Uncertainty and Management of Cellular Telephone Networks</= title> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"country-region"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"address"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"Street"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"City"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"State"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PostalCode"/>  <style>  </style>  </head> <body lang=3DEN-US style=3D'tab-interval:.5in'> <div class=3DSection1> Proceedings of the International F= uzzy Engineering Symposium ’91 = 220;Fuzzy Engineering toward Human Friendly Systems”.Vol.2. <st1:pla= ce><st1:City>Yokohama</st1:City>, <st1:country-region>Japan</st1:country-region></st1:place> 1991, pp.929-94= 3 <o:p> </o:p> Uncertainty and Management of Cellular Telephone Networks<o:p></o:p> <o:p> </o:p> = &nb= sp; = Ziny = Flikop<o:p></o:p> NYNEX Science = & Technology, Inc. <st1:address><st1:Street>500 Westchester Ave.</st1:Street>, <st1:City>White Plai= ns</st1:City>, <st1:State>NY</st1:State> <st1:PostalCode>10604</st1:PostalCode></st1:addr= ess> <o:p></o:p> <o:p> </o:p> Abstract<o:p></o:p> <o:p> </= o:p> This article discusses so= me aspects of the development of the management system for the Cellular teleph= one networks. The system is intended to analyze and optimize cellular network performance. Networks are considered as loosely coupled heterogeneous distributed nonstationary nonli= near statistics systems. Fuzzy sets terminology is used for the network analysis= . <o:p> </o:p> <ol style=3D'margin-top:0in' start=3D1 type=3D1> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l1 level1 lfo1; tab-stops:list .5in'>Introduc= tion<o:p></o:p></li> </ol> The first articles addres= sing cellular network performance analysis and optimization were published long before ac= tual full-scale cellular networks were created. For instance see [1,2]. Publication of such articles continues. For examp= le, see[3,4] However, the cellular network management prob= lem is so complex that is still very far from resolution. This article does not pretend to answer all questions but shell tried to discuss some problems, directions and suggestions that can bring to us close to the solution. <o:p> </o:p> Optimal design and measur= ement of the cellular radio network is a very complicated tesk<= /span>. This complexity is caused by a number of different factors. Major of which = are: <o:p> </o:p> <ol style=3D'margin-top:0in' start=3D1 type=3D1> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>Traffic varies from region to region and depends = on the sizes and shapes of service zones, the covered roads and the densi= ty of car traffic on them, the penetration of the cellular service and so= on.</li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'> In = turn, the service zones of the cell sites depend on power levels of the transmitters, the terrain, access thresholds, and other parameters.</l= i> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>Telephone traffic in the same region can fluctuate widely, depending on the time of day the day, the day of the week, the seasons of the year, car traffic conditions,= unusual events and so forth.</li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'> Cha= nnel assignment and = hand-off algorithms are designed to provide improved and reliable service. However, they create such a complicated call migration pattern that a mathematical m= odel that is adequate to real cellular networks has not yet been developed.= </li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>Distribution of telephone traffic in the system depends not only on size and shape of the services zones, but also on = the values of the different network attributes, such as hand-off threshold= s, directed retry assignments, biases and so on.</li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>The results of cellular network analysis are valid only for a short period of time because real networks are in state of constant change.</li> </ol> 7. Cause-and-effect trials that are ma= de at the same time but in different regions can show different relationships bet= ween the same parameters. 8. Linear increments of the control attributes produce non-linear affects. 9. Cellular network is loosely couplet= distributed system. Of of this unwise is shows that only co= mpany hence if management system that considers all the above. This analysis shows that = only comprehensive management system that considers all the above described feat= ures can provide efficient management. To create a classical control loop the management system should be composed of three interrelated subsystems Monitoring, Decision Support and Executive. However, in this article we will only discuss problems relevant to the Decision Support Subsystem design. </= p> <o:p>&n= bsp;</o:p> <![if !supportLists]>2.<sp= an style=3D'font:7.0pt "Times New Roman"'> </spa= n><![endif]>Decision Support System<o:p></o:p></b= > This subsystem is an inte= lligent module or the Management system. It should study cellular network behavior, analyze its performance and provide a system engineer with the information = and tools that are necessary for the decision making. The size and complexity o= f real cellular networks is the reason that neither adequate hard (precise) models= nor comprehensive hard management methodology based on precise methods have yet been developed. This situation exists because the traditional modeling appr= oach requires significant simplification of real networks to allow the use of av= ailable theories. As a result models, proposed in the literature are inadequate to actual management tasks. To resolve these difficul= ties and keep simplification to the minimum, we suggest the use of soft (imprecise) models and soft management methodologies hat mimic a human reasoning for st= udy, modeling, and optimization. As an object for study we intend to use real networks. To avoid analysis of whole network we shall try to create a netwo= rk decomposition technique that take advantage of network looseness. <o:p>&n= bsp;</o:p> For the following discuss= ion, let’s introduce some definitions.