ASSESSMENT OF NODE DENSITY IN CARTESIAN AD HOC ROUTING PROTOCOLS (CARP)

Imran Raza, Mohammad Hasan Raza

Abstract:- With the rapid development in the geographical positioning system (GPS) technology, the geographical routing category of the MANET protocols has recently been a hot research area. The Cartesian Ad hoc Routing Protocols (CARP) are a set of three adaptive and connectionless protocols that address the problem of routing and power consumption in MANET. These protocols are used to limit the number of forwarding nodes in a logical transmission area. Density of an ad hoc network is considered a network parameter in CARP, and is used in the calculations to form a logical transmission area. The CARP assume that the nodes have some knowledge about the density from previous activity of the network, but no specific density determining mechanism has been described. This research paper presents a density determining mechanism for location aware nodes that use CARP. As the nodes are location aware, the location information is used as a key parameter to conduct a census of nodes. The nodes in a network with implementation of CARP can use this density value to form the logical broadcast area. As the nodes in MANET are potentially in motion, density may change over time. The proposed algorithm also tracks the density value over time and keeps it updated as per situation of the network. The simulation results in OPNET Modeler 10.5 validate the performance of this density determining algorithm for CARP Keywords: Density, census, counting, area, location, number of nodes.

I. INTRODUCTION

A mobile ad hoc network or MANET is an autonomous collection of mobile nodes that communicate over wireless links. This mobility means that the network topology may change rapidly and unpredictably over time as the nodes move, or adjust their transmission and reception parameters. The nature of MANET is decentralized, meaning that the nodes must execute message delivery independent of any centralized control [1, 2]. With the rapid development in the geographical positioning system (GPS) technology, the geographical routing category of the MANET protocols has recently been a popular research area.

I. Raza is with the Department of Computer Science, COMSATS

Institute of Information, Technology, Lahore, Pakistan, iraza@ciitlahore.edu.pk

M. H. Raza is with the Department of Engineering Mathematics and Internetworking, Dalhousie University Halifax, N. S., Canada, B3J 2X4 hraza@dal.ca

The Cartesian Ad hoc Routing Protocols (CARP) [3] is

one of the geographical routing ad hoc protocols. The CARP are a set of efficient broadcast control mechanisms for geographical location aware nodes. In CARP, when a source node tries to transmit a packet in the direction of a destination node, a logical transmission area is formed. To reduce the flooding traffic, only those nodes that are located inside this area will forward the packet. The CARP present three distinct protocols to conserve power and bandwidth by reducing the broadcast area and controlling flooding.

Density of an ad hoc network is considered a network parameter in CARP, and is used in calculations to form a logical transmission area. The CARP assume that the ad hoc nodes have some knowledge about the density from previous activity of the network, but no specific density determining mechanism has been described. The density of the network in CARP is guessed by the number of responses a node has received in the previous transmissions. Each node is supposed to maintain the statistic record of the transmission to represent the density of the network. The value of the transmission area is determined on the basis of this statistic record of transmissions.

We consider that this argument about the assessment of density may be unrealistic due to the following reasons:

1) Density assessed on the basis of the number of transmissions received by a node may be incorrect, because of the broadcast nature of the MANET. A previously received message may be received repeatedly and the density value may be incorrect.

2) The assessment of density may vary node by node to give a different picture of density in different parts of the network.

3) Recording and analysis of the statistics by each node in the network may consume more power, whereas the power consumption is an issue in many ad hoc devices.

4) It is not clear that what factors make a node start and stop collecting statistics, and at what stage density is determined?

5) It is also not clear that what attributes fall under the heading of statistics?

This research paper addresses all the above mentioned

issues, and proposes a structured mechanism that determines density by avoiding repeated count of nodes, and updates the density value regularly.

978-1-4244-4609-4/09/$25.00 ©2009 IEEE

The remainder of this paper is as follows: the next section briefly describes CARP. Section 3 describes design of the proposed algorithm. Section 4 presents simulation results and Section 5 consists of conclusions.

II. CARTESIAN AD HOC ROUTING PROTOCOLS (CARP)

The Cartesian Ad hoc Routing Protocols (CARP) [3] are a set of three adaptive and connectionless protocols that address the problem of routing and power consumption in MANET. Each protocol operates at the physical layer and the network layer; all nodes are location aware. The authors claim that the design of CARP has three objectives: restrict flooding, reduce power consumption, and save bandwidth. The authors of CARP have also proved its better performance against the other leading geographical ad hoc protocols.

All Cartesian Ad hoc Routing Protocols attempt to restrict transmission to those nodes that lie between the source and the destination. These protocols are used to limit the number of forwarding nodes in a logical transmission area.

As nodes in the network are location aware, when a source node transmits a packet, a logical rectangular transmission area is formed by comparing the coordinates of the source and destination nodes. An approach of Rectangular Transmission Area (RTA) in CARP reduces the size of the transmission area, and limits traffic within the transmission area. Although the Rectangular Transmission Area (RTA) tries to reduce traffic, the volume of the flooding traffic may still be problematic in a very dense network. The Trimmed Transmission Area (TTA) algorithm and Transmission Area with Limiting Angle (TALA) attempts to modify the shape of the transmission area through a simple optimization.

