Application of Grey Relational Analysis to Network Selection: A Case Study

Transcription

1 Inter national Journal of Pure and Applied Mathematics Volume 113 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Application of Grey Relational Analysis to Network Selection: A Case Study KSS Anupama 1, S Sri Gowri 2 and B Prabakara Rao 3 1 Department of E&I, VRSEC, AP, INDIA cssanupama@gmail.com 2 Department of E&C, SRKIT, AP, INDIA sajjasrigowri@yahoo.com 3 Department of E&C, JNTU Kakinada, AP, INDIA vcjntuk.drbpr@gmail.com February 7, 2017 Abstract Multiple wireless network availability has become a norm rather than an exception for the mobile users due to the advent of wireless technologies. In this context, user faces uncertainty in two situations, one in selecting the best network and another is maintaining connectivity while roaming through the heterogeneous networking environment. Network selection depends on multiple decisive factors like cost, bandwidth, delay, jitter, network utilization and packet loss etc., making selection process an uncertain and complicated task. To resolve such uncertainty, an efficient mathematical model Grey Relational Analysis (GRA) is applied to the problem of network selection. The selection process involves three stages normalizing the multi-parameterized attributes, formulating weights to each attribute based on the user priorities and ranking the networks based on Grey Relational Coefficient(GRC). The results drawn through GRA model is compared with a conventional outranking method. AMS Subject Classification: 90B30, 90B50, 90C29, 91B06 Key Words and Phrases: Call continuity, Grey Relational Analysis, Handoff, MADM, Network selection, PROMETHEE ijpam.eu

2 1 Introduction The explosive growth in the field of wireless and telecommunication technology lead to the rapid deployment of multiple diversified networks in a given geographical area. The mobile users now have access to more than one network at a single point of time and most often these networks fall under varied wireless accessing technologies such as UMTS, HSPA, WIFI, LTE, EDGE and WIMAX. Though the recent wireless technologies have advanced features like rich bandwidth and new network paradigms, reasons like expensive billing, power consumption, low quality connection and security etc., are making the user decisive in switching among network technologies. This results in the problem of selecting the best network from available heterogeneous networks by the user. The success of network mainly depends on providing ubiquitous coverage and seamless handoff to the user. Handoff refers to the process of maintaining the mobile users voice/data sessions active by associating the user equipment(ue) to the network that provides the required level of Quality of Service (QoS)[1]. Associating the UE to a network using same technology is called horizontal handoff and different technology is called vertical handoff. In heterogeneous network environment, a UE, most often undergoes vertical handoff. Multiple attributes like Cost (CB), Allowed Bandwidth (AB), Packet Delay (D), Packet Jitter (J), Network Utilization (U) and Packet Loss (L) has been identified as effective parameters for testing the QoS provided by each network. Since multiple attributes are involved network selection becomes a multi attribute decision making(madm)[2] problem. 1.1 Background In general, a multi attribute decision making involves m alternatives A i such that i = 1, 2,...m, each having criteria C j where j = 1, 2...n. As per users requirement, weights W = [w j ] can be introduced to prioritize each criteria C j. While assigning the weights, two basic constraints need to be followed. First, the total of all the weights must be summed up to 1. Secondly, the weights must obey the relative ranking given by the pairwise comparison. Criteria is classified as Benefit Criteria where the higher value of a ij gives the better value for the decision making and Cost Criteria where the lower value of a ij gives the better value to the decision. These criteria are reflected in the decision matrix shown in Table 1. ijpam.eu

