a robust routing strategy for density spanner based wireless

A Robust Routing Strategy for Density Spanner based Wireless Ad Hoc

Networks

Divi Mydhili1, K.R.R.Mohana Rao2

1Pursuing M.Tech(CS), Nalanda Institute of Engineering & Technology,Siddharth Nagar, Sattenapalli,

Guntur., Affiliated to JNTUK, Kakinada, A.P., India.

2Professor & Head, Department of Computer Science Engineering, Nalanda Institute of Engineering &

Technology, Siddharth Nagar, Sattenapalli, Guntur., Affiliated to JNTUK, Kakinada, A.P., India.

[email protected]

Abstract - An important problem for wireless ad hoc

networks has been to design overlay networks that

allow time- and energy-efficient routing. Many local-

control strategies for maintaining such overlay

networks have already been suggested, but most of

them are based on an oversimplified wireless

communication model. We address cooperative caching

in wireless networks, where the nodes may be mobile

and exchange information in a peer-to-peer fashion.

We consider both cases of nodes with large and small-

sized caches. For large-sized caches, we devise a

strategy where nodes, independent of each other,

decide whether to cache some content and for how

long. In the case of small-sized caches, we aim to

design a content replacement strategy that allows

nodes to successfully store newly received information

while maintaining the good performance of the content

distribution system. Under both conditions, each node

takes decisions according to its perception of what

nearby users may store in their caches and with the aim

of differentiating its own cache content from the other

nodes’. In this paper, we suggest a model that is much

more general than previous models. It allows the path

loss of transmissions to significantly deviate from the

idealistic unit disk model and does not even require the

path loss to form a metric. Also, our model is

apparently the first proposed for algorithm designs that

does not only model transmission and interference

issues but also aims at providing a realistic model for

physical carrier sensing. Physical carrier sensing is

needed so that our protocols do not require any prior

information (not even an estimate on the number of

nodes) about the wireless network to run efficiently.

Keywords - Routing, Protocols, ad hoc networks,

spanner, dominating set.

1.Introduction Providing information to users on the move is one of

the most promising directions of the infotainment

business, which rapidly becomes a market reality,

because infotainment modules are deployed on cars and

handheld devices. The ubiquity and ease of access of

third- and fourth-generation (3G or 4G) networks will

encourage users to constantly look for content that

matches their interests. However, by exclusively

relying on downloading from the infrastructure, novel

applications such as mobile multimedia are likely to

overload the wireless network (as recently happened to

AT&T following the introduction of the iPhone [1]). It

is thus conceivable that a peer-to-peer system could

come in handy, if used in conjunction with cellular

networks, to promote content sharing using ad hoc

networking among mobile users [2]. Any cast is an

addressing mode in which the same address is assigned

to multiple hosts. Together, these hosts form an any

cast group and each host is referred to as an any cast

group member.

Packets from a client destined to the group

address are routed to the any cast group member closest

to the client, where ”closest” is in terms of the metrics

used by the underlying routing protocol. The most

prominent use of any cast today is in the Internet to find

replicated DNS root servers or to locate rendezvous

points in multicast trees [3]. However, any cast has also

many potential applications in wireless ad hoc

networks. For example, any cast can be used in wireless

mesh networks to route data packets to an Internet

gateway, or in sensor networks to send data to any data

sink when multiple sinks are accessible. Today’s any

cast routing protocols are most commonly

modifications of existing unicast routing protocols. For

example, link-state routing protocols such as OSPF [4]

have been extended to support any cast routing by

adding a virtual node that represents the any cast

service [5]. With distance vector routing algorithms

such as RIP [6], any cast routing is implemented by

group members that advertise their any cast address

with a distance of zero [5]. Also in the context of ad

hoc networks, link reversal algorithms such as TORA

[7] were extended to support any cast routing by

assigning a height of zero to all members of a given any

cast group [5]. Since these proposed any cast protocols

are designed as extensions of unicast routing

techniques, they are easy to implement and to deploy.

Divi Mydhili et al ,Int.J.Computer Technology & Applications,Vol 3 (1), 396-400

IJCTA | JAN-FEB 2012 Available [email protected]

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However, as a consequence, they all follow the routing

strategy determined by the corresponding unicast

routing technique: packet delivery to the closest group

member using shortest-path forwarding.

