Implementation of Fuzzy Multiple Objective Decision Making Algorithm in a Heterogeneous Mobile Environment

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1 Implemetatio of Fuzzy Multiple Objective Decisio Makig Algorithm i a Heterogeeous Mobile Eviromet P.M.L. ha, Y.F. Hu, R.E. Sheriff, Departmet of Electroics ad Telecommuicatios Departmet of yberetics, Iteret ad Virtual Systems Uiversity of Bradford, UK Abstract- Mobile satellite etworks are ow beig utilized to provide complemetary service coverage to their terrestrial couterparts. The migratio from voice-domiated service delivery to a data-cetric eviromet implies that the choice of oe particular access etwork over aother will eed to take ito accout may differet criteria, which previously eed ot have bee cosidered. For this reaso, it is importat that a suitable decisio makig algorithm is desiged to esure that all of the differet characteristics of the system are take ito accout whe makig the segmet selectio for a particular service delivery. I this paper, a segmet selectio algorithm based o the fuzzy multiple objective decisio makig algorithm is preseted. This algorithm is aalyzed to show how the overall performace of a multi-access segmet etwork ca be improved by varyig the relative importace of certai service ad etwork characteristics. I. INTRODUTION Mobile satellite etworks are ow beig utilized to provide complemetary service coverage to their terrestrial couterparts. At preset, the services o offer to the mobile user are limited to voice ad low data rate applicatios, be it via terrestrial or satellite modes of delivery. Such a service sceario is set to chage with the itroductio of evolved secod-geeratio etworks, such as the GSM derivative GPRS, followed closely by third-geeratio (G) mobile techologies. Shortly, the sophisticated mobile user will be able to access a multitude of ew services ad applicatios at data rates of 44 kbit/s ad beyod, icorporatig packetorieted as well as traditioal circuit-switched forms of delivery. It is aticipated that future-geeratio mobile techologies will rely o both satellite ad terrestrial etworks to deliver services with the desired Quality of Service (QoS). I compariso to today s mobile etworks, i the future, the mobile user should have a much greater choice ot oly i terms of the type of services ad applicatios o offer but also the preferred mode of delivery, for example, either through terrestrial or satellite access etworks. It ca be evisaged that the user may wish to trade-off cost agaist quality, for example, or perhaps to determie the proposed access etwork accordig to the applicatio o offer. Similarly, etwork operators may be able to arrage a choice of service packages that are catered towards particular categories of user, for example, a busiess user would have a differet service profile i compariso to a tourist. urretly, i areas where a satellite is operatig alogside a terrestrial etwork, the terrestrial etwork will always be give priority whe establishig a call. I the ear future, however, the selectio of a certai access etwork for the iitiatio of a particular commuicatio sessio could rely o a sophisticated algorithm, icorporatig ot oly the basic QoS criteria, such as sigal quality, but also other cosideratios, such as the mobile termial s available battery power, required badwidth, service priority ad so o. Here, it ca be see that the choice of oe etwork over aother is o loger black or white but rather depeds o a umber of iter-related parameters. Ideally, it should be possible to maximize the efficiecy of the heterogeeous eviromet by takig ito accout the various cosideratios that eed to made whe establishig a sessio, such that both terrestrial ad satellite resources are optimally utilized. I this paper, the cocepts of fuzzy logic are applied to a future heterogeeous mobile eviromet, i which terrestrial ad satellite mobile etworks operate alogside each other. The use of fuzzy logic allows a sesitivity aalysis to be performed i order to determie which factors are critical to the efficiet utilizatio of the etwork. I this paper, two specific parameters are give particular attetio: hargig ad Quality of Service. The paper is orgaized as follows: I the ext sectio, a brief itroductio to multiple objective decisio makig (MODM) is preseted followed by a discussio of relevat segmet selectio criteria. The costituets of the algorithm are described i Sectio III, followed by a descriptio of the proposed algorithm i Sectio IV. The simulatio ad aalysis of the proposed algorithm is the preseted before drawig coclusio o the algorithm s performace. II. MULTIPLE OBJETIVE DEISION MAKING I multiple objective decisio problems, all alteratives available to the system are evaluated accordig to a umber of criteria. Each criterio will iduce a particular orderig of the alteratives ad a relevat procedure is the implemeted to costruct oe overall preferece orderig []. There are may variatios o the methods used for MODM. The algorithm proposed here uses the model proposed by Yager i []. This method is chose sice it is suitable for solvig /0/$.00 (c) 00 IEEE.

