (L
1→2
and L
7→8
) and f
4→6
traverses both congested
regions while the other two flows traverse only one. Roughly
speaking, f
4→6
receives congestion notification twice as often
as the other flows, and therefore reacts more aggressively.
Thus, WCP is not maxmin fair. WCP appears to assign rates
to flows in inverse proportion to the number of congested
regions traversed.
HalfDiamond (Figure 11). The optimal maxmin rates for
this topology are 315 kbps for f
4→6
and f
7→9
, and 335 kbps
for f
1→3
; the asymmetry in this topology permits f
1→3
to
achieve a slightly higher rate. Relative to other topologies,
TCP performs fairly well for this topology. WCPCap achieves
1 2 3 4 5 6 8 7 8 9 Fig. 5. Diamond topology
1 2 3 4 5 6 8 7 8 9 Fig. 6. HalfDiamond topology
9 8 4 1 2 3 10 5 6 7 11 10 Fig. 7. ChainCross topology
400 500 600 700 800 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 300 TCP WCP  strip Goodput (kbits/sec) Fig. 8. WCP without congestion and RTT
sharing, Stack
400 500 600 700 800 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 300 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 9. WCP and WCPCap, Stack
400 500 600 700 800 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 300 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 10. WCP and WCPCap, Diamond
rates within 14% of the maxmin optimal rates. WCP assigns
comparable rates to f
4→6
and f
7→9
as they traverse both
congested regions L
4→5
and L
7→8
. f
1→3
achieves a higher rate
as it traverses only one congested region (L
4→5
) but its rate is
not twice the rate of the other flow. Thus WCP achieves a
form of fairness in which the rate allocations depend not only
on the number of congested regions a flow passes through, but
also the intensity of congestion in those regions.
ChainCross (Figure 12). The optimal rates for this topology
are 420 kbps for f
6→7
and 255 kbps for all other flows. TCP
starves the flows traversing the most congested link 1→ 2.
WCPCap achieves rates within 15% of the optimal maxmin
rates. WCP achieves rates that depend inversely on the number
of congested regions traversed, with f
1→7
achieving lower
goodput and f
1→2
, f
10→11
, f
8→9
achieving equal rates. WCP
is able to utilize available network capacity efficiently; f
6→7
does not traverse L
1→2
and gets higher goodput.
Fairness Achieved with WCP . WCP assigns rates inversely
proportional to the number of congested regions a flow passes
through and the intensity of congestion in these regions. More
the number of congested regions a flow passes through and
higher the intensity of congestion in these regions, the more
will be the congestion notifications received at the source,
and lower will be the throughput. Note that the intensity of
congestion depends on the local topology of the region and the
number of flows passing through the region. As an example,
consider Figure 14 where we plot the evolution of flow rates
with WCP in the ChainCross topology. When the queue at
1→ 2 gets congested, the rate of flows f
1→2
, f
1→7
, f
8→9
and
f
10→11
is cut by half (for example, at 10s, the rate of all these
flows is reduced); and when the queue at 4→ 5 gets congested,
the rate of flows f
1→7
and f
6→7
is cut by half (for example, at
30s, the rate of both the flows is reduced). Flow 1→ 7 receives
congestion notifications from both congested regions, hence
it receives a lower throughput than others. Since there are
more flows passing through L
1→2
, it has a higher congestion
intensity. So, we see more notifications from L
1→2
, and hence
a lower throughput for f
1→2
, f
8→9
and f
10→11
.
The property of assigning rates inversely proportional to
number of congested regions a flow passes through is not
unique to WCP. In wired networks, the AIMD algorithm of
TCP was observed to assign rates inversely proportional to
the number of congested links a flow passes through [19].
However, in wireless networks, TCP does not retain this
property as we observe in the simulation results presented for
TCP. By making the AIMD algorithm neighborhoodcentric,
WCP is able to ensure that this property holds in wireless
networks also.
C. Discussion
Impact of Physical Losses. Thus far, we have assumed perfect
wireless links in our simulations (losses do occur in our
simulations due to collisions, however). Figure 13 shows the
performance of WCP and WCPCap for the Stack with a loss
rate of 10% on each link. The results are qualitatively similar
to Figure 9. As expected, the goodputs drop by about 10%
for WCP and WCPCap, as do the optimal rates. We have
conducted similar experiments for the other topologies, but
omit their results for brevity. We also illustrate the efficacy of
goodput correction in dealing with packet loss (Section IIIA).
