The quality of the topology of wireless networks is assessed using various criteria. This requires previously making a proper choice of the assessment criteria and then selection the optimization algorithm. This paper presented a number of criteria for the assessment of wireless networks and discusses the results of comparative analysis optimal topologies for different criterion. It also discusses the brute force algorithm and its possible application for the design of the wireless networks topology and the computational complexity of this process. In order to apply the brute force algorithm the task of wireless network topology optimization is defined as discrete optimization task. It has been shown that the proposed approach is invariant respectively to the various criteria. The workstation with two Quad Core CPU Intel Xeon co-processors and 7120P Intel Xeon Phi co-processor with 60 cores has been used for computation experiments. Finally we showed the visual presentation for all decisions.
Electronic Commerce is supposed that there are some business transactions between actors, either as businessto-business, business-to-consumer, consumer-to-consumer or consumer-to-business. All this transactions are aimed to buying and selling of goods and services, or the transmitting of funds or data, over a network, primarily by the Internet. E-commerce is supported by some technologies such as mobile commerce, electronic funds transfer, supply chain management, Internet marketing,on-line transaction processing, electronic data interchange (EDI), inventory management systems, and automated data collection systems. Of course, modern electronic commerce widely uses the World Wide Web for at least one part of the transaction’s life cycle although it may also use other technologies such as e-mail (“E-commerce,” n.d.).
All kinds of electronic services are strongly influence on the level of society development and that must be used by young democracies. And all this advantages we can get if existence the infrastructure of wireless networks. 2
The population of Myanmar in 2016 is about 55 Millions, 65 percent is rural and 35 percent urban; most of the rural areas are actually agricultural villages(“Worldmeters,” n.d.).
In 2006 - 2010, Myanmar had established the first national ICT (information and communication technology) master plan to build telecommunications services for developing society. The works scopes were: ICT infrastructure, ICT industry, ICT HRD, E-government, E-education and Awareness, E-commerce. In 2016 the ICT development of Myanmar ranked 140 among 175 countries (“ICT Development Index 2016,” n.d.). ICT technologies can reduce the digital difference between the urban and rural areas of Myanmar and to get better communication of citizens. Developments in ICT are changing all aspects of societies. One of the most important ones is the e-Government services.
Myanmar citizens have a low level of Internet access due to lack of infrastructure. It is necessary to improve the speed, quality, coverage and reduce cost of Internet. Most of users go on-line via cell phones, which are comparatively more affordable. World Internet Statistics of June 2012 showed that Myanmar had over 534; 930 Internet users (1:0% of the population) with the vast majority of the users hailing from the two largest cities, Yangon and Mandalay(“Internet in Myanmar,” n.d.). Most of the country’s 40; 000 Internet connections were ADSL circuits, followed by dial-up, satellite terminal and WiMax. The Internet users significantly increased to 12:6% in 2015 with the introduction of faster mobile 3G Internet by transnational telecommunication companies - Telenor Myanmar (Norwegian group), Ooredoo Myanmar (Qatar-based) and later national Myanmar Post and Telecommunications (MPT). Nowadays Internet networks upgrades to 4G in the largest cities of Myanmar (“Internet World Stats,” 2016).
When compared to its regional neighbors, the need in the development of broadband Internet access in Myanmar becomes even clearer. One of the biggest challenges facing Myanmar concerns the roll-out of mobile infrastructure. Although as per current forecast, some 5; 800 towers will have been made operational in 2015, serving the 56:3 million people who live in Myanmar will require around 20; 000 towers to be built over the next few years. The mobile network population coverage is expected to grow from the current level of 12% to 70% by 2017; by 2020, 95% of people must be covered. Another objective is to increase the uptake of broadband Internet to at least 25% by 2018 and the number of base stations should grow to 17; 300 sites by 2017 (“Alliance for Affordable Internet,” 2015).
Installation of fixed lines has expanded mostly in major cities and highly populated areas, with high installation costs and geographical barriers in rural areas inhibiting installation and complicating maintenance of physical infrastructure such as cables [Kee-Yung Nam et al., 2015]. Wireless technology can cover a wide range of areas without using cables and its equipment is relatively easy to install. One of the possible decisions of this problem is using the WiMAX technologies.
