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Using Derived Mobility Model Metrics to Evaluate the Impact of Transmission Range in Vehicular Networks.


Mobile communication is the bedrock of the 21st century technological innovations. It has deployed several services and applications making mobile devices to have greater influence in many lives that multitudinous people cannot do without them. The most popular among mobile devices is the mobile phone, which is mainly for communicating around the globe. MANET is a highly dynamic wireless communication technology deployed among the most recent advancement in mobile communications [2].

MANETs and VANETS, have the characterized features of all mobile and wireless networks. MANET is an infrastructure- less network with the ability to self-configure networks [2]. This means that there is no need for an Access Point (AP) or router to deliver message to the next MN, rather the MNs have freedom of movement in the environment and obtain assistance from other intermediate nodes. With the prospects in mobile communications, there are tremendous growth and extensive research interest in VANETS, which is a special application of MANETs [1, 3]. The research on MANETS has been popular since late 1990s [4], since then, mobile communications have experienced a progression trend of about 26.5percent with about 33 Million subscribers of mobile phones in Japan since September, 1997 [5].

Mobility has great influence in the behavior of MNs, which may be exhibited negatively or positively. It predicts the pattern to be produced by the MNs, since different mobility schemes influence the pattern obtained by the MNs. As MNs change location to exchange information through communicating, they tend to deviate from the Road Side Unit (RSU), and base station or AP depending on the network settings. Mobility is an inherited trait in vehicles, because in the real world, vehicles cannot permanently remain static, hence must exhibit mobility at some point in time. In this paper, derived mobility metrics is used to implement the impact of mobility in mobile networks with an Adapted Context-Aware Rate Selection (ACARS) mobility model. ACARS is one of the RAs used in this simulation to implement mobility model [6].

Derived mobility metrics is a mathematical technique applied for modeling mobility model. In this paper, the metric is modeled and used for simulation in MATLAB. Details of the mathematical models are discussed in later sections.

The rest of the paper is organized as follows: Section II reviews on several mobility metrics, while Section III deals with network connectivity and the factors that influence signal reception. Mathematical model and analysis is considered in Section IV, while Section V analyze the results obtained from simulation and the paper is concluded in Section VI.


A. Background

The aim of Mobility model in mobile communication is to analyse the movement of nodes, which have substantial impact on the performance of the network [7]. Several mathematical models and simulations have been proposed in literatures on improved methods to apropos mobility in mobile wireless networks [8-17].

MNs have the freedom to move from one direction to the other while communicating with each other. These movements depend on the randomness and pattern exhibited my MNs during communicating [18-22]. However, mobility models can be classified into three categories based on their degree of randomness [23]. They are the traced-based with built on traces, the constrained topology-based, which is based on only partial randomness, and static-based, which is based on total randomness. To analyze the behavior of MNs, mobility metrics play a major role to determine the ideal mobility model to adopt in mobile communication networks. Direct and derived are the two known types of mobility metrics. They are explained in the next section.

B. Mobility Metrics

One of the major factors that affect the performance of ad hoc wireless networks is node mobility [24, 25]. This is not strange because of the natural traits of MNs, since they are meant to be mobile and not to remain static like an office type network, which communicates without moving, but there is random movement in wireless mobile networks whose performance grossly rely on the type of mobility model in place.

This section considers mobility metrics developed to model the performance of vehicular networks so as to analysis the impact of communication range on connectivity of MNs.

i. Direct Mobility Model

In direct mobility model, the MNs move in such a way to minimum or maximum speed in which speed is directly measured. Measurement of other parameters such as relative speed can be made. The Random Waypoint mobility model is a good example of a mobility model that exhibit direct mobility metrics. The goal of this model is to measure different mobility models. Nevertheless, it is not all the models that possess the capacity to capture different characteristics of the models [26]. This type of model also perform same task as that of the trace type mobility model since trace mobility also does direct measurement of parameters. In essence, it is likened to traces in mobility models.

ii. Derived Mobility Model

This type of mobility metric is established primarily by using mathematical models to establish generic network performance. Derive mobility metrics are also derived from graphs and other probabilistic models [26]. The major difference between this model and the former is that the parameter measured in this metric model is derived from mathematical models, while the former is a direct measurement of these parameters. In both metrics, parameters such as speed and velocity that has impact on MNs can be measured by implementing any of these metrics. Derived mobility metrics also perform similar role as that of the synthetic mobility model, because it involves mathematical models, which is the preferred type of mobility model [26].