2 problems where the objectives are of varyig degree of importace. Detailed descriptios of other types of MODM models ca be foud i [] ad [4]. I geeral, MODM ca be implemeted i ay system where various alteratives ad criteria exist. However, this methodology has yet to be implemeted i a heterogeeous wireless eviromet. urretly, the primary applicatio of MODM lies i cotrol ad idustrial egieerig. Other parameters could iclude the type of applicatios used ad the choice of priority or prohibited segmets. As a example, the user ca be provided with the followig set of questios, as illustrated i Fig.. III. ONSTITUENTS OF ALGORITHM The segmet selectio criteria is importat as it iflueces the choice of the target segmet. As metioed previously, several criteria, which ca iclude user-based QoS parameters ad other etwork characteristics, ca be cosidered i the proposed algorithm. For example, i additio to the sigal stregth, other parameters such as the available badwidth, reliability, latecy ad etwork coverage ca be take ito accout. Whe cosiderig userbased parameters, the types of applicatio, chargig model ad the preferred ad prohibited user segmet ca be icorporated i the algorithm. If the chage of segmet occurs whe the user is curretly usig aother segmet, the QoS perceived by the user ca also be cosidered i the algorithm. Seve example criteria are used i the algorithm described i this paper, amely, sigal stregth, badwidth, cost, reliability, latecy, battery status ad the user s preferred segmet (priority). This ca be see i Fig., where the iput from the system is cosidered. I additio to the criteria metioed above, several o-fuzzy or crisp criteria could also be cosidered i the algorithm such as the availability of segmet ad also the termial type. These criteria are cosidered as crisp sets sice a segmet ca oly be classed as either beig available or ot, ad ot both simultaeously. A similar argumet applies to termial type. System User SS SS Averagig Badwidth hargig Reliability Latecy Battery Status Applicatio Used QoS Segmet Prohibited Segmet Termial Type Fuzzifier Determie Weightig of riteria SS Badwidth hargig Reliability Latecy Battery Status W_SS W_Badwidth W_hargig W_Reliability W_Latecy W_Battery Status W_ Multiple Objective Decisio Makig Fig.. Block Diagram for Segmet Selectio hose Segmet The role of the user i the algorithm is detailed i the ext sectio. Geerally, the iput from the user is used to determie the weightig give to each of the seve criteria. This iput, for istace, could be the importace of cost compared to the importace of received quality of service. Fig.. A Example User Iterface The mai purpose of the segmet selectio algorithm is to select a segmet for a particular service which ca satisfy the followig objectives; low cost, good sigal stregth, optimum badwidth, low etwork latecy, high lik availability, log battery life, while takig ito accout the preferred segmet of the user. There are two differet stages i the algorithm. The fuzzificatio procedures ad the weightig of the criteria are performed i the first stage. The former ivolves the evaluatio ad compariso of the available segmets, whereas the latter is used to evaluate the importace of each criteria based o the istructios received from the etwork provider ad the user. IV. SEGMENT SELETION ALGORITHM I the first stage, data from the system are fed ito a fuzzifier, to be coverted ito fuzzy sets. A fuzzy set is a set without a crisp, clearly defied boudary ad therefore, has a varyig degree of membership. This is differet from a crisp set i which elemets are oly cosidered members of a set if its membership is assiged a value of. For example, if the chargig model is cosidered i a crisp set, the cost of usig a segmet ca oly be classed as expesive or iexpesive. If it is classed as expesive, it will be give a membership value of ; otherwise, it will have a membership value of 0. However, i a fuzzy set, the cost of a segmet ca be represeted by aythig betwee 0 ad depedig o the membership fuctio. The membership fuctio is a curve or lie that defies how each datum or value is mapped oto a membership value. I order to obtai the membership values for the fuzzy sets, the measuremets for a particular parameter are mapped oto a membership fuctio. As a example, if the objective of the target segmet is low cost, a membership fuctio with the objective low cost ca be costructed, as show i Fig. a. From the diagram, it ca be iferred that if cost is low, the membership values will /0/$.00 (c) 00 IEEE.