The WiMAX is based on 802:16 standards. It serves as both a fixed and wireless access technology. Coverage of 50 km, that enough to provide connections in major cities and capacity of around 70 Mbit/s is a reality with this technology. But at higher speeds over greater distances and for a greater number of users and WiMAX as access technology is offered in distances of 5 to 10 km. WiMAX has the ability to provide service even in areas which are inaccessible for traditional wired infrastructure due to the ability to overcome the topological limitations. 4
Topological designing of wireless networks supposes the determining the position of all network elements. We can define this task as a discrete optimization problem and solving it by using the brute force algorithm.
In order to apply the brute force algorithm the task of wireless network topology optimization is defined as following:
1. Let define a final set of N network elements {A} and a set of K their possible positions {P}. In practice the number of positions K is much bigger than the number of elements N.
2. During the distribution of the elements {A} on to positions {P} it is necessary to provide an extremum of some functional F. In the result of optimization we define the solution of the problem as N -dimensional vector D [Aye Min Thike et al., 2016], which elements belong to {P}:
R ≤ Rmax
F (D) → max
This problem definition allows the brute force algorithm to be implemented also as a multi-threaded application [Posypkin & Sigal, 2006].
The quality of the wireless networks topology may be assessed using various criteria. If we need to optimize them simultaneously this task transforms to multi-criterial.
A choice of the criteria defines the decision. Below we present a number of criteria for the assessment of efficiency of wireless network topology and the results of comparative analysis the optimal topologies for them. It also discusses the brute force algorithm and its possible application for the design of the wireless networks topology and computational complexity of this process. Finally we present the visual presentation for all decisions.
For optimal spatial arrangement of antennas it is necessary to define the criteria using the following considerations: 1. Power of signal (S) receiving at a certain point R is inversely proportional to the square of the distance =∥ R − T ∥ between this point and the point where the transmission antenna is located (T); S0 is the transmitter output power:
S(T,R) = S0= (T,R)2 2. We assume that the reliable transmission the information between the network nodes is provided under the following condition: (1) (2) (3) (4) 3. The set {T} represents the particular coordinates ( x,y ) of L cities locations and a quantity of inhabitants in them (C):
Ti = (xi; yi; Ci)
In this paper we consider utilization one of the following equations as the main criterion of topology optimization.
1. Maximizing the number of residents having the access to network services, without consideration the signal power:
L ∑ V (Ti; D):Ci → max i=1 V (Ti; D) = { 1; if ∃Pj ∈ D : (Ti; Pj ) ≤ Rmjax
0; otherwise 2. Maximizing the number of residents which placed in zones with high power signal: Thus, in case of the presence of several antennas, the antenna having the maximum signal power is selected (3). 3. Maximizing the square of territory with high power propagated signal: for M -dimensional grid, each part of which is ∆ (∆i,j is the center point of this cell), its size is |∆| = Ω=M 2 , where Ω is the square of the land.
The city residents are not taken into account in this criterion.
4. Maximizing the number of residents having the access to network services with the consideration of the space distribution of cities’ residents (like F1):
F2(D) =
L ∑(max S (Ti; P ):Ci) → max i=1 P 2D F3(D) = ∆ · ∑M ∑M(max S(∆i,j; P )) → max
i=1 j=1 P 2D
M M F4(D) = ∑ ∑ (i; j)V (∆i,j; D) → max
The station of first type costs $100 (contingently) and can ensure reliable communication at the maximum distance 10 km, the station of the second type costs $200 and provides reliable communication at 20 km.
We provide experiments for different sets of antennas-common number always equal 3, but we combine it from different quantities of two types of stations.
Map on fig.1 shows the real fragment of Myanmar map (50*50 Km), which used for the computational exercises. There are 21 settlements on it.
We use the simple and compact tabulated description of map. The coordinates of the settlements and corresponding population are given in Table III. The required decision representing the set of network elements {A} may consist up to three antennas − N=3.
