Transcript A Scalable Position-Based Deployment and Routing Approach

A Position-based Deployment and
Routing Approach for
Directional Wireless Mesh Networks
Speaker: Weisheng Si
Supervisors: Dr. S. Selvakennedy
Prof. A. Zomaya
1
Outline
• Background
• Overview of our work
• Literature survey and Uniqueness of our
work
• Theoretical Background
• The PDT generation algorithm
• The BE-GF protocol
• Conclusions and future work
2
Background
• What is wireless mesh networks (WMNs)?
• Two developing trends in WMNs
• Architecture of Directional WMNs
3
WMNs
A WMN is a set of mesh routers that communicate with each
other via wireless links and form a mesh topology. The basic
functionalities of these mesh routers are:
• Provide the backhaul connection for WLANs
• Perform routing for the backhaul.
INTERNET
wired connection
Mesh Router
MR
MR
wireless connection
MR
MR
MR
Mesh Router
AP & Mesh Router
WLAN
WLAN
WLAN
WLAN
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WMNs (cont’d)
Based on their additional functionalities, the mesh routers can
be classified into three categories:
• gateways: also interface with the Internet.
• APs: also serve as Access Points (APs) for WLANs.
• pure mesh routers: only have the above basic
functionalities.
My research mainly focuses on the basic functionalities of the
mesh routers. For brevity, the mesh routers are also referred to
as “nodes” hereafter.
5
Two developing trends in WMNs
• Multiple radios and multiple channels:
– Each node is equipped with multiple radios, each of
which uses a distinct channel
– By enabling multiple channels to carry network traffic
simultaneously, this trend multiplies the available
bandwidth for network nodes.
• Directional antennas:
– Used in the backhaul connections, enabling the pointto-point communication.
– The interference among links sharing identical
channels is eliminated.
6
Architecture of Directional WMNs
• We call such WMNs with multiple radios/channels and point-to-point
backhaul links the Directional WMNs (DWMNs).
• Our research is targeted at the DWMNs.
GW: gateway
AP: access point
MR: pure mesh router
AP
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AP
1
3
1
GW
GW
3
2
2
3
AP
MR
MR
1
AP
1
4
2
1
AP
2
4
AP
3
AP
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Overview of our work
• A strategy of position-based joint
deployment and routing for DWMNs
proposed
• A concrete approach under this strategy
given
8
The position-based deployment and
routing strategy
• Main philosophy:
– Perform whatever can be planned to simplify the
operation of WMNs, so as to achieve efficiency and
scalability.
– A lesson from the Internet is the Simplicity Principle:
Complexity is the primary aspect that impedes the
scalability and increases the expenditures of the
networks.
• Main idea:
– First, deploy the DWMNs with certain kind of geometric
graph as the network topology
– Then, design a position-based routing protocol by
exploiting this graph’s routing properties.
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Justifications for the proposed strategy
• Possible:
– The network topologies of many WMNs can be planned by the
deployers, making this joint deployment and routing strategy
possible.
• Localized:
– Position-based routing protocols are localized protocols in that the
routing decision is solely based on a constant amount of
information stored in the packets and the positions of the current
forwarding node, its neighbors and the destination. Thus, positionbased routing protocols are highly efficient and scalable.
• Dynamic:
– WMNs have significant network dynamics such as link failure and
congestion, making the static routing protocols unsuitable. However,
position-based routing protocols can easily handle such network
dynamics.
10
Justifications for the strategy (cont’d)
• Making maintenance of WMNs easy:
– This localized property also significantly eases the maintenance of
WMNs, since the reconfiguration to one part of the network does
not need to be notified to the other parts.
• Low overhead:
– The periodical exchange of positions among them is obviated. In
contrast, such overhead is considerable when the position-based
routing protocols is used in mobile wireless networks.
• Practical:
– With the interference among backhaul links eliminated, the metrics
related to positions become practical for making routing decisions.
Otherwise, the interference-aware routing metrics (e.g., WCETT
and MGF) seem more promising.