2. Anycast Routing Model

In this section, we present our field-based model for

any cast routing. First, we give an overview of the basic

concepts. Then, we introduce our definition of potential

fields in a networking context and describe how

packets are routed along those fields. Finally, we

discuss convergence limitations of the model due to

undesired local maxima in the fields that might occur in

particular network topologies.

Overview:

Our model is inspired from field theory in physics.

Every group member creates a potential field which

decreases with d−k

, where d is the distance to the group

member, and k determines how quickly the field

decreases. The field of an entire anycast group is the

linear superposition of all individual fields from the

group members. An example field for an anycast group

with four members (marked as black nodes) is depicted

in Figure 1. The peaks in the field are at the locations of

the group members. Note that only one field is drawn in

the figure, but as each anycast group requires its own

field, multiple fields will generally co-exist

simultaneously. We achieve anycast routing by

forwarding packets towards the steepest gradient of the

field. This is in analogy to field diffusion in physics. By

following the steepest gradient, packets eventually

reach a field maximum, i.e., a group member. The

steepest gradient at each node is determined by

comparing the potential values ϕ of its neighbors. The

steepest gradient is towards the neighbor with the

highest potential value.

Fig. 1. Example potential field. Black nodes represent

group members.

The proposed routing model allows for different

anycast strategies comprising proximity, density, and

combined routing strategies. Which routing strategy is

applied is determined by the value of the parameter k.

We will show in the next section that a proximity-based

routing strategy (the routing strategy of existing anycast

routing protocols which consists of forwarding packets

to the closest member along the shortest path) is

modeled by setting k > μ, where μ is a constant

depending on the network size and the anycast group

size. We also show that for 0 < k ≤ ǫ (where ǫ <

μ), a pure density based routing strategy is modelled

where the proximity of the group members is no longer

considered for routing decisions. By choosing a value

for k between μ and ǫ, we are able to model

combinations of these two one-sided routing strategies.

3. Field-Based Anycast Routing

Protocol To evaluate the performance of density-based anycast

routing in dynamic networks, we designed a distributed

routing protocol to establish potential fields and

forward packets along the steepest gradient. Note that

the focus of this paper is not on the performance of the

routing protocol itself, but on the comparison of the

different anycast routing strategies.

Therefore, we designed a relatively simple protocol for

the only purpose of comparing the different strategies,

and leave possible enhancements of the protocol to

future work.

A. Potential field establishment

To establish a potential field, every node in the network

must know its distance to the existing group members.

For this purpose, the group members periodically flood

the network with a message indicating the anycast

group they belong to, and their identity (i.e., an

identifier that uniquely identifies the group member).

These flooded messages also include a time to live

(TTL) value indicating how many hops the packet has

traveled. The TTL value serves two purposes. First, it

allows every receiver to determine its distance to the

group member who initiated the flooding. Second, it

allows to limit the flooding scope by only rebroad

casting messages which have a TTL value greater than

0 which reduces the communication overhead produced

by such messages. By listening to those messages, each

node calculates its potential value according to

Equation (2). The interval at which the member should

advertise such messages is a tradeoff between accuracy

and protocol overhead. In this paper, we do not focus

on finding the best compromise with regard to this

tradeoff, but we study the relative performance

resulting from different anycast strategies using the

same advertisement interval. Note that the impact of the



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TTL value on the performance of the routing is

evaluated.

B. Gradient determination

To determine the steepest gradient of a field, the nodes

in an ad hoc network must know the potential values of

their direct neighbors. For this, neighboring nodes also

exchange their potential values on a periodic basis.

Such messages are one-hop broadcast packets and

include a list of all the known anycast groups and the

corresponding potential value for each group. Again,

the rate at which such messages are exchanged is a

tradeoff between accuracy and protocol overhead.

C. Packet forwarding

Packet forwarding is simply forwarding along the

steepest gradient. Therefore, packets are forwarded to

the neighbor with the highest potential value. If for any

reason, the neighbor with the greatest potential value is

unreachable (e.g., this neighbor might have moved

away), the packet is simply forwarded to the neighbor

with the second highest potential value. In case this

node is also unreachable, the packet is forwarded to the

neighbor with the next highest potential value, and so

on. A node continues with this procedure until there are

no neighbors left with a higher potential value than its

own. Note that nodes are not allowed to forward to a

neighbor with a lower potential value to make sure that

routing eventually converges and loops do not form. If

a node has no neighbors left with a larger potential

value than its own, it drops the packet.