The set of positions {P} is defined by dividing the X and Y axes by MX and MY steps respectively. The antennas can be allocated only in the middle of such squared. In order to simplify the task consideration both numbers are equal: Mx = My = M. Thus the number of antenna positions is equal to K=M 2.
Thus, the topology of the wireless networks should be defined as the optimum distribution of antennas (Table II) between cities (Table III).
The serial application has been implemented using programming language C++. The computational complexity of the brute force algorithm depends on the number of the analyzed variants [Aye Min Thike et al., 2017]. In this example, the number of the topology variants is (M 2)N . For this large number of variants the parallel programming is being employed in the environment of Intel Parallel Studio 2017 and OpenMP library.
Technology OpenMP (Open Multi-Processing) is the most popular for the designing of multi-threaded programs [Evtushenko et al., 2009]. It allows creating the multi-threaded applications for multiprocessor or also for multi-core with shared memory.
If the program is realizing the brute force algorithm then all the calculations in threads are data independent. This is due to each thread estimates different variants of the topology. But there is only one common variable for all threads, it is current record. It means that if the value of criterion for a certain variant is less than the value in record, this value must be redefined. Of course, we can collect the local records after all threads finish their work and thus minimized the interaction between them.
The grid dimension equals M 2 = 302 = 900 in all cases. The number of analyzed positions is (M 2)N = 9003 = 7:29 ∗ 108. The computational time was varying from 2 seconds to one hour. The computational time depends not only from quantities of positions and antennas, but also from type of criterion. The solution using criteria F2 and F4 requires a little bit longer time than using the criterion F1 whereas calculation time for function F3 is much longer. Next pictures show the optimal topology for different criteria.
Figures 2-5 shows the results of optimization for the 3 antennas network segment. The optimum allocations of antennas are shown on the background of the Myanmar map fragment. Since two different types of antennas are used for the topology synthesis, they are also marked by different signs in the figures - the small triangles indicate the positions of the antennas A1 whereas the large triangles indicate the position of the antenna A2.
Graphic presentations the results show that the optimal topologies for the criteria F2 and F4 are quite similar. The solutions for criteria F1 and F3 are also quite similar, but are much different from previous pair. It is necessary to remark-visual presentations the signal distributions for optimal topologies give us the additional instrument for their design and comparison.
The results of the numerical comparison of the optimal topologies are shown in Table IV. For all the variants of decisions (columns topology) the values of another three criteria have been defined. It can be seen that the value of criterion is marked by color. It is interesting to note that solutions with a similar topology have fairly close values for all criteria.
Some words about the computational platform. We use the workstation having two Quad Core CPU Intel Xeon for all calculation, excepting the criterion F3, where 7120P Intel Xeon Phi co-processor with 60 cores has been used. All threads run simultaneously in the parallel application and each of them uses one core. Hyper threading regime has not been used for the calculation. The examples presented in this paper demonstrate that the brute force algorithm can be effectively implemented for the design of the optimum wireless networks topology. Moreover, it has been shown that the proposed approach is invariant respectively to the various criteria. The application does not require a serious modification if the optimization criteria are changed.
The further work will investigate the applicability of the proposed algorithm for analysis and design of the topology for the wireless network having the directional antennas. It is expected that the computational complexity of the algorithm will be significantly increased which will require implementation of Intel Xeon Phi co-processor.
Acknowledgements This work was supported by the Russian Foundation for Basic Research (RFBR) as part of the research project No 16 − 07 − 01055\165 “Adaptation of resource demanding algorithms to distributed computational environment”. [E-commerce. (n.d.).] E-commerce. Retrieved from https://en.wikipedia.org/wiki/E-commerce.
Retrieved from [ICT Development Index 2016.(n.d.)] ICT Development http://www.itu.int/net4/ITU-D/idi/2016.
from [Internet in Myanmar. (n.d.).] Internet in Myanmar. Retrieved from https://en.wikipedia.org/wiki/Internet in
Myanmar.
Population Statistics). Retrieved from