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The concrete approach
• The PDT Generation Algorithm: we use Delaunay
triangulations (DT) as the basis to generate the network
topologies. Specifically, this algorithm produces first
refined and then pruned DTs (called PDTs by us). The
PDTs have the advantages of (1) being practical for the
deployment of DWMNs and (2) retaining good routing
properties of the complete DTs.
• The Backward-Enabled Greedy Forwarding protocol
(BE-GF): this protocol extends the well-known greedy
forwarding algorithm by enabling the delivery of a
packet farther from the destination at certain hops
without causing loops. BE-GF has the advantages of (1)
being localized and (2) considering the network
dynamics of link failure and congestion.
12
Literature survey and uniqueness of
our work
• To our best knowledge, ours is the first joint
deployment and routing approach based on
the positions for DWMNs.
• Next, the related work and our uniqueness
in two areas are discussed:
– Node Deployment
– Position-Based Routing
13
Node Deployment
• WMN Deployment
• Wireless Sensor Network (WSN) Deployment
• Cellular Base Station (BS) Planning
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WMN Deployment
• With WMN as a new research area, we have not
seen a concrete approach proposed for the
WMN deployment in community up to now.
• We only find an InfoCom07 paper that conducts
a performance study on the influence of the
following factors on the WMN deployment. This
study is done by Monte Carlo simulations.
–
–
–
–
Network Capacity
Connectivity
Node Density
Installation Cost
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WSN Deployment
• Main factors to consider
– Coverage
– Event Detection
– Connectivity
– Cost
• Compared with coverage and connectivity,
routing is not an important factor for
deployment
• Mostly use a Poisson or grid deployment
strategy
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Cellular BS Planning
• Main factors to consider
– Coverage
– Traffic Distribution
– Signal Quality
– Installation Cost
• No routing
• Mostly use a hexagonal deployment
strategy
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Our Uniqueness in Deployment
• The main factors considered:
– Routing: the most important functionality
provided by the WMNs
– Installation cost: a primary concern of
deployers.
• A novel kind of geometric graph, PDT, is
proposed as the network topology.
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Position-Based Routing
• There is a vast literature in exploiting various geometric
graphs to facilitate routing in wireless networks. These
graphs mainly include:
–
–
–
–
Relative neighborhood graph (RNG)
Gabriel graph (GG)
Yao graph (YG)
Delaunay triangulation
• The wireless network environment is modeled by the unit
disk graph (UDG)
– All network nodes use omni-directional antennas with an identical
transmission range
– Two nodes have a link between them if their distance is no more
than the transmission range.
– There exists significant interference among links that are near
each other, making the routing protocols solely based on position
information not appealing.
19
Position-Based Routing (cont’d)
• The network topology needs to be maintained by
exchanging control messages among the nodes,
which adds significant overhead to the network.
• In forwarding a packet to the destination, if the
forwarding node does not have a neighbor closer
to the destination than itself, face routing is used
to guarantee the delivery.
• Face routing can guarantee the delivery in static
networks, it cannot do this in dynamic networks
where link failures make the forwarding loops
possible.
20
Our Uniqueness in Position-Based
Routing
• The UDG model is replaced with the point-to-point link
model due to the use of directional antennas, thus the
interference from nearby links is avoided.
• With the network topology planned in advance, the
overhead of maintaining network topology is obviated.
• When the forwarding node does not have a neighbor closer
to the destination, a simple technique of routing backward
under certain conditions is used to increase the delivery
ratio. This technique has the advantage that no forwarding
loops can occur under network dynamics.
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Theoretical Background
• The greedy forwarding (GF) algorithm
• The Delaunay triangulation (DT) graph
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The GF algorithm
• A position-based routing algorithm
• Finds a path from a source node s to a destination
node t in the following method:
– At each node (say u) along the path to t, u chooses the
neighbor v that has the smallest d(v, t) as the next hop,
where d(x, y) denotes the direct Euclidean distance
between node x and y
– Ties are broken arbitrarily.
• Characterized by simplicity
– Localized
– Makes the routing decision simply by one search of the
neighbor list.
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The DT graph
Definition: No node lies inside the circumcircle of any triangle. Also, the
dual of the Voronoi diagram.