The CARP attempt to optimize the transmission area by using some simple calculations based on the location information. The CARP allow a transmitting node to vary the size of the transmission area associated with a packet, adapting it to the density of the nodes. The CARP consist of the following subsystems:

1) The Direction and Location Determination subsystem: It provides location information (using GPS) and direction information (using an electronic compass) to the other subsystems. It works on the physical layer.

2) The Location Verification subsystem: It determines whether the node is inside or outside of the transmission area using the location information. It works on the network layer.

3) The Transmission Area Creation subsystem: It creates a new transmission area for the next hop using the location information. It works on the network layer.

4) The Antenna Selection subsystem: It selects the right antenna(s) facing the direction of the destination. It works on the physical layer.

One of the contributing factors in reducing the size of transmission area is the density of a network, but no precise mechanism has been presented in CARP. The density determining technique proposed in this paper is based on the population census of nodes.

III. DESIGN Density of an ad hoc network can be determined by

applying an anthropogenic counting concept called population census. A population census is a survey of an entire population conducted on a scientific basis after a specific period of time [4]. The population census can be applied to determine density in an ad hoc network as the presence of a number of nodes in an area can be exploited by the concept of population census to determine density.

The following subsections describe the design of a density determining algorithm to be used in CARP, and design is based on the census of ad hoc nodes.

A. Determining Density From A Node Census The objective of this algorithm is to determine the

density of an ad hoc network where the number of nodes in the network and the area of the network may be unknown. This algorithm conducts the census of location aware ad hoc nodes, and determines the lowest and the highest Cartesian addresses of the enumerated nodes. The census algorithm is explained in the following subsections.

a. Census Announcement By An

Enumerating Node The enumerating node announces a census by

sending a message (census announcement) under the controlled broadcast mechanism [5] to all other nodes asking for their respective Cartesian addresses. The controlled broadcast, in conjunction with a unique sequence number for each broadcast and the enumerating node’s identity, eliminates duplicate retransmission of the same message.

b. Acknowledgement From Other Nodes In The Network

This part of the algorithm describes the way acknowledgements to the census announcement are sent by enumerated nodes in the network. Every node that receives a census announcement sends its Cartesian address by unicasting an acknowledgement to the enumerating node. This acknowledgement is sent by using the Cartesian ad hoc routing protocol (CARP) [3], as now all the nodes know the enumerating node’s Cartesian address, from the census announcement.

c. Avoiding Counting An Enumerated Node More Than Once

It is important to ensure that each enumerated node’s Cartesian address is not counted more than once. An approach based on statistical sampling is proposed to handle duplicate count. The statistical sampling economizes power consumption, memory requirements, and CPU cycles. The enumerating node works in one of two states: sampling or counting. Sampling consists of collecting a sample of non-duplicate Cartesian addresses, and counting duplicate addresses detected during the collection of the sample. Thereafter, the regular counting begins and continues until the end of the census period (determined by enumerating node from a timeout), at this point the size of the population can be estimated. The regular counting counts every packet without consideration of the duplicates.

The choice of the sample size can reduce the probability of errors. There are few sample size guidelines in exploratory factor analysis (EFA) and principal components analysis (PCA). Some statisticians who tried to set a cut-off point of large sample size have adopted a sample of 30 as the cut-off [6]; the same sample size is used in the density determining algorithms.

As per algorithm for handling sampling and counting of enumerated nodes, the number of duplicate Cartesian addresses (dup count), determined during the initial sampling, is used to estimate the duplicate addresses in the node count during the counting stage. Estimated number of duplicate Cartesian addresses: (1) Estimated number of non duplicate addresses:

(2) The value of the sample size is also added to NNDA to get the total number of estimated non-duplicate addresses.

d. End Of A Node Census The census of ad hoc nodes, once started, needs a

mechanism to indicate that the census has ended. An adaptive approach based on a timeout is proposed to determine the end of acknowledgement to a census announcement. If the time to wait for the next packet exceeds the timeout, the enumerating node assumes that there are no more acknowledgements to receive.

The value of the timeout is derived from the mean time that is calculated by dividing the sum of the duplicate addresses (dup count) and the sample size, by the time taken in receiving them. The timeout is proposed to equal 3 × meantime, as this is considered to be a sufficient time for receiving a response from any of the enumerated nodes.

e. Calculation Of Density Value This segment of the algorithm determines density

from the number and addresses of the enumerated nodes.

The following abbreviations are used to describe the algorithm:

1) : is the Cartesian address of the enumerating node.

2) : is the Cartesian address of any enumerated node.