Figure 15 shows the goodputs achieved in the Stack topology
with 10% loss on all links, when goodput correction is
disabled. Goodputs are no longer fair.
300 400 500 600 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 11. WCP and WCPCap, HalfDiamond
800 1000 1200 1400 1600 1800 Goodput (kbits/sec) 1→2 1→7 6→7 8→9 10→11 0 200 400 600 800 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 12. WCP and WCPCap, ChainCross
300 400 500 600 700 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 300 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 13. WCP and WCPCap over lossy links,
Stack
0
50
100
150
200
250
0 50 100 150 200
Instantaneous Rate of Flows (pkts/sec)
Time (sec)
1>2
1>7
6>7
8>9
10>11
Fig. 14. Evolution of flow rates with WCP in
ChainCross
150 200 250 300 350 400 Goodput (kbits/sec) 1→3 4→6 7→9 0 50 100 150 WCP WCP w/o Goodput
Correction Goodput (kbits/sec) Fig. 15. WCP without goodput correction,
Stack
300 400 500 Goodput (kbits/sec) 1→2 1→7 6→7 8→9 10→11 0 100 200 At  source In  network Goodput (kbits/sec) Fig. 16. WCP with innetwork rate adaptation,
ChainCross
300 400 500 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 At  source In  network Goodput (kbits/sec) Fig. 17. WCP with innetwork rate adaptation,
Stack
300 400 500 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 At  source In  network Goodput (kbits/sec) Fig. 18. WCP with innetwork rate adaptation,
Diamond
300 400 500 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 At  source In  network Goodput (kbits/sec) Fig. 19. WCP with innetwork rate adaptation,
HalfDiamond
InNetwork Rate Adaptation. The WCP AIMD rate control
algorithms described in Section IIIA are implemented at
the source. These algorithms can also be implemented per
flow within the network. Although this approach has scaling
implications, it is still interesting to consider. It can reduce the
feedback delay in control decisions, and a router can avoid
reacting to congestion when the rate of a flow traversing it
is lower than the rates of flows traversing the congested link.
Indeed, in our simulations, such a scheme performs uniformly
better than WCP implemented at the source. For example,
for ChainCross (Figure 16) f
1→7
gets the same rate as other
flows in L
1→2
improving overall fairness while preserving the
higher goodput allocated to f
6→7
. Similar performance can be
observed for Stack (Figure 17) Diamond (Figure 18), and Half
Diamond (Figure 19) in addition to low variation in goodput
across various runs.
Choice of ρ and β in WCPCap . The stability of WCPCap
depends on the values of ρ and β. Similar to the stability
studies of XCP and RCP in wired networks [16], [29], we
consider a network with a single bottleneck. Since a bottleneck
in wireless networks corresponds to a congested region, we use
the Stack topology which has only one congested region to
understand the stability of WCPCap. We run WCPCap for the
Stack topology for varying values of ρ and β and determine
the values for which it remains stable. Figure 20 shows the
stability region of WCPCap. For the parameter values lying
below the curve shown in the figure, WCPCap is stable.
Without RTS/CTS Our simulation results have used
RTS/CTS so far. Note that the design of both WCP and
WCPCap is insensitive to the use of RTS/CTS. Both WCP and
Fig. 20. Stability region of WCPCap. For the
parameter values lying below the curve shown
in the figure, WCPCap is stable.
