International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 8, August 2015
ISSN 2319 - 4847
DETECTION OF OPTIMAL PATH USING
QUADRATIC ASSIGMENT TECHNIQUE IN
WIRELESS SENSOR NETWORKS
1
Vinoba.V,
2
Indhumathi.A
1
Department of Mathematics, K.N. Government Arts college, Tamil Nadu, India.
2
Department of Mathematics, R.M.K College of Engineering and Technology, Research Scholar, Bharathidasan University,
Tamil Nadu, India
ABSTRACT
Wireless sensor networks (WSNs) consist of three nodes which are sensor nodes, intermediate nodes and destination nodes
(sink). The function of sensors is to collect data from the physical environment and sending them to the sink. The intermediate
nodes relay the data to the sink. After detection of an event, this data must be sent to the sink immediately. To send this data
to the sink, there exist several paths in which finding a suitable path can improve the performance of the network. In
this paper a protocol on routing has been proposed, in which protocol sensors cache the identity of neighbouring nodes,
and by first sending a group of the identity of intermediate nodes will be named as the selected path till arriving the sink
node or destination node, during which the next sending will only be carried out through that path.
Keywords:- WSNs; Routing, Coordination, Sensor, Sink node; Quadratic Assignment Technique
1.INTRODUCTION
In recent years, wireless communication has experienced exponential growth caused by the need for connectivity.
Wireless sensor networking is a broad research area, and many researchers have done research in the area of power
efficiency to extend network lifetime. In order to achieve high energy efficiency and increase the network scalability,
sensor nodes can be organized into clusters [1]. This type of networking very useful in industrial, agricultural,
vehicular, residential, medical sensors and actuators have more relaxed throughput requirements [2]. This type of
network consists of a group of nodes and each node has limited battery power. There may be many possible
routes available between two nodes over which data can flow. Assume that each node sensed and generated some
information and this information needs to be delivered to set of destination nodes. A node can easily transmit data to a
distance node, if it has sufficient battery power.
A node transmits its data to other node without any interference, if node lies in its vicinity. A large battery power is
required to transmit the data to a node which is situated far from source node. After few transmissions a node
reaches to its threshold battery level and it may exclude from network path and there will come a condition that no
node is available for the data transmission and overall lifetime of network will decrease. Whereas network lifetime is
defined as the time until the first node in the network dies. For maximizing the lifetime of network, the data
should be forwarded such that energy consumption is balanced among the nodes in proportion to their energy
reserved, instead of routing to minimize consumed power.
2.RELATED WORKS
Routing in WSNs is very challenging due to the inherent characteristics that distinguish these networks from other
wireless networks like mobile ad hoc networks or cellular networks. First, due to the relatively large number of sensor
nodes, it is not possible to build a global addressing scheme for the deployment of a large number of sensor nodes as the
overhead of ID maintenance is high. Therefore, classical IP-based protocols cannot be applied to sensor networks.
Second, in contrary to typical communication networks almost all applications of sensor networks require the flow of
sensed data from multiple regions to a particular sink. Third, generated data traffic has significant redundancy in it
since multiple sensors may generate same data within the vicinity of a phenomenon. Such redundancy needs to be
exploited by the routing protocols to improve energy and bandwidth utilization. Fourth, sensor nodes are tightly
constrained in terms of transmission power, on-board energy, processing capacity and storage and thus require careful
resource management.
Due to such differences, many new algorithms have been proposed for the problem of routing data in sensor networks.
Almost all of the routing protocols can be classified as data-centric, hierarchical or location-based although there are
few distinct ones based on network flow or QoS awareness.
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 8, August 2015
ISSN 2319 - 4847
Flooding and gossiping are the very traditional ways of transmitting data to the destination. LEACH [3] follows a
hierarchical based cluster formation technique and also proposes a method for the selection of proper cluster heads.