3 be high. Note that the x-values for cost are ormalized betwee 0 ad. I the same diagram, the method by which the membership values are assiged is demostrated. If the ormalized cost for UMTS is 0.5, the membership value for UMTS is 0.8. The same priciple applies to all three segmets. Membership Values,µ Membership Values, µ GPRS UMTS ost (a) Objective: Low ost Badwidth (a) Objective: High Badwidth SAT Fig.. Membership Fuctio ost ad Badwidth O the other had, the weightig of criteria is developed by obtaiig a ratio scale for the criteria based upo a paired compariso of each criterio. This ratio scale is iflueced by the user s preferece i terms of cost, quality ad applicatio used. This procedure is also kow as the aalytic hierarchy process (AHP), which was developed by Saaty [5] for allocatig resources accordig to priority levels. AHP cosists of three mai priciples: decompositio of the decisio problem, comparative judgmet of the elemets ad sythesis of the priorities. I the first step, the problem is decomposed ito its costituet parts (idetificatio of segmet selectio criteria). The secod step is the compariso of the criteria. Here, the criteria are compared i pairs. Fially, i the third step, the weightigs for all the criteria are obtaied usig the eigevector method. The procedures ivolved i obtaiig the weightig are described below: Assume that = {,..., p } is a set of p decisio criteria. A set of values of relative importace is the assiged to each criterio by performig a pairwise compariso betwee the desigated criterio ad the other criteria. For example, if is the desigated criterio, the the set of values of relative importace for i compariso with the other criteria ca be writte as {a, a,... a p }, where a j, j is determied by comparig the importace of criteria to j. The values of a j are determied by the system desiger based o the etwork capability, service requiremets ad the user s iput. The defiitio of the values assiged for the compariso is show i Table. TABLE DEFINITION FOR OMPARING IMPORTANE OF RITERIA [5] Importace Defiitio Equal Importace Weak importace of oe over the other 5 Strog importace of oe over aother Demostrated importace of oe over the other 9 Absolute importace of oe over the other, 4, 6, 8 Itermediate values; two adjacet judgemets The a matrix, B, of dimesio p x p ca be created where: b ii = () bij= aij, i j () bji= /bij, () A example of the compariso is show i the followig matrix. Here, criterio is first compared to, ad so o. I [], it was show that by fidig the uit eigevector, W, correspodig to the maximum eigevalue of B produces the cardial ratio scale of the compared elemets. I this example, has a higher importace level whe compared to. However, it is give the same importace i compariso to the other five criteria. B W To obtai the fial weightig matrix,, used i the decisio process, W is multiplied with the umber of criteria,. W The secod stage of the algorithm uses the methodology itroduced i []. I this stage, the weightigs are applied to each criterio. This is performed by raisig the correspodig /0/$.00 (c) 00 IEEE. 4

4 elemets i the fuzzy set to the correspodig matrix elemets i. A decisio fuctio is the obtaied, which ca simultaeously satisfy all the decisio objectives. This is give by the itersectio of all objectives sets, such that: 4 D 4... (4) Several rules are importat whe cosiderig fuzzy logic. The AND (itersectio) of ay two fuzzy variables results i the miimum truth value, whereas the OR (uio) of two fuzzy variables results i the maximum truth value. AB AB mi( max( A,, A B B ) ) Oe decisio fuctio ca be calculated for each segmet ad sice D is obtaied usig the miimum truth value, the chose segmet is the segmet with the maximum or highest membership values of D. A. Testbed V. PERFORMANE EVALUATION Three wireless access segmets are cosidered i the the experimets that follow; Geeral Packet Radio Service (GPRS), Uiversal Mobile Telecommuicatios System (UMTS) ad a geostatioary satellite system. GPRS is a service desiged to trasfer o real-time services over existig GSM radio etworks, whereas UMTS is capable of supportig both o real-time ad real-time services with data rates of up to Mbps. The satellite system cosidered here is capable of supportig user data rates i the rage correspodig to those specified for Satellite-UMTS, that is up to 44 kbps i a mobile eviromet. B. Experimet Two sets of experimets are performed. I the first experimet, the same weightigs are applied to all seve criteria. The mai focus of this experimet is to defie a set of coditios that will make the satellite segmet to be competitive with its terrestrial couterparts, despite the fact that it is sigificatly more expesive, as idicated by the value of the chargig model value ( ). This will be achieved by offerig services at a greater badwidth. The ivestigatio aims to determie the miimum badwidth ( ) required by the satellite segmet that is required to make it a possible target segmet. With this iformatio, the etwork operator ca the have a idicatio of how certai criteria or etwork characteristics for a particular segmet ca be optimized to make it o par with the other wireless segmets. The service provider ca subsequetly use this iformatio whe specifyig the characteristics of each segmet. The parameters for Experimet are show i Table. Here, the membership fuctio for is ot icluded, sice this is to be determied by the experimet. As oted previously, the values for are obtaied by providig equal (5) importace to all the seve criteria. The criteria are rated from a scale of 0 to, with 0 beig the least likely to satisfy a