400 500 600 700 800 900 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 300 400 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 21. WCP and WCPCap with no
RTS/CTS, Stack
300 400 500 600 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 TCP WCP WCPCap Optimal Goodput (kbits/sec) Fig. 22. WCP and WCPCap with no
RTS/CTS, HalfDiamond
10 15 20 25 30 35 40 45 Delay (ms) WCP WCPCap 0 5 10 1→3 4→6 7→9 1→3 4→6 7→9 1→3 4→6 7→9 1→2 1→7 6→7 8→9 10→11 Stack Diamond Half Diamond ChainCross Fig. 23. Average endtoend delay with WCP
and WCPCap
0
100
200
300
400
500
600
0 50 100 150 200
Instantaneous Rate of Flows (pkts/sec)
Time (sec)
1>2
1>7
6>7
8>9
10>11
Fig. 24. WCP with delayed flow arrival
0
100
200
300
400
500
600
0 50 100 150 200
Instantaneous Rate of Flows (pkts/sec)
Time (sec)
1>2
1>7
6>7
8>9
10>11
Fig. 25. WCPCap with delayed flow arrival
WCPCap without RTS/CTS (Figure 21) perform just as well as
(and get higher goodputs than) with RTS/CTS (Figure 9). The
goodputs increase as the overhead of exchanging RTS/CTS
is removed. Other topologies show similar results, except for
HalfDiamond (Figure 22). Without RTS/CTS, 1→ 2 and 7→
8 become the most congested links in HalfDiamond, changing
the dynamics of congestion in this topology. Qualitatively, this
topology starts to resemble the Diamond, with two overlapping
congested regions. A lower goodput for f
7→9
than f
1→3
results
from additional links 4→ 8 and 6→ 8 in L
7→8
which reduces
the capacity in the region.
Randomly Generated Topologies. We generate two topolo
gies by distributing nodes in a square area uniformly at
random. The sourcedestination pairs also randomly generated.
We use AODV to set up the routes. The first random topology
has 75 nodes and 5 flows. Figure 26 compares the performance
of TCP and WCP for this topology and we observe that WCP
allocates fairer rates than TCP. The second random topology
has 150 nodes and 15 flows. Figure 27, and 28 compares the
performance of TCP and WCPCap for this topology and we
again observe that WCPCap allocates rates fairer than TCP.
Performance under Network Dynamics. In the simulations
above, all flows start and end at the same time. Figures 24
and 25 show the instantaneous sending rate r
f
(Section III)
of all the flows in the ChainCross topology for WCP and
WCPCap respectively, when flows do not start and stop at
the same time. Specifically, f
1→7
starts at 25s and ends at
100s, while the rest of the flows start at 0s and end at 200s.
It is evident from the plot that both WCP and WCPCap are
fair not only when all flows are active, but also before the
arrival and after the departure of f
1→7
. Note that the rate of
f
6→7
decreases and then increases between 30s and 100s. This
variation occurs to clear the queue and adaptively set the value
of U at edge 4→ 5.
Delay and Convergence. Since WCPCap keeps the network
within the achievable rate region, it is able to maintain smaller
queues than WCP. Hence, WCPCap has smaller average end
toend delay than WCP (Figure 23). The one exception is the
ChainCross: since the throughput of flows 1→ 7 and 6→ 7 is
higher in WCPCap than WCP, the total traffic over 6→ 7 is
much higher for WCPCap (Figure 12). This results in a higher
delay for these two flows.
WCPCap converges quickly as can be seen in Figure 25.
It converges to θ < 1 of the final rate within within
log(1−θ)
log(1−ρ)
iterations of the algorithm (see the proof of Lemma 2); which
implies that for ρ = 0.3, it will converge to 90% of the
final rate in 7 iterations of the algorithm, which, for all
our topologies, takes less than 10s. Also, as is evident from
Figure 24, WCP’s convergence is slower as the rate per flow
is additively increased by a constant α per RTT. Also, the
evolution of flow rates exhibit a sawtooth pattern which is
expected from an AIMD algorithm.
WCP Performance with Larger Interference Range.
In all the simulations above, the sense signal threshold
(PROPAGATIONLIMIT in Qualnet) is set equal to the receive
signal threshold (RXSENSITIVITY in Qualnet) to make the
Fig. 26. WCP with a randomly generated
topology with 75 nodes and 5 flows.
Fig. 27. TCP with a randomly generated
topology with 150 nodes and 15 flows.
Fig. 28. WCPCap with a randomly generated
topology with 150 nodes and 15 flows.
interference range equal to the transmission range for all
the nodes. Figure 29 shows the performance of WCP for
ChainCross where the interference range is greater than the
transmission range and nodes 10 and 8 are moved farther away
from node 2 such that they are within interference range of
node 2 but not in its transmission range. While node 10 and
8 can sense any transmission from node 2 and vice versa
they cannot decode any packet transmission from node 2.