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The appealing routing properties of DT
• Let n denotes the number of nodes, e the number of edges,
k the number of convex hull edges, we have e = 3n – 3 – k.
This implies that in a DT, the average node degree is
slightly less than 6 and hence bounded.
• For any node u to any destination t, there always exists a
neighbor v of u satisfying that d(v, t) < d(u, t). Hereafter, we
call this property backward-free. Since a DT is backwardfree, GF can always find a path between any two nodes.
Besides, we also say that u routes a packet backward, if u
routes this packet to its neighbor v with d(v, t) d(u, t).
• The length of the shortest path between any two nodes u
and v is guaranteed to be less than c·d(u, v), where c is
proved a constant.
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The PDT Generation Algorithm
• Problem formulation
• Algorithm description
• Algorithm evaluation
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Problem formulation
We make the following assumptions on the DWMNs:
• The positions of the AP nodes are essentially given.
• A deployer can decide:
– The positions of gateways and pure mesh routers
– The existence of links between any pair of nodes
• The angle between any two links incident on a node should
be no less than a threshold value θ_min, so as to fully
avoid the inter-channel interference. Hereafter, an angle
less than θ_min is referred to as a bad angle.
• The length of a point-to-point link cannot exceed a
threshold value l_max. Hereafter, a link longer than l_max
is referred to as a bad link.
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Problem formulation (cont’d)
The DTAP of given 39 AP nodes
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Problem formulation (cont’d)
Given a set of AP nodes and the thresholds θ_min and l_max,
find a graph T as the network topology by adding pure mesh
routers into the DTAP and recalculating the triangulation, such
that:
• T has no bad angles or bad links.
• T is backward-free.
• The number of pure mesh routers added is as small as
possible.
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Algorithm description
Our PDT generation algorithm has the following three stages:
•
•
•
DT construction: construct the DTAP of the given AP
nodes.
DT refinement: add pure mesh routers to remove bad
angles and links in the interior of the DTAP, producing a
refined DT (denoted DTR hereafter) that has bad angles
and links only near the boundary.
DT pruning: remove the remaining bad angles and links
in DTR by eliminating certain related edges, while
guaranteeing that the resulting graph (called PDT) is still
backward-free.
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Algorithm description — stage 1
The DT construction  DTAP
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Algorithm description — stage 2
The DT refinement  DTR
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Algorithm description — stage 3
The DT pruning  PDT
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Algorithm description — the DT pruning algorithm
1. // Initialization
graph T = DTR;
v = an arbitrary node on the boundary of T;
2. // Traversing each node on the boundary of T clockwise
do {
// examining triangles at node v
for (each triangle with v as a vertex) {
// to keep the triangulation structure during the
// examination, only mark for deletion here
if (it is a bad triangle)
mark the edge opposite to its right or obtuse
angle, the longest edge in this triangle, for deletion;
}
T = T – those marked edges;
// advance v in clockwise order
v = next node on the boundary of T;
}
until (no bad triangles are found on a boundary node)
3. Output T as the final PDT;
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Algorithm description — properties
To justify the backward-free property of PDTs, we prove the
following theorem.
Theorem 1: The PDTs obtained by our topology generation
algorithm are backward-free.
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Algorithm evaluation
•
•
•
•
•
Experiment setup
The ratio of added pure mesh routers
The ratio of pruned edges
The path efficiency of hops
The path efficiency of Euclidean distance
36
Experiment setup
• The given AP nodes are assumed to be randomly
distributed in a square area with a constant density
– Note that since a DT exists for any set of points on the
plane, our PDT generation algorithm works for any kind
of AP distributions.
• A minimum distance of 50m between any two AP
nodes is assumed.
• Experiments are conducted on network sizes of 50,
100, 200, 400, 700, and 1000 given AP nodes
respectively.
• For each network size, 200 random topologies are
generated and the average result of them is
calculated.
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The ratio of added pure mesh routers
Defined as the number of added pure mesh routers divided by the total
number of nodes after the topology generation.
Ratio of pure mesh routers
0.48
0.46
0.44
0.42
0.4
0.38
0.36
0
100
200
300
400
500
600
700
800
900 1000
Number of given AP nodes
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The ratio of pruned edges
Defined as the number of pruned edges divided by the total number of edges
after the topology generation.