objective ad beig the most likely to meet the requiremet of a objective. To be more precise, if the chargig model is cosidered, 0 idicates a very expesive segmet whereas a ratig of shows that the segmet is iexpesive. These parameters ca be obtaied usig the membership fuctios show i Fig.. Also ote that other tha cost, the other criteria have bee assiged membership values of 0.9, so as ot to ifluece the compariso betwee badwidth ad cost. TABLE PARAMETERS FOR EXPERIMENT riteria Membership Values GPRS UMTS SAT hargig Latecy Reliability Sigal Stregth Battery Segmet Sice the itersectio fuctio is used to determie the target segmet, the miimum membership value of the chose criteria has the most ifluece o the target segmet. Therefore, for the satellite segmet to be chose, the followig coditio must hold true. This is obtaied by applyig equatio (5) to (4). Mi ( SAT ), Mi ( GPRS), Mi ( SAT ), ( SAT ), Mi ( UMTS), ( GPRS), ( SAT ), ( UMTS), ( SAT ),... ( GPRS),... ( SAT ),... ( UMTS),... ( SAT ) ( SAT ) ( GPRS) AND ( UMTS) I experimet, the membership value of for the satellite segmet is give as 0.. Therefore, for the satellite segmet to be selected, (SAT) AND (GPRS) AND (UMTS) The same argumet ca be applied for the UMTS ad GPRS segmets.. Experimet I the Experimet, differet weightigs are the applied to the criteria to demostrate the ifluece of the weightigs o the fial decisio. I particular, the weightig of badwidth is give a demostrated importace over cost. Therefore, it ca be assumed that the applicatio is tailored to suit a busiess user. Table shows the weightig applied to each criterio. Two scearios are cosidered i this simulatio: ) both cost ad badwidth are of equal weightig; ) Badwidth has a higher (6) /0/$.00 (c) 00 IEEE. 5

5 weightig tha cost. The matrix used to obtai for Sceario is the same as the matrix example show i Sectio IV. The membership values used i this experimet are the same as those assiged to Experimet. TABLE PARAMETERS FOR EXPERIMENT riteria Weightigs, Sceario Sceario hargig Badwidth Latecy Reliability Sigal Stregth Battery Segmet The results obtaied for Experimet are show i Table 4. Agai, the results show are aimed at selectig the satellite segmet as the most suitable segmet sice this segmet is cosidered the most udesirable whe the chargig model is first take ito cosideratio. TABLE 4 RESULT FOR EXPERIMENT Equal Weightig Higher Weightig for hargig Badwidth hargig Badwidth ( ) ( ) ( ) ( ) GPRS UMTS SAT The membership value of ( ( )) i Table 4 is obtaied from the simulatio parameters show i Table. is the calculated by usig the values of i Table. I order to make the satellite segmet the preferred segmet, values for GPRS ad UMTS have to be set to be equal or less tha the miimum value of for the satellite segmet, as explaied i Experimet. Therefore, i the first sceario, where equal priority ad hece weightig is implemeted, the maximum value of permissible i both GPRS ad UMTS i order for the satellite segmet to be selected is 0.04, which coicides with the miimum value of i the satellite segmet. The required membership values of for GPRS ad UMTS are the foud to be 0.99, whereas for the satellite segmet, this value is 0.0. O the other had, i the secod sceario, whe a higher priority (weightig) is assiged to badwidth, the required membership values of for GPRS ad UMTS are both For the satellite segmet, this is I cotrast to the first sceario, i order for the satellite segmet to be selected, the available badwidth to be provided eed ot be sigificatly more tha that provided by the UMTS or GPRS segmets. I other words, whe equal priority is assiged to all criteria, the selectio of the satellite segmet is i practice, ulikely. However, from Experimet, it ca be see that whe the user expresses a preferece of badwidth agaist cost, the satellite segmet ca provide a viable alterative to its terrestrial couterparts. VI. ONLUSION This paper has preseted a segmet selectio algorithm based o the cocept of fuzzy multiple objective decisio makig (MODM). This method is suitable for the segmet selectio algorithm as it provides approaches to makig decisios i complex situatios where more tha oe decisio objective should be cosidered. The results show that eve though the access segmets utilized i the algorithm might have differet behaviors, it is possible to choose a segmet that was iitially thought to be usuitable by adjustig the characteristics of other criteria. Furthermore, the sigificace of the weightig method ad the coditios required to make a segmet more attractive to the user has also bee discussed. The ext stage of the work ivolves improvig the method i which each of the criteria is raked based o the actual performace measuremets of each etwork. I additio, further aalysis ivolvig a larger umber of criteria to be compared could be ivestigated. AKNOWLEDGEMENT This article is based o work that was performed as part of the SUITED project, which is partially fuded by the Europea ommissio uder the Iformatio Society Techologies (IST) Program. REFERENES [] G.J. Klir, B. Yua, Fuzzy Sets ad Fuzzy Logic, Pretice Hall P T R, USA, 995. [] R.R. Yager, Multiple Objective Decisio Makig usig Fuzzy Sets, Iteratioal Joural of Ma-Machie Studies, Vol. 9, pp. 5-8, 9. [] R. Fuller,. arlsso, Fuzzy Multiple riteria Decisio Makig: Recet Developmets, Fuzzy Sets ad Systems, Vol. 8, pp. 9-5, 996. [4] T.J. Ross, Fuzzy Logic with Egieerig Applicatios, McGraw-Hill, Ic., USA, 995. [5] T.L. Saaty, The Aalytic Hierarchy Process: Plaig, Settig, Resource Allocatio, McGraw-Hill, Ic., USA, /0/$.00 (c) 00 IEEE. 6

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