This paper implements a derived mobility metric with RA to validate the impact of communication range on network connectivity.


Single-hop Cellular Networks

The basis of all wireless communication networks is the single-hop cellular networks. In this network model, all communicating MNs depend absolutely on the wired backbone and fixed base stations as shown in Fig.1, which is in contrast to that of MANETs that does not involve any of the above-mentioned characteristics. There is unpredictable network change due to the dynamic nature of mobile environments with infrastructure [4, 25, 27, 41]. In mobile networks, connectivity is a factor that depends on communication range and the number of MNs sharing the network resources. This means that it depends on the number of nodes per unit and their radio transmission range [29].


MANET is a spontaneous network that is self-configured, self-organized, and self-maintaining with limited services such as processing power, on-board memory, and battery [30, 31]. The role of MANET is to establish an efficient routing protocol to enhance the performance of the network [30, 32]. This type of network is useful when dealing with wireless devices in which some of the devices are part of the network ONLY for duration of a communication session as shown in Fig.2 [31].

Some of the challenges in MANETS at the Network Layer, Physical Layer (PHY), and Transport Layer are:

* Efficient routing

* Power control

* Quality of Service (QoS)

Despite some of these challenges susceptible to MANETs, one of the important advantages is that it grants MNs access to information and services.

MANETs offer numerous applications in mobile and wireless communications. It has much usefulness in safety and better network delivery. Some of the applications of MANETs are:

* disaster-rescue operations

* emergency search

* Classrooms

* military activities

* time-critical applications

* tactical communication

* Rescue operation

* QoS (good reception for mobile phone communication)

* Reliable safety messaging in vehicular networks etc. [4, 33-36].


VANETs are a sub-class of MANETs with great promising trend for future Intelligent Transport System (ITS). In an ad-hoc network, wireless MNs interact to form a temporary network independent of any control device such as router or AP [37-40]. There is no fixed infrastructure in this type of network, rather MNs communicate with each other directly and rely on each other for network functionality as shown in Fig.3. One of the peculiar characteristics of VANETs is the mobility pattern exhibited by MNs due to the mobility model. These characteristics are quite different from that of the MANETs. The mobility patterns generated in VANETs actually have greater influence on the participating MNs, which predicts the performance measure of the MNs on the network [41]. Due to the performance criteria expected in VANETS, it has some applications such as mobile application, routing information, safety messaging, and traffic control [42]. VANET is a new approach in wireless communications with some of these advantages over the traditional single-hop cellular networks: lower latency due to direct communication, and broader network coverage.

The aim of extending data networks is to handle mobility to provide continuous network connectivity [43]. This makes routing protocol an important aspect of mobile communications to be considered. Due to the frequent mobility act prone to MNs, they change location constantly resulting to problem of connectivity. Various factors are responsible for creating difficulty in connectivity. These include node moving away from the base station, propagation effect, and out of transmission zone etc.


This section expatiates on the mathematical model used in implementing the mobility metric for the simulation. Mobility in wireless networks determines the signal strength as nodes move randomly from one location to the other. As they communicate with each other on the network, the Received Signal Strength (RSS) varies depending on the mobility model, which is peculiar to all MNs [11].

A. Distance and position of MNs

We developed an algorithm with mathematical model using (1-11). These equations are to generate node positions; get the speed of the nodes, and communication range of MNs. Fig.4 shows how MNs change position generating angular inclination.

B. Constant Speed (ConstSpeed) Mobility Model

In the ConstSpeed mobility model, MNs can move along a lane with constant speed to a randomly chosen target, and when the target is reached, it will randomly select a new one. With this model, MNs select their speeds uniformly over this range as shown in (1-6). Initial positions of MNs are generated randomly.

C. Transmission and Communication Range Algorithm

Mathematical analysis in (12-16) is use to determine MNs that are in communication range and those out of range in the simulation. The communication range is the limit set for MNs to determine their access to the AP during communication. The simulation setup drops MNs that are out of range. This means that as the MNs change position, some of them move out of the range and are not consider to per take in the network resources.