0.1
Ratio of pruned edges
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
100
200
300
400
500
600
700
800
900
1000
Number of given AP nodes
39
The path efficiency of hops
Given a routing algorithm, the path efficiency of hops for a pair of source and
destination (s, t) is defined as the ratio of the minimum number of hops between
s and t versus the number of hops in the path found by this algorithm from s to t.
Path efficiency of hops
1
0.95
0.9
0.85
0.8
0.75
DT_AP
PDT
0.7
0
100
200
300
400
500
600
700
800
900 1000
Number of given AP nodes
40
The path efficiency of Euclidean Distance
Given a routing algorithm, the path efficiency of Euclidean Distance for a pair of
source and destination (s, t) is defined as the ratio of the distance of shortest
path between s and t versus the distance of the path found by this algorithm from
s to t.
Path efficiency of Euclidean
distance
0.98
DT_AP
PDT
0.97
0.96
0.95
0.94
0.93
0.92
0.91
0
100
200
300
400
500
600
700
800
900 1000
Number of given AP nodes
41
The BE-GF Protocol
• Protocol Overview
• Protocol description
• Protocol evaluation
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Protocol Overview
• Based on the GF algorithm. When no network dynamics
exist, it reduces to GF and fully exploits the backward-free
property of PDTs.
• Extends GF by considering two kinds of network dynamics:
– link failure
– link congestion
• Both kinds of network dynamics can be monitored locally by
nodes, such that no exchanges of network-layer control
packets are involved.
• Supports routing a packet backward to increase its delivery
ratio. To prevent loops, BE-GF stipulates that a node u can
route a packet with destination t backward, only when d(u, t)
< d(b, t), where b is the node that routes this packet
backward last time (if exists); otherwise, this packet is
dropped.
• A packet only needs to remember one node (i.e., b) in its
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header while traversing the network.
BE-GF versus Face routing
• Advantages:
– In case of network dynamics, no forwarding loops can occur,
while face routing can incur loops.
– The amount of information stored in the packet header is
significantly less than that of face routing; for instance, in GPSR,
a well-known face routing protocol, five new fields are added into
the packet header.
• Disadvantages:
– Since packets are dropped under the aforementioned condition
d(u, t) ≥ d(b, t), they may not be delivered to the destination
when there exists a path.
– Face routing performs better in this aspect, because it
guarantees to find a path if the network is connected and static.
– Note that, with the PDTs being backward-free and having an
average node degree of approximately six, the packets drops in
BE-GF is not significant, which is verified in our simulations.
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Protocol description — packet format
Required by BE-GF, three new fields are added to a packet’s
network-layer header:
• Dst Coords: the (x, y) coordinates of the destination
node.
• Backward Flag (BF): this flag is used to indicate whether
a packet has ever been routed backward. That is,
whenever a packet is routed backward by a node, its BF
is set to 1 by this node and will not change later.
• Backward Coords: This field is present only when the BF
is 1. When a node sets the BF of a packet to 1, it also
copies its (x, y) coordinates into this field. If a packet is
routed backward by one node and later by another node,
the later node’s coordinates will overwrite the previous
node’s coordinates.
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Protocol description — pseudo-code
1. // search the neighbor list
u looks for a neighbor v with the shortest d(v, t) that satisfies:
(1) link uv is up;
(2) packet buffer of link uv is not full;
// avoid sending P back to b
(3) v is not b (if Backward Coords exists in P);
2. // all neighbors are not available
if (v is not found) {
u drops P;
return;
}
3. // v is closer to t than u
if (d(v, t) < d(u, t)) {
u forwards P to v;
return;
}
4. // otherwise, check whether to route this packet backward
if ( BF in P == 0 || d(v,t) < d(b,t) ) {
u puts 1 into BF of P and puts its coordinates into Backward Coords of P;
u forwards P to v;
} else {
u drops P;
// BF in P == 1 and d(v,t) >= d(b,t)
}
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Protocol description — properties
We prove the following two theorems regarding the loopfreeness and complexity of BE-GF.