4. Constant Density Spanner

In the next two subsections, we describe phases II and

III in detail. We use the following notation. The

constant d1 refers to the number of active nodes that

are within the interference range ri of any node. The

constant d2 refers to the number of active nodes that

are within the ri ri-range of any node, and the

constant g refers to the maximum number of required

gateway connections for any active node. Finally, D

refers to the density of the network, i.e. the maximum

number of nodes within the transmission range of a

node.

4.1 Phase II - Distributed Leader Coloring

Similar to phase I, each node organizes the time into

time frames consisting of cd1 rounds for some constant

c that is the same for every node. Also here, the rounds

are synchronized but frames do not have to be

synchronized among the nodes. We again assign active

nodes to distinct rounds using a coloring mechanism.

While the coloring in phase I was done with respect to

Grt , we now need a coloring of the active nodes with

respect to Gri ri , that is, we need the active nodes to

be at least ri ri apart in order to receive the same

color. Every active node from phase I tries to own one

of the rounds.

An active node u is said to own a round if no other

active node within its ri ri range is using that round.

Active nodes are in one of the states {owner, volatile}.

An active node is in owner state if it already owns a

round and is in volatile state if it is still trying to own a

round. Active nodes in owner state always send their

ID in the first time slot of their round. Initially, every

active node is volatile. Active nodes in volatile state

choose an active round from the cd1 possible rounds

uniformly at random. Active nodes in owner state use a

sensing threshold To with CST range ri and active

nodes in volatile state use a sensing threshold Tv with a

CST range being equal to the CSI range of To, rii.

Active nodes do the following repeatedly. Every time a

node reactivates, it sets its time stamp to 0. This time

stamp is used by active nodes in Phase III to compare

entries.

1. Every active node in owner state that is in its active

round sends out a LEADER message containing its ID

and its current time stamp and increases its time stamp

by one afterwards.

2. Every active node in owner state that is in its active

round decides with probability 1/2 to send out an

OWNER message either in the first or second substep

of step 2.

3. Every inactive node that sensed a LEADER message

with threshold Tv sends out a BUSY signal. Every

active node in volatile state that senses a BUSY signal

in its active round chooses a new active round

uniformly at random.

4. Every inactive node that sensed OWNER messages

in both substeps of step 2 with threshold To sends out a

COLLISION signal.

If an active node in owner state senses a COLLISION

signal and sent an OWNER message in the second

substep, it changes into volatile state and chooses a new

active round uniformly at random. If an active node in

volatile state did not sense a BUSY or COLLISION

signal in its active round, it becomes an owner.

THEOREM4.1. Once a stable set of active nodes is

available, it holds: If c ≥ 4, then all active nodes will be

in owner state after O(log n) rounds of the protocol,

w.h.p. The theorem implies that after O(log n) rounds,



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all active nodes have chosen rounds so that for any two

active nodes L and L` with the same round and any

inactive node v within the interference range of L,L` is

outside of the interference range of v. Hence, L can

transmit messages to nodes within its transmission

range without interference problems, and these nodes

can transmit messages to L without causing

interference problems at L. Both properties are

important for phase III to work correctly.

4.2 Phase III - Gateway Discovery

In this section we describe the protocol for phase III.

The goal of this phase is for the active nodes from

Phase I to discover gateway connections to other

leaders that are within a hop distance of at most 3 in

Grt . During this phase, the active nodes use an aCST

range of rt.

Figure 2: Two consecutive rounds of the spanner

protocol

The active nodes use the rounds reserved in phase II to

achieve interference-free communication with the

inactive nodes within their transmission range. Each

round consists of four time slots for communication in

phase III, where each time slot represents a

communication step as shown in Figure 2. In the first

time slot, inactive nodes send CLIENT messages and in

the second time slot the active node sends a response

accordingly; in the third and fourth time slots, an

inactive node u may broadcast to its (active and

inactive) neighbors all the information it has regarding

possible gateways between the leader owning the

reserved round and other leader nodes it has heard

about. For simplicity, we assume that all active nodes

are reactivated at the same time and hence that we can

directly compare the time stamps with respect to the

different active nodes.

In reality, each inactive node u would keep

track of the offsets of the (constant number of) time

stamps it receives (in the corresponding slots allocated

to the different leaders in phase II) and use these offsets

when comparing time stamps from different leaders.