This illustrates a case where nodes sharing a wireless channel
(and thus the capacity) are unable to communicate control
information (like congestion status) among themselves. Thus,
when congestion occurs at node 2, nodes 10 and 8 are not
able to receive any congestion information from node 2. In
the absence of this information flows traversing nodes 8 and
10 do not receive any congestion notification leading to unfair
throughput to flows in the network.
However, the effect of a larger interference range is not
equally detrimental to WCP’s performance for the Stack, the
Diamond, and the HalfDiamond as shown in Figures 30, 31,
and 32 respectively. With a larger interference range, more
nodes can sense each other’s transmission causing Stack and
HalfDiamond to exhibit characteristics (in terms of the most
congested links) and performance similar to Diamond but with
reduced overall goodput (due to reduction in capacity due to
larger sensing range).
We believe that current advancements in radio technologies
can help mitigate the effect of interference by increasing
the cochannel interference tolerance (or capture effect), i.e.,
increasing the ability of a receiver to successfully decode the
stronger of the signals from two transmitting node. With such
advancements, reception at a given node would not be affected
by transmissions from other nodes that are not within the
transmission range of the given node. It would then eliminate
the need to consider such nodes i.e., nodes that are outside the
transmission range of a node, as part of the neighborhood of a
given node. (The above results are without any capture effects
as the current version of Qualnet does not simulate it.) In
addition, techniques like transmitting congestion information
at the base rate (rate with a larger transmission range) could
further help mitigate the problem.
WCP Performance with AutoRate Adaptation. Autorate
adaptation affects two characteristics of a topology: Link rates
of individual links, and the transmission range of each link.
With nodes continuously adapting their link rates, the snapshot
of the network at any given instant consists of links with
different rate. Figure 34 shows WCP’s performance when the
rate of each link is fixed for the complete simulation run to the
rates shown in Figure 33. Since WCP implements fairness at
the transport layer, it is able to adapt to different physical rates
at the link layer. The lower rates for all the flows compared to
Figure 9 is due to reduction in the network capacity because
of lower link rates compared to 11Mbps in Figure 9.
However, with a change in the link layer rate, the trans
mission range of a node changes leading to a change in the
number of nodes that can successfully receive a packet from a
node. This causes the topology of the network and, therefore,
the neighborhood of each node to change. Table II shows the
rates achieved by WCP during different simulation runs for the
Stack topology with autorate adaptation. In these simulation
802.11 MAC, incorrectly, adapts the link layer rates when
losses occur due to congestion. Since the resulting changes
in topology occur at a time scale faster than the convergence
time of WCP, WCP is unable to converge to a fair rate.
Simulation Run 1→ 3 4→ 6 7→ 9
1 120kbps 102kbps 117kbps
2 118kbps 29kbps 74kbps
3 112kbps 12kbps 116kbps
4 66kbps 39kbps 70kbps
TABLE II
STACK WITH AUTORATE ADAPTATION
WCP Performance in the absence of Link Layer Retrans
missions. Figures 35, 36, 37, and 38 show the performance
of WCP with no link layer retransmissions for data packets.
WCP is still able to achieve fairness without link layer
retransmissions since it implements fairness at the transport
layer. A lossy link with no retransmissions increases the packet
loss rate p (section IIIA) for all flows traversing the lossy
link. Since sources in WCP send at a rate r
f
/p, increase in
the path loss rate causes faster packet transmissions from the
source of flows traversing the lossy link. This causes queues
to build up on the lossy link, initiating congestion control in
the neighborhood which in turn leads to convergence to a fair
rate.
D. Summary
We summarize the throughput properties of WCP and WCP
Cap observed via simulations in this section. (i) WCP allocates
Fig. 29. WCP with larger interference range,
ChainCross
Fig. 30. WCP with larger interference range,
Stack
Fig. 31. WCP with larger interference range,
Diamond
Fig. 32. WCP with larger interference range,
HalfDiamond
Fig. 33. Stack topology with different link
rates
Fig. 34. WCP over links with different link
rates, Stack
Fig. 35. WCP with no link layer retransmis
sions, Stack
Fig. 36. WCP with no link layer retransmis
sions, Diamond
Fig. 37. WCP with no link layer retransmis
sions, HalfDiamond
rates that depend inversely on the number of congested neigh
borhoods traversed by a flow and the intensity of congestion
in those regions. (ii) WCPCap allocates to each flow a rate
within 15% of the rate allocated to it by the maxmin fair rate
allocation. The main reason for this loss in throughput is the
use of a conservative value for U(= 0.7). WCP is less efficient
that WCPCap because it is an AIMD algorithm. For the Stack
topology where the rate vector achieved by WCP has fairness
properties similar to the maxmin rate allocation, it is within
20% of the optimal. (iii) Finally, WCPCap exhibits low delays
and fast convergence.
