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Mobile Ad hoc Networks COE 549

Topology ControlTarek Sheltami

KFUPMCCSECOE

www.ccse.kfupm.edu.sa/~tarek

Outline

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Static networks Connect Biconnect

Networks with mobile nodes Local Information No Topology

(LINT) Local Information Link-State

Topology (LILT)

What is Topology? A topology consists of a set of nodes and links, and

it describes the connectivity information of the network

Links in topology are the result of some controlled parameters, such as transmission power and channel assigned.

A good topology is critical to network performance. too dense energy consumption & interference

throughput too sparse long path, disconnected network

Reducing energy consumption and interference may be conflicting goals. [Burkhart 2004]

In this lecture the topology control for power reduction

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Overview The topology of a network changes because of many

different reasons: Some reasons we can not control: Node mobility, nodes

malfunction, fading. Some reasons we can control: Direction of antennas,

transmitter power (any other?) There has been a lot of research on how to respond to

changes in topology. Research in Routing.

There has been very little research on how to induce changes in topology.

Research in Topology Control.

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Network Model A network M is described as M = (N,L) where N is a set of

nodes, and L is a vector with their location. Each node u transmits with power p(u). For nodes u, v to be able to successfully communicate with

each other, it is necessary that: p(u), p(v) ≥ λ (d(u, v))

Where: d(u, v) is the distance between u and v, and λ (d(u, v) is the least-power between u and v

Given a network M, p, and λ a least-power function = (V,E) is induced.

Where: where V is a set of vertices corresponding to nodes in N,

and E is a set of undirected edges such that (u,v) є E if and only if p(u), p(v) ≥ λ (d(u, v))

Example

Example..

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What does a good graph look like?

It must be connected, otherwise some nodes are not reachable.

Even if it is connected, it must not have bottlenecks.

If it is too dense: Nodes consume more power than needed. There is not a lot of spatial reuse.

With no topology control, networks with random and dynamic topologies will be in one of the two states for a lot of time.

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Connected MinMax Power (CMP) Problem Problem 1: Given:

A static network M = (N,L) A least-power function λ

Find an assignment of powers p such that: The induced graph G(M, λ , p) is connected . Maxu є N (p(u)) is minimum. In other words: We want every node to be able to

communicate with everyone else, and everyone using as little power as possible.

Question: Is this an interesting problem? Are we neglecting anything important?

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Solution: Algorithm CONNECT

1. sort node-pairs in non-decreasing order of mutual distances

2. initialize |N| clusters, one per node3. for each pair of nodes (u, v) in sorted order do:4. if cluster(u) ≠ cluster(v) then5. p(u) = p(v) = (d(u, v))6. merge cluster(u) with cluster(v)7. if number of clusters is 1, then end8. perNodeMinimalize(M,λ,p,1)

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Example

1-11-1

3-23-2

4-34-3

2-12-1

5-45-46-46-4

Greedy algorithm

Side-effect edge problem

AA BB

CC DD

Example..

Example..

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1. let S = sorted pair list2. for each node u do3. T = {(n1, n2) є S : u = n1 or u = n2}4. sort T in non-increasing order of distance.5. discard from T all (x, y) such that λ(d(x, y)) >

p(u)6. for (x, y) є T using binary search do7. if graph with p(u) = λ (d(x, y)) is not k-

connected, stop8. else p(u) = λ (d(x, y))end

Procedure perNodeMinimalize(M,λ,p,k)

Network Properties

K-connectivity The k-connected graph contains at least k

independent paths between any pair of nodes. Two or more paths are independent if none of

them contains an inner node of another The deletion of any set of less than k nodes in the k-

connected graph still leaves a connected graph

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K-connected Graph Definition: A graph is k-vertex/edge-connected if and

only if there are k vertex/edge disjoint paths between every pair of vertices.

If a graph is k-vertex connected, it is also k-edge connected.

For k = 1, the graph is connected. For k = 2 the graph is biconnected.

In the following, we only consider vertex connectivity.