3) : is the lower Cartesian address of the enumerated addresses and is initialized to

4) : is the upper Cartesian address of the enumerated addresses and is initialized to

On receiving each acknowledgement, the enumerating node works as per the following algorithm to get the area of the ad hoc network. For lower and upper x:

For lower and upper y:

From and , area of the network is determined that is equal to the multiple of the two sides of Figure 1:

(3) The ratio of the total number of non-duplicate addresses (determined in Section 3.1.3) to the area, corresponds to the density of the ad hoc network.

f. Tracking Changes In The Values Of Density

Ad hoc networks are dynamic in nature, meaning

that the density determined at one instant may not be the same as another due to the potential of node mobility. This section describes an algorithm that reacts to these changes and takes corrective action by varying the frequency of the density calculation.

Figure 1. Calculation of area

The spread in density is monitored by using variance that is the most commonly used measure of the spread of a data. Variance (S2) is the average squared deviation of values from mean; for example, if the values of density are represented by , the variance is calculated as followings:

(4)

(5)

If the values of the density are observed to have wide spread, it requires a more frequent determination of density, thus needing a shorter time interval (time_ interval). The new value of the time_interval is determined by applying the following formula:

(6) If the time to determine density is represented by dentime, the upper threshold for the time_interval between two consecutive density calculations is equal to the three times of dentime, and the lower threshold for the time_interval equals dentime. If the value of time interval becomes 0, it is reset to the upper threshold.

IV. SIMULATION RESULTS The density determining algorithms are implemented in

OPNET Modeler 10.5. Different network scenarios are defined to imitate an ad hoc network such as a conference, and the transmission range of each node is 50 meters. A sample size of 30 is applied in all tests. The mobility model used in the network model is Random Waypoint.

A. Simulation Results For The Census Of Nodes The purpose of these simulations is to verify the node

population that is defined in a test scenario, and to determine the unknown area of the network in which these

nodes are present. In order to verify the performance of the census algorithm, three network scenarios of 90, 240, and 840 nodes are simulated. The nodes are aware of their respective geographical positions.

The test results are shown in Table 1. The first test has a node population of 90. At the end of acknowledgements, using the values of the sample, duplicates in sampling, and the number obtained during counting, the total number of non-duplicate addresses is calculated as 90 that verifies the node population of the test scenario. The area of the network is shown as 121, 00 , calculated from the overall lower bound (4,945, 3,695) and upper bound (5,055, 3,805). The value of density is 0.0074 nodes per that is determined from the area (12,100 ) and the number of non-duplicate nodes in this area.

The node population for the second and the third tests were 240, 840 respectively. The number of non-duplicate addresses that is 240 in the second test, determined as the result of census, verifies the corresponding node population. Similarly, the number of non-duplicate addresses for the third test is 840 that equals to the number of nodes in this test scenario.

Table 1. Results for the census of nodes

Test

Overall Area

Counting Dup in Sampling

Non-dup nodes

Density nodes/

1 12,100 78 9 90 0.0074 2 27,225 350 20 240 0.0880 3 81,000 1350 20 840 0.0103

B. Simulations For Tracking Changes In The Values Of Density

The density determined at one instant may not be the

same at another. The simulations in this section verify a segment of the algorithm that reacts to these changes in density. The test scenario consists of a network of ninety mobile nodes under Random Waypoint mobility model. The data in Table 2 explains the changes in time between two density calculations with respect to the variance. For each iteration in Table 2, the variance is determined and the next value of time interval is changed with respect to the value of the variance; for example, in the first iteration, the initial time interval was set to the upper threshold of time interval as 4.8 second, and with a variance 0.078, the new value of time interval between two densities becomes 4.425 seconds. In the following iterations, the value of the time interval changes with respect to the variance. The data in Table 2 is represented in the form of line graphs in Figure 2 to show the reaction of the density determining algorithm over the changes in the network environment. The changes in density measured as the variance in density values and the difference between the existing and new time intervals are shown on the vertical axis of the graph. It is obvious that

the variance in the density value triggers the next density calculation sooner or later.

Table 2. Tracking changes in density Index Initial

Time_inter (s)

Variance New time_inter (s)

Difference Time_inter (s)

1 4.8 0.078 4.425 0.375 2 4.425 0.073 4.102 0.323 3 4.102 0.065 3.857 0.245 4 3.857 0.074 3.335 0.522 The corresponding points that represent variance in density and the difference in time interval show that when variance decreases the time interval between two density calculations also decreases and vice versa.

Figure 2. Changes in time interval due to variance in density

The simulation results in this subsection have verified the ability of the density algorithms to track density, and if required, revise the time interval between two consecutive density calculations.

C. CONCLUSIONS

A novel density algorithm was described to work with CARP, and this algorithm was based on the census of nodes. The density determined by this algorithm can be used as a key parameter to define a logical transmission area under CARP. This algorithm also takes care of the changing values of density, and can dynamically change the time between two consecutive density calculations. In the future, a census of nodes in a three dimensional plain will be exploited to determine density for tuning CARP in a multistory corporate scenario.

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