A Model for the Selection of Internet Service Providers

Transcription

1 ISSN , Autoatic Control and Coputer Sciences, 2008, Vol. 42, No. 5, pp Allerton Press, Inc., Original Russian Text I.M. Aliev, 2008, published in Avtoatika i Vychislitel naya Tekhnika, 2008, No. 5, pp A Model for the Selection of Internet Service Providers I. M. Aliev Institute of Inforation Technologies, National Acadey of Sciences of Azerbaijan. ul F. Agaev 9, Baku, Az-1141 Azerbaijan e-ail: ici-ai@inco.gov.az Received March 20, 2008; in final for, July 28, 2008 Abstract A fuzzy odel for the selection of Internet service providers is presented in the article. Indicators characterizing the providers are represented by linguistic variables with triangular fuzzy nubers. Entropy easures are used as a etric for coparing different alternatives. Key words: Internet service providers, fuzzy nuber, ebership function, linguistic variables, entropy DOI: /S INTRODUCTION The developent of inforation technologies has led to the creation of a global inforation ediu on the basis of the Internet network, which is exerting an influence on the ost diverse spheres of activity. Whereas in its first stages the Internet was used ainly to gain access to generally available international resources, today it is successfully eployed for the transission of ultiedia data and applications that are actively used for coercial applications. Many firs have developed corporate networks and have integrated the into the Internet, carrying on their business in this environent. Internet services are provided by Internet service suppliers (ISP). At the present tie there exist dozens, and even hundreds of providers within each country, each provider supplying different Internet services. Under these conditions, the proble of selecting an ISP, especially for corporate users, has becoe increasingly ore coplex. Moreover, there is always soe risk in selecting an ISP. The reasons for this risk are various, on the one hand, the objective incopleteness or insufficiency of inforation, and on the other hand, the subjective perception of inforation and the possibility that the decision aker ay arrive at a false decision. It is, therefore, iportant to ake a correct choice of an ISP. In the present article a odel for selecting ISP that priarily takes into account the qualitative nature of the indicators which characterize the operation of ISP will be discussed. 2. INDICATORS CHARACTERIZING ISP AND THEIR ANALYSIS At the present tie ISP provide an extreely broad range of services, fro switched connections to highspeed Internet with the use of xdsl technology. In selecting an ISP it is necessary to ensure not only econoic rationality, but also support the perforance and reliability of the services provided. Table 1 presents certain additional indicators and inforation that serve to characterize the level of perforance and reliability of the services provided by ISP. Thus, suarizing the above rearks it ay be said that a decision to select a particular ISP is also coplicated by a nuber of features of the ISP, the principal of which are the following: the need to take account of a large nuber of ISP indicators in evaluating and selecting an ISP the qualitative nature of the principal indicators that characterize the operation of an ISP These features ake it difficult to apply traditional atheatical ethods. The apparatus of the theory of fuzzy sets is the technique which is used the ost often in evaluating and selecting an alternative under conditions of uncertainty [1, 2]. In this case the indicators that characterize an ISP ay be expressed by eans of linguistic variables. For exaple, the load on a channel ay be low, high, interediate, etc. Siilarly, the distance to the connection site ay be very great, great, short, etc. 249