D. Log-normal Shadowing

Communication channel is a time varying power gain, which consists of path loss, log-normal shadowing, and multipath fading. The receiver experiences a desired signal gain with respect to the transmit power [P.sub.t] used by the transmitter. Algorithm 1 shows the RSS, while Table I shows the shadowing deviation used in the simulation. In addition, Fig.5. and (20) are used to determine RSS in Algorithm 1.
Algorithm 1: Received Signal Strength Algorithm

1: Take transmitted signal strength Pt
2: Calculate the distance between sender and receiver d}
3: Calculate the cross distance [d.sub.c]
4: IF d>[d.sub.c] then
5: Calculate Friis path loss l
7: Calculate received signal strength [P.sub.r]= [P.sub.t]-l
Definition I (movement of the Mobile Nodes (MNs))
[mathematical expression not reproducible] (1)
Where d is distance in meters, x and y are node positions
in the x and y coordinates, t is tinre and [theta] is angle.
[mathematical expression not reproducible] (2)
Where 13 is last speed, [??] is the direction, and v is
[mathematical expression not reproducible] (3)
Where [??] is elapsed time, [??] is simulation time, and [??] is
last update.
[mathematical expression not reproducible] (4)
Where [??] is last position, [??] is the last speed, and [??] is the
elapsed time.

Definition II (Speed of MN)

Assuming a set of nodes n = {[u.sub.1],..., [u.sub.n]} is moving along a road model with length, i.e., R = [0, 1]. Considering N MNs moving on [0, 1). At some random times 0 < [t.sub.1] < [t.sub.2] <... a new speed and a new direction (also called orientation) are selected. The selection of the speed and direction at time [t.sub.k] (k [greater than or equal to] 1) initializes the jth movement of the mobile. Let [tau]j = [t.sub.k]+1 -[t.sub.k], j [greater than or equal to] 0, During the interval [[t.sub.j], [t.sub.j+1]] the MNs travels at constant speed sj [member of] S, where S is any topological subset of (0,[varies]). Typically, S = ([sigma]1, [sigma]2) with 0 < [sigma]1 < [sigma]2 or S = {[sigma]1,...,[sigma]k} with [sigma]i > 0 for i = 1,..., j Let [[theta].sub.k] [member of] {-1, +1} be the new direction selected at time [t.sub.j], j > [greater than or equal to] 1, with [[theta].sub.k] = +1 (resp. [theta]j = -1). Let [[theta].sub.0] be the orientation of the MNs at time t = 0., and [theta](t) is the direction of the MNs at time t [greater than or equal to] 0. We assume that [theta](t) is right-continuous, so that [theta]([t.sub.j]) = [theta]j for j [greater than or equal to] 0. The selection of the new direction at time [t.sub.k], k> [greater than or equal to] 1, is done as follows. Let [gamma]1, [gamma]2,... be {-1, +1}. Each MN is assigned to a determined mean speed, [??], and mean direction [??] of its movement. For each determined time period, a MN calculates the speed and direction of its movement by referring on speed and direction during the previous time period, throughout with a certain degree of randomness joined in the calculation. Then MN is moved with assumed calculated speed and assumed calculated direction during the time period. For a specified time period t, the speed and direction of a node is calculated as follows [4] :

[mathematical expression not reproducible] (5)

[mathematical expression not reproducible] (6)


[[nu].sub.n] and [d.sub.n] are the new speed and direction of MN at time interval n;

[alpha], where 0 [less than or equal to] [alpha] [less than or equal to] 1, is the tuning parameter used to vary the index of randomness;

[alpha] = 1: mobile nodes move linearly;

[nu] and d are constants, represent mean value of speed and direction at n;

[[nu].sub.xn-1] and [d.sub.xn-1] are random variables from a Gaussian distribution.

To determine the degree of randomness, which is a combination of speed and direction that predicts the direction of movement for a certain period; we define the parameter [alpha] (0 [less than or equal to] [alpha] [less than or equal to] 1). The value of [alpha] is increased from 0 to 1, the degree of randomness decreases. And when it is close to 0, the degree of randomness becomes high that may result in consistent sharper turns. On the other hand, when [alpha] is nearest to 1, speed and direction of the previous periods are temporally dependent, which means that MN move in close to what it previously had [4].

Definition III (transmission range)

Let [Z.sub.r] be the route or flow of traffic in the network. There are several nodes in the network to form the sequence. And let R be a set of possible routes and r be the set of nodes.