GEAR [4] protocol says that the entire network is divided in to partitions and within partitions, flooding technique is
adopted. Geographic adaptive fidelity GAF [5] is an energy- aware location-based routing algorithm designed primarily
for mobile ad hoc networks, but may be applicable to sensor networks as well. GAF conserves energy by turning off
unnecessary nodes in the network without affecting the level of routing fidelity. It forms a virtual grid for the covered
area.[6] suggested The sensor data is classified using ART1 Neural Network Model. Wireless sensor network populates
distributed nodes. The cooperative routing protocol is designed for communication in a distributed environment. The
classified sensor data is communicated over the network using two different cases of routing: cooperative routing and
diffusion routing. [7] have proposed a different hierarchical routing algorithm based on three tier architecture. Sensors
are grouped into clusters prior to network operation. The algorithm employs cluster heads, namely gateways, which are
less energy constrained than sensors and assumed to know the location of sensor nodes. In this paper, we propose a
model which computes the selection of neighbours and route establishment using updated neighbours.
The minimum energy routing protocol is proposed in [8] this approach minimize the energy consumption to reach the
destination by sending the traffic to same path but if all the traffic follows the same path then all the nodes of that path
will drain out there energy quickly. The maximum lifetime problem is a linear programming problem and solvable in
polynomial time [9]. DBF was used in [10–12] and authors in [13] to generate shortest distance paths in WSNs due to
the distributed structure. However, their overheads are significantly high and the message complexity of these
algorithms is unbounded since the algorithms are asynchronous. In [14], the algorithm was synchronized and the
message complexity is O V .E  . Thus, these algorithms are not suitable for WSNs due to energy problem. On the other
hand, shortest hop path algorithms are used instead of shortest distance path algorithms by many protocols for WSNs.
In [15, 16], the shortest hop paths are constructed in the PEQ and ICE protocol respectively.
Even the method used for shortest hop path construction is straightforward and easy; since the algorithm is
asynchronous, the message complexity cannot be calculated. Furthermore, due to lack of termination detection, the
initiator node cannot know whether the algorithm terminates. Multipath routing techniques have been discussed in the
literature for several years. There are two different approaches including disjoint and braided multipaths. Generally, the
multipath is used in [17–20] for fault-tolerance, load-balancing and security. Very recently, in soliton theory, the linear
superposition principle applies to Hirota bilinear equations to construct soliton solutions [21]. As known, Hirota
bilinear equations are linked to binary Bell polynomials. In this authors showed that a linear superposition principle of
exponential waves applied to Hirota bilinear equations, under some additional condition on the exponential waves and
possibly on the polynomial as well. This is an interesting mathematical problem in the study of polynomials whose
zeros form a vector space, and it determines one class of Hirota bilinear equations possessing the linear superposition
principle of exponential waves. They analyzed some such specific Hirota bilinear equations. In this paper, by using
Quadratic Assignment Technique optimal route in WSN is found.
3.NETWORK MODEL AND PROBLEM DEFINITION
Consider a wireless sensor network with set of N nodes N  1,2,3,....n. Let s i
represent the set of immediate
 N , e t ( avg ) i , j indicates the average energy consumed for data transmission from node i to
node j and E i be the initial battery energy level of node i . Let there be multiple links, where a set of source node and
destination node forms a link. There are set of source nodes S in an application area where information is generated at
node i with rate Qi and a set of destination nodes D among which any node can be reached in order for the
information transfer of link to be considered done. Let  ij be the traffic generated at node i and destined for node
neighbors of node i
j and  ij be the amount of data that needs to be transmitted from node i to node j .
The main objective of this paper is to minimize the energy consumption of each sensor node during transmission and
reception by using optimal path algorithm. The above problem can be solved by using QAP that can be stated as
follows: Let the set of nodes are N  1,2,3,....n and three nxn matrices F  ( f ij ), D  ( d ij ) and C  (cij ) the
quadratic assignment problem with coefficient matrices F , D and
n
n
n
n
C shortly denoted by QAP can be stated as follows:
n
n
minxX  f ik d jl xij xkl  Cij xij
i 1 j 1 k 1 l 1
i1 j 1
(1)
Such that
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 8, August 2015
ISSN 2319 - 4847
n
x
ij
1
, i N
ij
1
, jN
i 1
n
x
j 1
xij  0 ,1
, i , j N
f ik denotes the amount of flow between facilities i and k, d jl denotes the distance between location j , l and C ij
denotes the cost of locating facility i at location j. A more general version of the QAP was introduced by Lawler(2). In
this paper we are using flow distance products f ik d jl instead of considering dimensional array.