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Biconnectivity Augmentation with MinMax Power (BAMP)

Problem 2: Given: A network M = (N,L) A least-power function λ An initial assignment of transmit powers p such

that the induced graph G(M, λ, p) is connected Find a per-node minimal set of power increases δ

such that: The induced graph G(M, λ,(p + δ)) is biconnected. maxuєN (p + δ)(u) is minimum

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Solution: Algorithm BICONN-AUGMENT

1. sort node pairs in non-decreasing order of distance2. Let G be the graph induced by (M, λ, p) 3. for each (u, v) in sorted order do4. if biconn-comp(G,u) ≠ biconn-comp(G,v)5. q = λ(d(u, v))6. p(u) = max(q, p(u))7. p(v) = max(q, p(v))8. add (u, v) to G9. perNodeMinimalize(M, λ, p, 2)End

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Example

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1. let S = sorted pair list2. for each node u do3. T = {(n1, n2) є S : u = n1 or u = n2}4. sort T in non-increasing order of distance.5. discard from T all (x, y) such that λ(d(x, y)) >

p(u)6. for (x, y) є T using binary search do7. if graph with p(u) = λ (d(x, y)) is not k-

connected, stop8. else p(u) = λ (d(x, y))end

Procedure perNodeMinimalize(M,λ,p,k)

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Simulations

Random Topology with 40 nodes. Powers decay polynomially with distance. For a signal to be successfully received, it must

exceed an SINR threshold, so interference is not ignored

Nodes access channel by using CSMA: Hidden and exposed terminals.

We determine throughput and delay versus node density.

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Simulation

With NONE, all nodes transmit with maximum power. With no topology control, throughput is good only for small densities. The biconnectivity algorithm avoids hotspots, and generally performs

better than the plain connectivity algorithm. Question: why is NONE better than our algorithms for small node

densities?

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Simulation ..

The biconnectivity algorithm requires significantly more power than the plain connectivity algorithm, because of occasionally isolated nodes.

Both algorithms are much better than no power control.

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Distributed Heuristics for Mobile Networks

When nodes are mobile, previous algorithms do not make sense.

They are centralized, and by the time the information is gathered at same place, topology has changed

We will consider two heuristics: Local Information No Topology (LINT). Local Information Link-State Topology (LILT).

They differ on how much they assume that each node knows. Both are zero-overhead protocols:

They use information that is available anyway, and do not require control packets.

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Local Information No Topology (LINT) We assume that nodes have no global information about the

topology Let the degree of the node be the number of neighbors it has Nodes try to keep their current nieghbor degree dc within

some interval (dl, dh) Ideally, dc should be target degree dd

If dc > dh, nodes power down If dc < dl, they power up NRP and NAP

Power up/down rule: pnew = pold ×

Question: What is the motivation for this rule, and what should be?

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Tradeoffs Basic tradeoff: As the target degree goes up, each node has more

neighbors, and the topology is connected with higher probability, but the power consumption goes up.

The protocol works best when the placement of the nodes is random and uniform

The protocol can not handle cases where nodes tend to cluster: To resolve these cases, it is necessary that we use global

information.

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Local Information Link-State Topology (LILT)

We assume that nodes have global topology information Question: Is this a realistic assumption?

Basic Idea: In the beginning, everyone transmits with maximum

power. The nodes start to power down, executing LINT When nodes realize that the network is connected

but not biconnected, they power up Nodes power up after a random interval Nodes close to the problematic area of the network

power up sooner

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Simulation

Now nodes move around in a random fashion, independently of each other With NONE, everyone transmits with maximum power LINT is better than LILT! (topology is not clustered) There is not a lot of improvement with any of the two protocols Any ideas why?

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Simulation..

With no power control, performance is actually better. Any ideas why?

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Reference

[1] R. Ramanathan, R. Rosales-Hain, ”Topology Control of Multihop Wireless Networks using Transmit Power Adjustments , Proc. of the IEEE INFOCOM, Tel Aviv, Israel, Mar. 2000, Vol. 1, pp 404-413.