Z = ([.sub.Zr],r[member of]R) (7)

[Pos.sub.old] = [] + [nu]Xt (8)

Where [Pos.sub.old] is Old position, [] is new position, v is velocity and t is time

[P.sub.n] = mod([P.sub.n], [x.sub.max]) (9)

Where [x.sub.max] is maximum range, mod = modulus function implemented in the MATLAB program, and [P.sub.n] = is the result positions of the nodes.

This ensures that nodes are in Communication range

d = abs([] - [Pos.sub.AP]) (10)

Where d is the distance, abs is absolute value, [Pos.sub.AP] is position of the AP

This gives the distance between the new position and AP.

d = |[] - [Pos.sub.Ap]... + [] - [Pos.sub.n-AP]| (11)

[Node.sub.inrange] = d < [t.sub.r] (12)

Where [Node.sub.inrange] is node in communication range, [t.sub.r] is communication range

This ensures that determines nodes in range and out of range.

[mathematical expression not reproducible] (13)

[mathematical expression not reproducible] (14)


[mathematical expression not reproducible] (15)

If C is a class of MNs in communication range, then from Eq.14 that [v.sub.1]... [v.sub.n] will be elements of C. i.e ([v.sub.1],[v.sub.2], ... [v.sub.n]) [member of]C. Equations(13-15) are used as counter to determine the MNs in communication range and those outside the communication range.

[mathematical expression not reproducible] (16)

Where [t.sub.r] is communication range, [rho] the node density, p is probability, n is the number of node. Equation (16) is used to determine MNs in communication range. The node density depends on the number of nodes and the area of coverage. This also results to the probability level of determining if node is in range or out of range, and when node density is neglected, (14) and (15) is to determine MNs in communication range and those out of range.

Definition IV (Free Space Path Loss)

Free space path loss model is a power off that relates to distance. Due to high mobility of nodes as speed changes, the distance between the transmitter and receiver changes. This makes empirical free space path loss necessary in order to model the effect of distance on packet delivery probability. This space loss accounts for the loss due to spreading of Radio Frequency (RF) energy as transmission of signals propagates through free space. From the equation of path loss, it is observed that the power density reduces by 1/[R.sub.2] as distance is increased.

[mathematical expression not reproducible] (17)

Where [P.sub.tx]/4[pi][R.sup.2] is the power density in free space, the power of electromagnetic radiation varies inversely with the square of the distance, making distance an ideal indicator of signal level, as well as loss rate. Due to imperfect propagation environment, in practice it is not exactly the inverse square. Distance between sender and receiver gives a high correlation between signal level and error rate as this affects the number of transmitted packets to be received [44].

One of the important parameters to evaluate propagation effect in the simulation is RSS. In order to analysis it, we first need the power gain, and transmit power. It can be derived from (15) and (16), and Fig.5.

g(t) = [g.sub.p(t)] + [g.sub.s(t)]+[g.sub.m(t)] (18)

[P.sub.rx] = [P.sub.tx] - [g.sub.t] (19)

RSS = [P.sub.rx] - [P.sub.noise] (20)

Where [g.sub.(t)] is power gain, [g.sub.p(t)] is path loss, [g.sub.s(t)] + [g.sub.m(t)] is shadowing and [g.sub.m(t)] is multipath fading and RSS is the received signal strength.


A. Discussion of Results

The simulation was implemented with three important parameters that are crucial to connectivity of signal in mobile and wireless environments shown in (17-20). Also, speed, distance, and the number of nodes on the network are also key variables that impact signal reception. The simulation was implemented with 100 MNs on the network to test the impact of congestion on the above-mentioned parameters. Simulation parameters are shown in Table I.

A. Evaluation of Results

From network theory, it is evident that congestion mitigates the performance of the network. Throughput is one of the basic metric of system measurement to test for QoS. From Fig.6, it is observed that AARF is not capable to withstand network congestion, especially sharing network resources with other RAs. It is observed from the graph that from the minimum to the maximum number of MNs utilizing network resources, AARF did not perform well under this propagation condition. The throughput achieved by ACARS and ModifiedCARS with 100 nodes is greater than that of AARF even at the least number of nodes. Although SampleRate and ONOE performed well under less congestion, but they are greatly affected as the number of MNs increases as they share in network resources.