4.PROPOSED PROTOCOL (OPFR)
In proposed protocol, sensor nodes broadcast their identification to the neighbour nodes; it means after
configuring the network, every node knows all neighbours. The sensor node sends the RTS signal and resends the
identification to the neighbours depending upon the event. Each node sends only its identification to all other nodes,
and receives identification of its neighbours, cached to its memory. Naturally, in some sensor memory, there exists
identification of sinks. Most of sensor memory only contains one type of identification, which is sensor identification.
Only little sensors have both the sink and sensor identification in the memory. Sensor with two types of
identification, that is, sensor and sink in its memory connects the sensor as a source and the sink as the base
station.
Therefore, there are two types of identification: sink identification and sensor node or source node identification. Every
node can receive two types of identification. The node that receives both these identifications are called boundary node
(BN). Upon receiving the two types of identifications, the task of BN is to send its identification to sink. On other hand,
sink identification attaches its identification sent to previous node. In this order every node receives identifications of
other nodes, and knows that all data will be sent and received along this path. According to Figure1, order of sink
identification will be fixed while passing through intermediate nodes, but sensor's identification modifies frequently by
the first packet that is sent to the source.
Figure 1 Routing and Sink selection
In this method, every sensor has one identification table is shown in Table 1, which contains two fields as Sid and Did.
Sid field is for sensors identification ie sensor receives data from them and Did field is for sink or destination ie
sensor receives messages from them. In total, the data in this table has four statuses: the first is the table can have no
data, it shows this node is out of network and do not have any neighbor; meaning this node has no communication
in the network (dead). Second is only Sid field of table contains data, which shows neighbor nodes are only sensor
node, therefore this node is considered only passing path for all nodes, and not as an interface node. The third is if
only Did column has data, means this node can only send the data to sink and is not able to route every nodes or
network. The fourth is if both columns of one table have data, it means the node can communicate with network and it
is near an sink. Moreover, it can have an interface node role.
A. Mechanism
Once the network is ready to use, every node sends its Id to neighbors by flooding and this way every node detects the
neighbors and saves its identifications (Ids) to its tables. When an event occurs, the sensor that detects the flooding
sends its Id to all its neighbors, and every neighbor saves this Id its table. Then column Sid and Did will be searched for
sink's Id. If in this column no sink Id is found, then the sensor will send its Id and data to all neighbors until it arrives
at the interfaced sensor. But, if sensor finds a sink's Id in its Did column, this means that sensor is near an sink, and can
act as an interface node. It will activate one of the sink Ids and sends its Id and data randomly. Sink node also after
receiving data caches sensor's Id that receives data of it and sends message to interface node that it is available and
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 8, August 2015
ISSN 2319 - 4847
reacts to the messages which receiving of that sensor. Interface node also sends sink’s Id and its Id to sensor that
caches it in its table. Previous node carries out this action until sink's id and id of one node are delivered to source
sensor. Then, source sensor sends every packet together with its Id destination to one neighbor randomly. In every
sensor, sink's id with data is fixed until data is received at end node, but sensor's id is attached with data, after passing
of every node has removed and gives neighbor's id it sensor. This identifiers show selected path, upon first sending
from sink to source sensor is fixed. Figure.2 shows group of this Ids contain one path that after it source sensor node
and every route node knows that data of source node must be sent to what sink.