3 Table 1: Decision criterion values Alternatives Criteria C 1... C j... C n W 1... W j... W n A 1 a a 1j... a 1n A i a i1... a ij.. ain A m a m1... a mj... a mn Once the basic elements needed to formulate decision making are collected, an effective MADM method must be applied to the inputs. A number of MADM techniques viz SAW [3], VIKOR [4], PROMETHEE [5], ELEC- TRE, TOPSIS, GRA [6] etc. can be found in the literature. In the next section, we will discuss Grey Relational Analysis(GRA). 2 Grey Relational Analysis In 1982, Julong Deng [6] explained the inter disciplinary theory of Grey systems. In Information systems terminology, Black represents the known information, White represents the unknown information and Grey represents the partially known and partially unknown information. The objects of Grey system theory consist of small samples of partially known and poor information. The information system is said to be partially known or incomplete when it satisfies any of the following four conditions: Let A be a factor set of grey relation, a 11 A the referential sequence and a ij A the comparative sequence with a 11 (p) and a ij (p)representing numerals at a fuzzy point p. If Grey Relational Coefficient GRC(a 11 (p), a ij (p)) and Grey Relation GR(a 11, a ij ) be real numbers that satisfy the below four axioms, then they confirmed their identity. The axioms are: 1. Norm interval: 0 < GR(a 11, a ij ) 1, p where GR(a 11, a ij ) = 1 iff a 11 = a ij ; GR(a 11, a ij ) = 0 iff a 11, a ij φ; where φ is an empty set. 2. Duality symmetric: a, b A; GR(a 11, a ij ) = GR(a ji, a 11 ) iff A = {a, b}. ijpam.eu

4 3. Wholeness: GR(a 11, a ij ) often GR(a ji, a 11 ) iffa = {a ij i = 1, 2,...m and j = 1, 2...n}, n > Approachability: GRC(a 11 (p), a ij (p))decreases along with increasing (a 11 (p), a ij (p)). Once the four axioms get satisfied, we can implement Grey Relation Analysis (GRA) model comparing the preference attributes towards outcomes or the weight comparison among the criteria. The evaluation procedure of GRA for the decision making to our heterogeneous wireless network context is discussed in the next section. 3 Evaluation Models 3.1 GRA Model Consider heterogeneous wireless environment of m networks each having n attributes of selection criteria. Let D =[d ij ] mxn be the Decision Matrix and W j where i=1,2,...n be weights attained according to user preference using Analytical Hierarchical Process (AHP). Then Grey Relational Analysis Model follows the steps listed below: 1. Normalize the values of the d ij keeping benefit and cost criteria discussed in previously in mind. Normalization is needed as the units of attributes are different and may range different scales. So, by preprocessing using normalization we bring each of the attribute to a single common scale of fractions. The matrix obtained is a reciprocal matrix R{r ij 0 < r ij 1} with values: For Cost attribute, r ij = For Benefit attribute, r ij = max i m d ij d ij max i m d ij min i m d ij where max i m d ij min i m d ij (1) d ij min i m d ij max i m d ij min i m d ij where max i m d ij min i m d ij (2) ijpam.eu

5 2. Construct the weighted normalized matrix V with values generated by multiplying each column of the matrix R to its respective weight. v ij = w j r ij where N w j = 1 (3) j=1 3. Calculate the ideal solution, a based on the user requirement. For benefit attributes: For cost attributes a = [a 1,..., a n] (4) a j = max{v ij, j = 1,...m} (5) a j = min{v ij, j = 1,...m} (6) 4. Calculate Grey Relational Coefficient (GRC i ) for each of the network using the formula GRC i = 1 n n min i m ( x j v ij ) + max i m ( x j v ij ) x j v ij + max i m ( x j v ij ) j=1 (7) The network having lowest GRC value is the best available wireless network for a mobile device. 3.2 PROMETHEE Model Preference Ranking Organization Method for Enrichment Evaluations [5] (PROMETHEE) is a outranking method quite simple in conception and application compared to other MADM methods for multi criteria analysis. The central principle of PROMETHEE is based on a pair-wise comparison of alternatives along each recognized criterion. For a set of n alternatives described by a set of q decision criteria, the stepwise procedure of PROMETHEE algorithm is as follows: D = (d 1, d 2,, d q ) be a set of q decision criteria. 1. Determine deviations based on pair-wise comparisons d k (a i, a j ) = d k (a i ) d k (a j ) (8) ijpam.eu