The trend of the graph obeys the theory of network performance as the throughput decreases proportionately with the increase in the number of nodes agitating for network resources. It is true in the fact that when the number of MNs increase on the network, many tends to access the network at same time leading to collision of packets and many of them are dropped, thereby reducing the number of successfully received packets at the destination. This means that, out of the 1000 packets that were sent per simulation, when the MNs increase, predominately sent packets will not arrive at the receiver because of collision encountered by participating nodes.

The speed of the vehicles was modeled using (2-6) to constrain the vehicles within the speed limit. From the graph obtained in Fig.7, result shows that the vehicles clustered within the speed limit for the simulation. Within this limit, ACARS performed better than the other algorithms, while AARF has poor performance because of the network conditions that is not favorable to this RA caused by the propagation conditions. There is just negligible difference between ModifiedCARS, SampleRate, and ONOE in performance measure as they all clustered almost at same level.

From Fig. 8, result shows that ACARS is a robust algorithm that is able to sustain connectively more than the others even as the vehicles move further from the base station. It can be observed that the throughput obtained by ACARS at 300m is even more than what AARF obtained within less than 10m from the base station. This shows that, AARF would not be a good RA at this point for connectivity because the MNs will easily loose communication at earlier movement. It also implies that mobility is concern to this algorithm especially with this propagation condition implemented in this simulation.

On the other hand, AARF may work better than others in other propagation condition with different configurations. The simulation was carried out with path loss exponent of 2.56, which correspond to the value of free space. Moreover, the shadowing deviation was 8.0, which is an outdoor. SampleRate also performs as good as ACARS as seen from the graph, and would also be a better recommendation for network connectivity for this environmental conditions.

From the results obtained as shown in Fig.6-8, it can be analyzed that these results validate the goal of network connectivity in mobile communications. From the results, network signal degrade as the MNs move further from the base station. It also deteriorates when congestion increases on the network as seen in (1-16) showing distance relationships. Any of the MNs depending on feedback from the base station would degrade in signal reception because of congestion, and this occurs as earlier seen when the number of nodes increases.


A Conclusion

The simulation results demonstrate the correlation between mathematical model and simulations. It is a combination of mathematical modeling, RA, and simulation. From the results obtained, different RAs have their peculiar characteristics and the environmental conditions that enhance their performances. The results from different RAs show that AARF cannot in any of the simulations perform as good as the others because of environmental factors. This means that in order to boost signal strength and sustain communication among vehicles, it is expedient to have the appropriate RA to be used. Safety is one of the core issues in vehicular communication; hence, if they lose communication, it could lead to accident and miss-direction with communicating vehicles.

The results will also help to estimate the minimum communication range needed to maintain signal strengths in mobile networks. The trade-off will be how to increase communication range and still maintain strong signal strength for QoS, and for application in rescue operation. Since mobility is a default characteristic of all MNs, the mobility model implemented here shows that not all RAs can combat with mobile environments as in this scenario.

B. Limitation and Future work

A typical infrastructure network was deployed in this article in which the vehicles communicate with each other via an AP. This network configuration results to delay in receiving messages because it will be faster to receive messages if they communicate directly with each other without an AP. In the future, the ad hoc network configuration will be considered, and will be nice to simulate for more vehicles to observe the trend of a densely populated network, say about 200 vehicles on the network.

Discrete Event Simulators (DES) such as Network Simulator (NS), OMNET++ will be an alternative choice to implement similar network configurations, as they are mainly designed for network purposes especially for mobile and wireless networks. Future work will also consider increasing the communication range between MNs and the base station, and on the other hand, implementing an ad hoc network (VANET) where MNs could communicate with each other without an intermediary node to deliver messages.


Our appreciation goes to Ken Saro-Wiwa Polytechnic for given us the opportunity for us to network from different departments to publish this article.