(a) Finding Neighbour Node
(b) Selecting suitable Sink
Figure 2 Routing and Sink selection
Since every sink is ready to act, this important source sensor registers first sink's id in its memory. This routing has
three advantages: first, selecting the nearest path to active sink, second: using other sink as backup, and third:
reliability to select optimum sink. A problem that maybe happens in this routing is because every node sends its id to
neighbors. Figure.1 shows sending data in infinitive loop, meaning one node sends its data to another node and
that node sends to node to the same node where it receives the data and this loop continues. Our solution for this
case is every node that receives data from previous node must send data to every neighbour except previous node. In
this case there exist two challenges: first, in neighbour of interface node maybe exist several sinks and interface node
must randomly select only one of them. Second, if two sinks arrive to source sensor at the same time, sink selected by
source sensor the solution is the sensor node must only select one of them randomly and must only send its data of its
path.
5.SIMULATION MODEL
In our simulation, we have varied the number of nodes from 10 to 100, which are randomly deployed using uniform
distribution in different parts of deployment area with a fixed density.. Here sink node is placed at the location of (50,
50) and (30,70) respectively. Assume that transmission range of each node is limited by 10 meter. The packet size was
kept at 64 bytes. We used Constant Bit Rate (CBR) as traffic source with average packet rate 0.5 packets /sec. We
assume the ns-2 radio energy model and assign each node with the same initial energy level of 10 J at the beginning of
each simulation in order to keep the simulation time within a reasonable time period. By experiment, we find that the
suitable value of θ to be 10 packet andwe have set the duration of each round to 1000 seconds. The input data is
generated randomly at each node every second duration. We assume that each sensor node carries an omni antenna.
Every 500m sec , we obtain the log of the energy level of each node.
6.SIMULATION RESULTS
A. AVERAGE NUMBERS OF MESSAGES FOR THE PROPOSED ROUTING
Average Number of Messages
1
DD
Flooding
Energy Aware Routing
OPFR
Average Number of Messages
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
20
30
40
50
60
70
Number of Nodes
80
90
100
Figure 3 Average numbers of messages Vs Number of Nodes
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 8, August 2015
ISSN 2319 - 4847
Figure. 3 shows that the numbers of messages are very much in direct diffusion and in flooding and energy aware
routing are almost larger than OPFR. Because in existing methods, sending acknowledgement by sensors cause
network’s congestion which reduces life time of network. The main reason for this congestion in flooding, direct
diffusion and energy aware routing is event area divides to several areas and clusters it. Every cluster sends and
receives messages, and this can cause a lot of congestion. Because of Shortest path method in this evaluation does
not have clustering; acknowledgement and sink request, hence can cause 20% reduction to send a message. Therefore,
in case that size of network is very large, using of OPFR has many advantages.
Average Latency
Average Latency
0.7
DD
Flooding
Energy Aware Routing
OPFR
0.6
Latency (Seconds)
0.5
0.4
0.3
0.2
0.1
0
20
30
40
50
60
70
Number of Nodes
80
90
100
Figure 4 Average Latency Vs Number of Nodes
Figure.4 infers that average latency with respect to number of nodes. Here direct diffusion method with much latency,
meaning increment to network size causes latency to increase very fast. In routing methods comparison of
latency parameters are very important. Latency in OPFR is very low, because transfer time between sensor and sink is
very low. Changing size of network in flooding, energy aware routing and our proposed method (OPFR) doesn't have
any influences.
C. Packet Delivery Ratio
Packet Delivery Ratio
0.8
DD
Flooding
Energy Aware Routing
OPFR
0.75
0.7
Delivery Ratio)
0.65
0.6
0.55
0.5
0.45
0.4
0.35
1
2
3
4
5
6
Packet Rate (P/Sec)
7
8
9
10
Figure 5 Packet Delivery Ratio Vs Packet Rate
Figure 5 show that OPFR increases the delivery ratio by 3.5% to 6.5% as the packet rate is varied. This is mainly
due to its neighborhood discovery does not allow the one-hop neighbor to reply if it is not in the direction to
the destination.
7.CONCLUSION
This paper presents the optimal path forwarding probability for OPFR which is designed for WSN. In general, the
proposed routing protocol OPFR provides high delivery ratio and spends less energy consumption if the optimal path
forwarding probability is used. In this paper we have checked and evaluated existing methods to present a routing
method that is better than existing methods in latency, energy consumption and packet delivery ratio.
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Volume 4, Issue 8, August 2015
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