2 250 ALIEV et al. Basic indicators characterizing the perforance and reliability of ISP services Indicator Capacity of channels Nuber of counication channels provided by ISP that links the ISP to the Internet Nuber of telephone lines in the ode bank Maxiu down tie The possibility of obtaining assistance Inforation backup Inforation security Availability of secondary services Distance to connection site Volue of statistical inforation provided Reputation of brand Professional experience Testionials and recoendations Description A very iportant indicator. If the ISP channels are overloaded, it will not be possible to aintain the perforance of services (rate of access to Internet). The network of providers ust possess a degree of redundancy. This is needed to ensure that if the fiber optic channel breaks, user traffic can still be transitted along a backup channel. The nuber of telephone lines in the ode bank ust be sufficient to reach the Internet on the first attept. This paraeter deterines the overall length and nuber of interruptions in providing services that are the fault of the provider. In the case of a failure, the user ust be able to obtain assistance so as to rapidly eliinate any failures. Certain ISP provide 24-hour assistance, while others provide assistance only at certain ties. One of the iportant procedures that ensure the integrity of inforation. To protect infrastructure and inforation, the ISP ust undertake certain required steps. It is iportant for the provider to possess a security policy. Soe ISP have groups that are responsible for responding to any breakdown in inforation security. For exaple, providing free Web-hosting site, ail roaing, tune-up or diagnostics of user coputer, ode, etc. The distance fro the user location to the ISP host is an iportant factor. Where the distance is great, the channel used for counication with the ISP passes through a series of interediate nodes, and this ay lead to a decrease in the quality of service. Providers usually supply statistical reports on the nuber of visits to the server. The ideal case is where, besides a standard report, the provider also supplies a coplete version of the protocol file of queries directed to the server. The reputation of a brand tells the custoer that the particular ISP has serious experience in the particular field, and that the fir has specialized in the particular business. Tie accuulated in the arket of Internet access services is of great iportance. Let us suppose that a length of tie, beginning with three years, indicates that the ISP has accuulated its own technical solutions to ensure service reliability. User testionials and recoendations are a source of useful inforation about the operation of the ISP. Another exaple. It is absolutely necessary to possess axially coplete inforation concerning the nuber of visits to the server in order to achieve successful realization of any strategy of Internet arketing. Usually, providers supply a statistical report on the nuber of visits to the server. The following data ay be present in such a report: total nuber of queries over the reporting period; ean-daily nuber of queries; nuber of successful and unsuccessful queries; volue of required data; distribution of queries by day of the week; distribution of queries by tie of day; and distribution of visitors by application doain. All of this inforation and certain other data usually included in the report supplied by the provider are the result of processing the protocol file of the queries that have been directed to the server. This file usually contains detailed inforation concerning all queries directed to the server. Therefore, the case in which the provider supplies, besides a standard report, a coplete version of the protocol file as well should be considered the ideal case. Any type of statistical report whatsoever ay be prepared once this file has been supplied. Unfortunately, far fro all providers are able to obtain statistical data without soe sort of constraints. The volue of statistical inforation supplied ay, therefore, be coplete, partially coplete, and so on. Those paraeters that are nuerical ay also be characterized by eans of perforance indicators (for exaple, the nuber of telephone lines in the ode bank ay be quite low, etc.).

3 A MODEL FOR THE SELECTION OF INTERNET SERVICE PROVIDERS 251 In the present study, therefore, we will apply the theory of fuzzy sets. 3. METHODOLOGY AND ALGORITHM There now exist a nuber of different decision ethods [2, 3]. The hierarchy analysis ethod proposed by T. L. Saaty [4] is the ost frequently used of such ethods. The ethod is based on pairwise coparisons of alternative variants with respect to different criteria using an estiation scale and subsequent ranking of the set of alternatives with respect to all criteria and objectives. The relationships between the criteria are taken into account through the construction of a hierarchy of criteria and application of pairwise coparisons for the purpose of identifying the iportance of the criteria and the subcriteria. The ethod is distinguished by siplicity and easily aps a correspondence by eans of intuitive representations. However, the ethod has a nuber of drawbacks, aong which is a constraint on the nuber of alternatives that ay be copared siultaneously (not ore than nine is recoended), the ipracticability of the exceedance scale used (equivalence, oderate exceedance, strong exceedance, etc.), the use of pairwise coparison for the purpose of obtaining quantitative values, and others. A ethod that ay be used to solve ulticriterion probles on the basis of an entropy easure was proposed in [5]. The efficiency of the proposed ethod by coparison with the hierarchy analysis ethod proposed by Saaty was deonstrated in the study. The Shannon forula was used here as a criterion for evaluating alternatives: where p j is the relative frequency. Let Y = {y ij },, n,,, be a atrix of estiators, where y ij is an estiator of alternative i relative to criterion j. If the atrix Y is noralized, the specific weights of an estiator of an alternative, defined as y ij s j n f ij = ----, where s j = y,,, will be the eleents of this atrix. ij Then, by (1), the entropy is calculated as: H = p j log 2 p j, And, finally, by noralizing the values with respect to all the indicators for each alternative, the weight of the entropy is deterined thus: After the entropy weight has been calculated for each alternative, the weights are sorted in decreasing order. The alternative which possesses the greatest value of the entropy weight is considered the best alternative. A correct choice of ISP also depends on the level of optiis held by the decision aker. Therefore, the index of this level ust also be taken into account in the odel. In light of the foregoing discussion, the choice of ISP ay be perfored according to the following algorith: Step 1. Specify a ebership function for each indicator. Step 2. Specify the coefficient of iportance of the indicators. Step 3. Copile a decision atrix. Step 4. Transfor the decision atrix into a atrix of γ-levels. H 1 = f 1 j log 2 ( f 1 j ), H 2 = f 2 j log 2 ( f 2 j ), H n = f nj log 2 ( f nj ). θ k H = , k k = 1, n. n H i (1) (2) (3)