6 2. Apply preference function 3. Calculate global preference index P k (a i, a j ) = F [d k (a i ) d k (a j )] (9) π(a i, a j ) = q Where w k is the weight associated with criterion k. 4. Calculate positive and negative outranking flows φ + (a i ) = 1 n 1 φ (a i ) = 1 n 1 5. Compute net outranking flow k=1 P k(a i, a j ) (10) π(a i, a j ) (11) a j ɛa π(a j, a i ) (12) a j A φ(a i ) = φ + (a i ) φ (a i ) (13) Rank the networks in descending order based on the net outranking flows. The network with highest outranking flow is identified as the best network for handoff. 4 Simulation and Result Analysis The simulation environment is a one kilometer area under HSPA coverage. Within this area, 1 LTE and 2 WiFi hotspots are deployed. The UE s are located randomly through the coverage area. Each UE is equipped with three radio interfaces: HSPA, LTE and WiFi. So, at any instant the UE can choose and access anyone of the three available access networks: UMTS, WiFi and LTE. GRA and PROMETHEE models are evaluated for on line gaming and streaming traffic applications. Table 2 shows the QoS parameters of the available networks at the time of decision making. ijpam.eu

7 Table 2: Decision criterion values C Rs/Mbps B Mbps L ms J ms NU % P L/ 10 6 WiFi WiFi LTE UMTS/HSPA The user preference is for quality of service and is not cost conscious. Accordingly, the weights computed by AHP methodology for each criterion is listed in Table 3. User Preference Table 3: Assignment of weights Traffic C B L J Rs/ mbps ms ms Mpbs NU % PL (per 10 6 ) QoS Gaming Streaming Table 4 illustrates the best network selected in each handoff scenario for online gaming and streaming traffic classes. For Grey Relational Analysis model, the GRC value is calculated with high cost attributes as cost, delay, jitter, network utilization and packet loss. Allowed Bandwidth is the benefit attribute. The ranking orders generated by GRA and PROMETHEE algorithms are different but they converge at LTE, as the best network. As LTE is a high-speed data network, selection of LTE as best network for online gaming and streaming applications by GRA and PROMETHEE algorithm is rightly justified. Table 4: Ranking order of candidate networks generated by GRA and PROMETHEE algorithms Networks Online Gaming Streaming GRA PROMETHEE GRA PROMETHEE GRC i (Rank) Φ(a i )(Rank) GRC i (Rank) Φ(a i ) (Rank) WiFi (3) (4) (3) (4) WiFi (4) (3) (4) (2) LTE (1) (1) (1) (1) UMTS/ HSPA (2) (2) (2) (3) The same procedure is run at 50 decision points. With GRA model, the probability of selecting an optimal network is 92% for online gaming and 87% for streaming application. PROMETHEE also exhibited good optimal ijpam.eu

8 network selection rate of 93% for online gaming but only 78% for streaming traffic class. This is because, for most of the UEs, selected LTE as best network, when a more appropriate network WiFi2 is available. This wrong decision resulted in loading of LTE network and consecutive handoff failure due to depletion of LTE network resources. 5 Conclusion In this paper an attempt is made to solve the problem of network selection by applying GRA algorithm. The performance of GRA algorithm is compared with PROMETHEE for online gaming and streaming traffic classes. Simulation results demonstrate a significant increase in optimal network selection by GRA decision framework. Future work includes the study of tradeoffs in new call blocking probability during network selection process. References [1] William C. Hardy,QoS: Measurement and Evaluation of Telecommunications Quality of Service, John Wiley & Sons, Ltd (2001). [2] Gwo-Hshiung Tzeng,Jih-Jeng Huang,Multi Attribute Decision Making:Methods and Applications, CRC Press, Taylor & Francis Group (2010). [3] Alireza Afshari, Majid Mojahed and Rosnah Mohd Yusuf, Simple Additive Weighting approach to Personnel Selection problem, International Journal of Innovation, Management and Technology,Vol 1:5 (2010), [4] Serafim Opricovici, Majid Mojahed and Rosnah Mohd Yusuf, Programski paket VIKOR za visekriterijumsko kompromisno rangiranje, SYM- OP-IS. [5] J.P. Brans & P. Vincke, A Preference Ranking Organisation Method: The PROMETHEE method for MCDM, Management Science, (1985). [6] Deng J.L.,Introduction to grey system theory, The Journal of Grey System, 1(1), (1989), 1-7. [7] Sifeng Liu and Yi Lin, Grey Systems Theory and Applications, Springer- Verlag, (2010). ijpam.eu

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