However, while WCP is implementable (indeed, we describe
results from an implementation in the next section), some
challenges need to be addressed before the same can be
said of WCPCap: the potentially high overhead of control
information exchange, and the ability to estimate the amount
of interference from external wireless networks so that the
collision probabilities can be correctly computed. None of
these challenges are insurmountable, and we plan to address
these as part of future work.
V. EXPERIMENTS
We have implemented WCP, and, in this section, report its
performance on a realworld testbed. We first validate our sim
ulations by recreating the Stack topology and showing that our
experimental results are qualitatively similar to those obtained
in simulation. We then demonstrate WCP’s performance on a
14 node topology running five flows in a realworld setting.
Our experiments use an ICOP eBox3854, a miniPC run
ning Click [37] and Linux 2.6.20. Each node is equipped
with a Senao NMP8602 wireless card running the madwifi
driver [1] and an omnidirectional antenna. Wireless cards are
operated in 802.11b monitor (promiscuous) mode at a fixed
transmission rate of 11Mbps with 18dBm transmission power.
300 400 500 600 700 800 Goodput (kbits/sec) 1→3 4→6 7→9 0 100 200 TCP WCP MaxMin
Achievable
Rate Goodput (kbits/sec) Fig. 39. Results from Stack experimental
topology
10
26 12 13 15 22 24 23 16 18 10 26 12 13 15 22 24 23 16 18 26 14 13 15 11 20 19 26 14 13 15 11 20 19 Fig. 40. Arbitrary experimental topology
300 400 500 600 700 Goodput (kbits/sec) 10→14 12→23 15→26 22→20 18→11 0 100 200 300 TCP WCP Goodput (kbits/sec) Fig. 41. Results from arbitrary topology
Fig. 38. WCP with no link layer retransmissions, ChainCross
RTS/CTS is disabled for the experiments. We empirically
determined, at the beginning of each experiment, that the
packet loss rate on each link was less than 10%.
On these nodes, we run exactly the same code as in our sim
ulator by wrapping it within appropriate userlevel elements
in Click. Furthermore, all experimental parameters are exactly
the same as in the simulation (Table I), with one exception:
we use receiver buffer sizes of 2048 packets so that flows are
not receiverlimited. For repeatability, all experiments were
performed between midnight and 8am. All our experiments
ran for 500 seconds and we show results averaged over five
runs.
We recreated the Stack topology by carefully placing nine
nodes across three floors, and by removing the antennas on
some nodes. Figure 39 shows that the experimental results are
similar to the simulation results (Figure 9). Furthermore, WCP
achieves goodputs within 20% of an empirically determined
maximum achievable rate. (We do not use our theory for deter
mining optimal rates, because we cannot accurately estimate
the amount of interference from external wireless networks.)
We determine this using CBR flows at preconfigured rates
while increasing the rates as long as the goodput of the flow
f
4→6
is within 10% of the goodput of the other two flows.
Finally, to examine the performance of WCP in a real
world setting, we created an arbitrary topology of 14 nodes by
placing them on one floor of our office building (Figure 40).
To create a multihop topology, we covered antennas of nodes
with aluminium foil. On this topology, we ran five flows
as shown. Figure 41 shows the endtoend goodput achieved
by the flows. TCP starves f
15→26
, f
22→20
or f
18→11
during
different runs. By contrast, WCP is able to consistently assign
fair goodputs to all five flows in each run of the experiment!
VI. CONCLUSIONS AND FUTURE WORK
Congestion control has vexed networking researchers for
nearly three decades. Congestion control in wireless mesh
networks is, if anything, harder than in wired networks. In this
paper, we have taken significant steps towards understanding
congestion control for mesh networks. Our main contributions
include: the first implementation of fair and efficient rate con
trol for mesh networks which yields nearlyoptimal through
puts; a plausibly implementable available capacity estimation
technique that gives nearoptimal maxmin fair rates for the
topologies we study; and, insights into the impact of various
factors (e.g., RTS/CTS, whether rate control is implemented
within the network or at the source) on performance.