4 252 ALIEV et al. Step 5. Copile a new decision atrix that takes into account the iportance of the indicators for level γ. Step. 6. Specify an optiis index and deterine the resultant decision atrix for level γ. Step 7. Copute the entropy with respect to all the indicators. Step 8. Copute the entropy weight for each alternative. 4. MATHEMATICAL STATEMENT OF PROBLEM A fuzzy ulticriterion decision proble ay be represented forally by a pair Z, K, where Z = {z i },, n, is a set of ISP fro which it is necessary to select one ISP with respect to specified criteria K = {K 1, K 2,, K j,, K }. With each indicator K j belonging to ISP z i there corresponds an estiator X ij,, n,,. In this case, for the set of ISP z i we obtain a atrix of estiators X = X ij,, n,,. We will represent the estiator of ISP z i with respect to criterion K j as a triangular fuzzy nuber the ebership function of which is characterized by the three paraeters {x ij1,x ij2, x ij3 } and has the for u ij x , ij1 x x ij2 x ij1 u ij x ij2 ij1 µ x ij ( u j ) = x ij3 u ij (4) , x x ij3 x ij2 u ij x ij3 ij2 0, otherwise where x ij1, x ij2, and x ij3 are the inial, ean, and axial values of the fuzzy nuber respectively. In solving practical probles for ipleenting arithetic operations on fuzzy nubers it is best to use sets of γ levels γ [0, 1]. X ij, X ij x ij1, x ij3 = [ ] = [ x ij2 ( 1 γ )α, x ij2 + ( 1 γ )β], (5) where α = (x ij2 x ij1 ) and β = (x ij3 x ij2 ) are the left and right scatters of the fuzzy nuber X ij, respectively, and ), the lower and upper bounds of the interval of values of X ij on γ level, respectively. x ij1 x ij3 Each eleent of the atrix X ij is characterized by its linguistic variable. It is necessary to take into account the type of criterion when selecting a ter set of linguistic variables. For this purpose, the set of criteria that characterize the ISP is partitioned into two subsets K and K. In subset K are found those criteria where high values ensure a better decision, whereas in subset K are found low-value criteria, lower values of which ensure a better decision. For exaple, we ay distinguish the following two criteria that are typical of ISP: nuber of telephone lines in the ode bank and the load of the channels. In this case, the criterion, nuber of channels, is in subset K, since the greater is the nuber of channels, the better is the ISP, while the criterion, load of a channel, is found in subset K, since a low load ensures a better decision. For exaple, the following ter sets ay be defined for the linguistic variable, load of a channel, occurring in subset K : {very high, high, ediu, very low, low}, while the following ter sets ay be defined for the linguistic variable, nuber of telephone lines, occurring in subset K : {very low, low, sufficient, any, very any}. In selecting an ISP it is necessary to take into account the coefficients of iportance of the indicators that characterize the ISP. This is due to the fact that indicators that characterize an ISP ay have different values for different users. For exaple, the cost of the services provided ay be the ost iportant indicator for one user, while the rate of access to the Internet (load on ISP channel) ay be the ost iportant indicator for another user. The choice of ISP is perfored individually for each custoer. We specify a vector of iportance coefficients of the indicators expressed in ters of the linguistic variable, iportance of indicators. Suppose that the iportance coefficient of the indicators is characterized by the fuzzy nuber W j,,, and is characterized by its own linguistic variable, iportance of criterion, with ters of the set {slightly significant, relatively significant, significant, sufficiently significant, very significant}.