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Kenneth S. Nwizege (1), Godson I. Ikhazuangbe (1), Friday O. Philip-Kpae (1), Stephen N. Agbeb (1), Bright G. Akoba (1), Hilary Frank (2) and Lelesi F. Nziidee (3)

(1) Electrical/Electronic Engineering,Ken Saro-Wiwa Polytechnic, Bori, Nigeria

(2) Computer Science, Ken Saro-Wiwa Polytechnic, Bori, Nigeria

(3) Mechanical Engineering,Ken Saro-Wiwa Polytechnic, Bori, Nigeria

Received 3 Dec. 2017, Revised 13 Feb. 2018, Accepted 9 Mar. 2018, Published 1 May 2018,,,,,,

Kenneth Sorle Nwizege graduated from Federal University of Technology, Yola in 2004 with a BEng degree in Electrical/Electronic Engineering, and obtained an MSC degree in Mobile and Satellite Communications in 2007 from University of South Wales, UK. He also obtained an MPhil degree from University of Swansea UK, in 2009, and a PhD in Advanced Telecommunications Engineering with University of Swansea UK in 2014. His area of nterest include: rate algorithms in vehicular networks, Performance evaluation of wireless mobile systems, safety in Vehicular communication, wireless networks and optimization, power control in wireless mobile communications. He is a member of both IET and IEEE and reviewer for many conference and journal papers. Has reviewed over 4,000 papers up till date. He is a senior lecturer with the Ken Saro-Wiwa Polytechnic, Bori, Rivers State, Nigeria.

Godson Ivbuobe Ikhazuangbe obtained a BEng degree in Electrical/Electronic Engineering in 1999 from Ambrose Alli University, Ekpoma, Nigeria and in 2007 he obtained an MTech degree in Electrical/Electronic Engineering (Electrical Power transmission) from Rivers State University of Science and Technology, Port Harcourt, Nigeria. He is presently a Ph.D. student at the University of Nottingham. He is a lecturer with Kenule Saro-Wiwa Polytechnic Bori, Rivers State, Nigeria. Research interest is in Renewable Energy, Electrical power and machines, Wind turbine lightning protection. He is a resource person to National Board for Technical Education (NBTE) and member of NSE, COREN and IEEE.

Friday O. Philip -Kpae holds a BEng in Electrical/Electronic Engineering from University of Port Harcourt and currently concluding his MEng in Electronic and Telecommunication Engineering with the same institution. He is a Member of National Association of Technologist in Nigeria (NATE), Nigeria Society of Engineers (NSE), Institute of Electrical and Electronic Engineering (IEEE), and Nigerian Institution of Electrical and Electronic Engineers (NIEEE). He is a registered Engineer in Nigeria. His research interest is in Communication Engineering with special interest is wireless communication. He is a lecturer with Kenule Saro-Wiwa Polytechnic Bori, Rivers State, Nigeria

Hilary Frank received his BSc. (Hons) degree in Computer Science / Mathematics from the University of Port Harcourt, Nigeria in 1998 and MSc. in Mobile & High Speed Telecommunication Networks from Oxford Brookes University, Oxford, England in 2014. His research interest is in Next Generation Mobile Networks. Hilary is due to join the University of Bristol, England for a PhD degree in Electrical and Electronic Engineering in 2018 and would research on the topic Massive MIMO Antenna Design Techniques for Interference Mitigation in Next Generation Wireless Networks. Over the recent years, he has attended and presented papers and received awards at academic conferences held in Asia, Europe and Africa. Hilary had been a member of the Institute of Electrical and Electronics Engineers and presently a member of the International Association of Engineers and the Nigeria Computer Society. He currently lectures in the Department of Computer Science Ken Saro-Wiwa Polytechnic, Bori, Nigeria.

Parameters (Units  Values
Maximum Retransmission                   4
Data rate (Mbps)                         3, 4.5, 6,9,12,24,27
Log Normal deviation (dB)                8
cwMinData  31
Carrier frequency (GHz)                  2.4
Simulation time (s)                      172,800
Mobility model  ConstantSpeed
[gamma] (Path Loss exponent, Urban area  2.56
cellular radio)


Parameters (Units  Values
Maximum Retransmission         4
Data rate (Mbps)               3, 4.5, 6,9,12,24,27
Log Normal deviation (dB)      8
cwMinData                      31
Carrier frequency (GHz)        2.4
Simulation time (s)            172,800
Mobility model  ConstantSpeed
Y (Path Loss exponent, Urban   2.56
area cellular radio)
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Author:Nwizege, Kenneth S.; Ikhazuangbe, Godson I.; Philip-Kpae, Friday O.; Agbeb, Stephen N.; Akoba, Brigh
Publication:International Journal of Computing and Digital Systems
Article Type:Report
Date:May 1, 2018
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