Much work remains. First, we plan to further investigate the
kind of fairness achieved by WCP by rigorously defining the
intuitive concept of congestion intensity. Second, we intend to
investigate efficient implementations of WCPCap. Finally, we
intend to explore the impact of shortlived flows and mobility
on the performance of WCP and WCPCap.
Our main focus in this work has been to make the case
for fair and efficient neighborhoodcentric congestion and rate
control schemes in the context of mesh networks. We plan to
keep on exploring the design space of such schemes with the
goal of creating even easier to implement schemes, as well
as schemes that get us even closer to the boundary of the
achievable rate region.
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Sumit Rangwala is a Ph.D. candidate at the Uni
versity of Southern California, Los Angeles, CA. He
received his B.E. degree in Computer Engineering
from Shri Govindram Seksaria Institute of Technol
ogy and Science, Indore, India. His research interests
include protocol design for wireless mesh networks
and wireless sensor networks.
Apoorva Jindal is a Ph.D. candidate at the Univer
sity of Southern California, Los Angeles, CA. He
received his B.Tech. degree in Electrical Engineering
from Indian Institute of Technology, Kanpur, India
in 1998. Apoorva works on the performance anal
ysis and design of protocols for multihop wireless
networks.
KiYoung Jang is a Ph.D. student at the Univer
sity of Southern California, Los Angeles, CA. He
received his B.S. degree in Computer Engineering
from Hongik University, Seoul, Korea in 2004. His
research interests are in wireless mesh and sensor
networks.
Konstantinos Psounis is an assistant professor of
EE and CS at the University of Southern California.
He received his first degree from NTUA, Greece, in
1997, and the M.S. and Ph.D. degrees from Stan
ford in 1999 and 2002 respectively. Konstantinos
models and analyzes the performance of a variety
of networks, and designs methods to solve problems
related to such systems. He is the author of more
than 50 research papers, has received faculty awards
from NSF, the Zumberge foundation, and Cisco
Systems.
Ramesh Govindan received his B. Tech. degree
from the Indian Institute of Technology at Madaas,
and his M.S. and Ph.D. degrees from the University
of California at Berkeley. He is a Professor in the
Computer Science Department at the University of
Southern California. His research interests include
scalable routing in internetworks, and wireless sen
sor networks.
Abstract (if available)
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Description
Sumit Rangwala, Apoorva Jindal, KiYoung Jang, Konstantinos Psounis, Ramesh Govindan. "Neighborhoodcentric congestion control in multihop wireless mesh networks." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 910 (2009).
Asset Metadata
Creator
Govindan, Ramesh
(author),
Jang, KiYoung
(author),
Jindal, Apoorva
(author),
Psounis, Konstantinos
(author),
Rangwala, Sumit
(author)
Core Title
USC Computer Science Technical Reports, no. 910 (2009)
Alternative Title
Neighborhoodcentric congestion control in multihop wireless mesh networks (
title
)
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
Tag
OAIPMH Harvest
Format
17 pages
(extent),
technical reports
(aat)
Language
English
Unique identifier
UC16269155
Identifier
09910 Neighborhoodcentric Congestion Control in Multihop Wireless Mesh Networks (filename)
Legacy Identifier
usccstr09910
Format
17 pages (extent),technical reports (aat)
Rights
Department of Computer Science (University of Southern California) and the author(s).
Internet Media Type
application/pdf
Copyright
In copyright  Noncommercial use permitted (https://rightsstatements.org/vocab/InCNC/1.0/
Source
20180426rozancstechreportsshoaf
(batch),
Computer Science Technical Report Archive
(collection),
University of Southern California. Department of Computer Science. Technical Reports
(series)
Access Conditions
The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.
Repository Name
USC Viterbi School of Engineering Department of Computer Science
Repository Location
Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Repository Email
csdept@usc.edu
Inherited Values
Title
Computer Science Technical Report Archive
Coverage Temporal
1991/2017
Repository Email
csdept@usc.edu
Repository Name
USC Viterbi School of Engineering Department of Computer Science
Repository Location
Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089
Publisher
Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA
(publisher)
Copyright
In copyright  Noncommercial use permitted (https://rightsstatements.org/vocab/InCNC/1.0/