5 A MODEL FOR THE SELECTION OF INTERNET SERVICE PROVIDERS 253 Siilarly, we represent the fuzzy nuber W j,,, by eans of γ-levels, as W j = [, ], γ [0, 1], where w j1 and w j3 are the lower and upper bounds of the interval of values W j on the γ-level, respectively. In view of the iportance coefficients of the indicators and recalling the rule for ultiplication of fuzzy nubers [1], a new atrix of estiators is fored, each of whose eleents for the γ-level is defined as To select an ISP it is necessary to transfor the interval atrices of estiators into atrices of fuzzy nubers. We denote by η the level of the decision optiis index. We will use the Hurwicz criterion, which is the weighted ean of the criterion of extree pessiis and the criterion of extree optiis with probabilities η and (1 η) [6]. In view of the definition of the Hurwicz criterion, we have Recalling that = in and that = ax we find fro (5) that The nuber η is selected in the range fro 0 to 1, depending on the propensity of the decision aker to optiis or to pessiis. With η = 0.,5, the optiis and pessiis indicators are equal. This eans that the decision aker behaves in neutral fashion when selecting the ISP. According to the algorith presented in Sec. 3 and in light of (8), we have where Y ij w ) j1 x ij1 w ) j3 x ij3 = W j X ij = [, ] = [ y ij1, y ij3 ],, n,,, γ [ 01, ]. y ij1 And, finally, using (3) we calculate the weight of the entropy for each ISP: In this case it is best to select an ISP that possesses greatest value of the entropy weight. Thus, in calculating the entropy for each ISP the entropies ay be ordered and the best decision selected. 5. CONCLUSIONS The perforance, reliability, and security of Internet services depend largely on the ISP, the nuber of which grows each year. A correct choice of ISP, therefore, is of great practical value. The existence of a set of indicators fro which a choice is to be ade akes it difficult to ake a correct choice and entails a scientific approach to the solution of this proble. In the present article a fuzzy odel for selecting an ISP that utilizes an entropy ea- ηin + ( 1 η) axỹ ij ax, η [ 01, ]. j Ỹ ij Ẑ Ỹ ij ŷ ij s j θ k = ηy ij1 y ij3 ŷ ŷ s 1 s 2 ŷ 21 s 1 + j Ỹ ij, i ( 1 η)y ) ij3, γ [ 01, ] ŷ s ŷ ŷ 2 = s 2 s = ŷ ŷ n1 n2 s 1 s 2 n ŷ ij ŷ n s f ij f 11 f 21 f n1 ŷ ij s j f ) 12 f 1 f ) 22 f 2 f ) n2 f n = and = ,,. n f kj f kj log 2 ( ) = , k = 1, n. f ij f ij log 2 ( ), w j1 w j3 (6) (7) (8) (9) (10)

6 254 ALIEV et al. sure has been proposed. The indicators that characterize the ISP were represented by linguistic variables with triangular fuzzy nubers. REFERENCES 1. Zadeh, L., The Concept of a Linguistic Variable and its Application to Approxiate Reasoning, Inforation Science, 1975, no. 8, pp , ; no. 9, pp Borisov, A.N., Kruberg, O.A., and Fedorov, I.P., Prinyatie resheniy na osnove nechetkikh odeley. Priery ispol zovaniya (Decision Making on the Basis of Fuzzy Models. Exaples), Riga: Zinatne, Hwang, C.L., Lai, Y.J., and Liu, T.Y., TOPSIS for Multiple Objective Decision Making, Europ. J. Oper. Res.,1994, vol. 76, issue 3, pp Saaty, T.L., The Analytic Hierarchy Process: Planing, Priority Setting, Resource Allocation, New York/London: McGraw-Hill, Mon, D.L. Cheng, C.H., and Lin, J.C., Evaluating Weapon Systes Using Fuzzy Analytic Hierarchy Process Based on Entropy Weight, Fuzzy Sets and Systes, 1994, vol. 62, issue 2, pp Labsker, L.G., Generalized Hurwicz Pessiis-Optiis Criterion, in Finansovaya ateatika (Financial Matheatics), Moscow: Moscow State University, 2001, pp