Theorem 2: For any network topology, BE-GF is loop-free in
that it either delivers a packet (denoted by P) to the destination
(denoted by t) or drops P.
Theorem 3: For any network topology with constant maximum
node degree, BE-GF runs with O(1) complexity in both time
and space at a node.
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Protocol evaluation
• Experiment setup
• Network throughput
• Packet drop ratio
• The ratio of packet drops due to no
available neighbors
• Backward ratio
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Experiment setup
• The BE-GF protocol is implemented in ns-2 (version nsallinone-2.31)
• The link failures are generated using the Exponential Model
included in ns-2.
– The up/down time for a link is exponentially distributed with the
mean up-interval and down-interval respectively,
– Both intervals are configurable.
• Experiments are conducted for each network size with the
following four scenarios:
–
–
–
–
Static: no link failures
Dyna1: for each link, up-interval = 10s, down-interval = 2s
Dyna2: for each link, up-interval = 10s, down-interval = 4s
Dyna3: for each link, up-interval = 10s, down-interval = 6s
• In each experiment, every node is found a peer randomly,
and then for each pair of peering nodes, two ftp flows in
opposite directions are generated.
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Network throughput
Defined as the total throughputs of all communicating node pairs in the
network.
Network Throughput (Mbps)
1400
1200
Static
Dyna1
Dyna2
Dyna3
1000
800
600
400
200
0
0
100
200
300
400
500
600
700
800
900
1000
Number of given AP nodes
50
Packet drop ratio
Defined as the total number of data packets dropped by all nodes during
routing divided by total number of data packets generated by all nodes.
0.1
Static
Dyna2
0.09
Dyna1
Dyna3
Packet drop ratio
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
100
200
300
400
500
600
700
800
900
1000
Number of given AP nodes
51
The ratio of packet drops due to no available
neighbors
BE-GF drops a packet in two cases: (1) no neighbors are available for
forwarding and (2) routing backward is prohibited.
Defined as the number of packet drops in case (1) divided by the total
number of packet drops.
Ratio of packet drops due to no
available neighbors
0.016
Static
Dyna1
Dyna2
Dyna3
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0
100
200
300
400
500
600
700
800
900 1000
Number of given AP nodes
52
Backward ratio
Defined as the total number of backward routing decisions made by all nodes
divided by total number of routing decisions made by all nodes.
0.08
Static
Dyna1
Dyna2
Dyna3
Backward Ratio
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
100
200
300
400
500
600
700
800
900 1000
Number of given AP nodes
53
Conclusions
• Proposed a position-based deployment and routing
strategy
• Gave a concrete approach under this strategy, which
consists of the following two parts
– The PDT generation algorithm
– The BE-GF protocol
• Both parts possess appealing properties
– The PDTs are feasible and cost-effective for the deployment of
DWMNs, and also support GF by being backward-free.
– BE-GF is a localized routing protocol, capable of dealing with
network dynamics, and loop-free.
• Formal proofs for these properties were provided when
applicable.
• Experimental results on both parts justified our approach
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Future work
• Our proposed strategy of position-based
deployment and routing for WMNs opens a
new area of research.
• Under this strategy, there are many novel
problems to explore.
• We plan to address the problems in both
theoretical and application aspects.
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Future work — theoretical aspect
• Investigating the sufficient and necessary
conditions for a geometric graph to be backwardfree.
– Whether a network topology satisfies the backward-free
property significantly influences the performance of
position-based routing protocols.
• Investigating the sufficient and necessary
conditions for a geometric graph to be GF-perfect.
– A geometric graph is GF-perfect if its path efficiency of
hops is one with GF as the routing algorithm.
– This property can also be defined in terms of the path
efficiency of Euclidean distance.
56
Future work — application aspect
• Exploring other kinds of backward-free graphs that
can be used as the network topologies according to
the various requirements of network deployment
and routing protocols.
• Comparing BE-GF against existing face routing
protocols with various traffic scenarios.
• Designing a routing protocol with less packet drop
ratio for DWMNs, especially when the network
suffers from frequent link failures.
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Slides and technical report available at my homepage
Thank you!
Questions?
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