We first describe the data structures that are maintained

during this phase. Each inactive node u maintains a

cache, called Pu, which has entries of the form (L, v, tL)

where L is an active node, v is an inactive node (with u

= v possibly), and tL is the time stamp with respect to L

at which the entry (L, v) is added to Pu. When

comparing entries in the cache, a * acts as a wild card

that matches any value. The operation enqueue(L, v, tL)

on Pu is used to add the new entry (L, v, tL_) to Pu.

Enqueue performs the following checks before actually

adding the new entry to Pu. When adding a new entry

(L, v, tL_), any entry of the form (L,*, tL) with t_ < t_ is

evicted. If no such entry exists and Pu is full, then the

least recently added entry (*,*,t`), that is t_ = min{t|t <

t_ and (*,*, t) Pu}, is evicted to make room for the

new entry. The cache Pu has space enough to store a

constant, d2, number of entries. Inactive nodes also

maintain a state that is either awake or asleep with

respect to each active node that is within their

transmission range. The asleep nodes just listen the

channel and become awake when they receive a FREE

or a ACK message.

5. Conclusion

In this paper, we have examined the existing any cast

routing strategies and introduced a new class of any

cast routing schemes: density-based routing. We have

presented a field based routing model that represents

both, the existing any cast routing schemes as well as

the density-based ones. We use the results from the

model evaluation to categorize the routing strategies

into three regimes: (I) proximity-based routing; (II)

routing as the tradeoff between proximity and density;

and (III) pure density-based routing.

Our results show that density-based any cast routing is

of particular interest in wireless and mobile ad hoc

networks. Due to the dynamic nature of these networks,

traditional proximity based routing schemes often fail

to find alternative routes when a group member moves

away or when intermediate links along the path to a

group member break.

Under these conditions, density-based any cast

routing outperforms proximity-based routing in terms

of successful packet delivery because the probability to

be able to re-route packets is increased when

forwarding towards a high population of group

members. From our simulation studies we learn that the

best routing strategy lies in a tradeoff between

proximity and density, obtained using a value of k ≈ 1

in our model. This particular tradeoff offers the

increased robustness of density-based routing without

introducing a significant path stretch compared to pure

proximity-based routing. It is noteworthy that many

potential fields in physics such as the electric field or

the gravitational field follow a potential decreasing law



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with a value of k = 1. It seems that physical laws can

inspire us to design better systems and algorithms.

References

[1] J. Wortham (2009, Sep.). Customers Angered as

iPhones Overload AT&T. The New York Times.

[Online]. Available: http://www.nytimes.

com/2009/09/03/technology/companies/03att.html.

[2] A. Lindgren and P. Hui, “The quest for a killer app

for opportunistic and delay-tolerant networks,” in Proc.

ACM CHANTS, 2009, pp. 59–66.

[3] D. Kim, D. Meyer, H. Kilmer, and D. Farinacci,

“Anycast Rendevous Point (RP) mechanism using

Protocol Independent Multicast (PIM) and Multicast

Source Discovery Protocol (MSDP),” RFC 3446,

January 2003.

[4] J. Moy, “OSPF Version 2,” IETF RFC 2328, April

1998.

[5] V. Park and J. Macker, “Anycast Routing for

Mobile Services,” in Conference on Information

Sciences and Systems (CISS), Baltimore, MD, USA,

March 1999.

[6] G. Malkin, “Rip version 2,” IETF RFC 2453,

November 1998.

[7] V. Park and S. Corson, Temporally-Ordered

Routing Algorithm (TORA), IETF Internet Draft, July

2001.

AUTHORS PROFILE

Divi Mydhili, Pursuing

M.Tech(CS) from Nalanda

Institute of Engineering &

Technology,Siddharth Nagar,

Sattenapalli, Guntur Affiliated to

JNTUK, Kakinada, A.P., India.

My research Interests are

computer networks.

R. Rammohan Rao, working as

Professor & Head, Department

of Computer Science

Engineering at Nalanda Institute

of Engineering &

Technology,Siddharth Nagar,

Sattenapalli, Guntur Affiliated to JNTUK, Kakinada,

A.P., India. My research Interests are Mobile

Computing, Network Security and Mobile Networks.

He is a Life member of AMIT.



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a robust routing strategy for density spanner based wireless

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