<o:p></o:p> By sell side controlled attributes = we mean attributes that can be changed by an </span= >operator. They are, for example, access and hand-off thresholds, neighbor lists and t= ransmitted power levels. Attributes that that changing as a = result of changes made to control attributes, we will call sell site (network) con= trolled attributes. This attributes are: percent of successfully processed calls, blocking ratio, percent of dropped calls, percent of covered area with sufficient SNR, and so on. We should consider that the change = of the control attribute can produce changes of more than one controlled attribute= s. The same change of controlled attribute can be a result of changes of different= control attributes. To achieve a desi= red change of a controlled attribute sometimes a set of control attributes of a number= of cell sites have to be changed. For the network modeling, decomposi= tion, management and optimization we need to know how changes of control attribut= es are mapped to changes of controlled attributes. This mapping reflects all t= he complexities and uncertainties cellular network behavior and constitute a m= ajor problem in the whole management task. As a possible solution to the problem= of mapping analysis we propose to use a cause-and-effect approach. It can be executed = either via preplanned changes of control attributes in the real network or by a mo= nitoring disturbances created in network by external sources with simultaneous evaluation of hollow controlled attribute became affected. (An example of disturbance is a cel= l site equipment failure.) <o:p> </o:p> Measurement of controlled attributes is a difficult task sense they are non-0stationery and noisy. For the filtration of a noise, we can recommend using seasonal time series anal= ysis forecasting algorithm because variations of majority of attributes contain a periodical component of the. In this approach, noise can be a partially filtered when real data are substituted with forecasted values. Good results can be achieved via model developed in corporation with Dr. A. Pankratz. </sp= an>In this model a one-hour-ahead forecast of a value of attribute z at hour t is calculated as: <o:p> </o:p> <![if !vml]><img width=3D188 height=3D24 src=3D"CellularNetworks_files/image002.gif" v:shapes=3D"_x0000_i1025"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; (1) <o:p> </o:p> where= : <![if !vml]><img width=3D17 height=3D16 src=3D"CellularNetworks_files/image004.gif" v:shapes=3D"_x0000_i1026"><![en= dif]>and <![if !vml]><img width=3D17 height=3D19 src=3D"CellularNetworks_files/image006.gif" v:shapes=3D"_x0000_i1027"><![en= dif]>are weight coefficients.= They are recalculated each time when new data are received. Calculat= ions are made via an optimization procedure aimed to minimize <o:p> </o:p> <![if !vml]><img width=3D65 height=3D45 src=3D"CellularNetworks_files/image008.gif" v:shapes=3D"_x0000_i1028"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; (2) <o:p> </o:p> One-step-ahead backward f= orecasts <o:p> </o:p> <![if !vml]><img width=3D168 height=3D24 src=3D"CellularNetworks_files/image010.gif" v:shapes=3D"_x0000_i1029"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (3) <o:p> </o:p> One-step-ahead forward er= rors <o:p> </o:p> <![if !vml]><img width=3D171 height=3D24 src=3D"CellularNetworks_files/image012.gif" v:shapes=3D"_x0000_i1030"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (4) <o:p> </o:p> One-step-ahead backward e= rrors <o:p> </o:p> <![if !vml]><img width=3D168 height=3D24 src=3D"CellularNetworks_files/image014.gif" v:shapes=3D"_x0000_i1031"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (5) <o:p> </o:p> Our experience shows ther= e for forecasting, a history of constantly moving 240 hours values can be conside= red sufficient. Even though some noise can be filtrated, the results of measurements of controlled attributes will still be uncertain. Mapping and measuring problems are a justification (from our point of view) for using s= oft methods for network analysis. As a descriptive and analytical tool we have chosen a Fuzzy Sets theory [5]. <o:p> </o:p> Network studies should st= art with preliminary self-educational phase, during which sufficient cause-and-effect data have been accumulated. After this phase we can start our analysis with= decomposition problem. Assume S is a set of all cell sites in the network; <![if !vml]><img width=3D25 height=3D24 src=3D"CellularNetworks_files/image016.gif" v:shapes=3D"_x0000_i1032"><![en= dif]> is a value = of a control attribute <![if !vml]><img width=3D49 height=3D21 src=3D"CellularNetworks_files/image018.gif" v:shapes=3D"_x0000_i1033"><![en= dif]> of cell sit= e<![if !vml]><img width=3D39 height=3D19 src=3D"CellularNetworks_files/image020.gif" v:shapes=3D"_x0000_i1034"><![en= dif]>; <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image022.gif" v:shapes=3D"_x0000_i1035"><![en= dif]> - is a valu= e of a controlled attribute <![if !vml]><img width=3D59 height=3D21 src=3D"CellularNetworks_files/image024.gif" v:shapes=3D"_x0000_i1036"><![en= dif]> of a cell s= ite<![if !vml]><img width=3D41 height=3D19 src=3D"CellularNetworks_files/image026.gif" v:shapes=3D"_x0000_i1037"><![en= dif]>; and <![if !vml]><img width=3D92 height=3D25 src=3D"CellularNetworks_files/image028.gif" v:shapes=3D"_x0000_i1038"><![en= dif]> are corresp= onding membership functions. (Using membership functions instead of precise values will provide the necessary “softness” in our studies. <o:p> </o:p> Decomposition can be base= d on the concept of an affected zone. For simplicity, let’s from now on consider <![if !vml]><img width=3D25 height=3D24 src=3D"CellularNetworks_files/image016.gif" v:shapes=3D"_x0000_i1039"><![en= dif]> as a value = of a change of a control attribute I= of cell site z (it is a cause) and= <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image022.gif" v:shapes=3D"_x0000_i1040"><![en= dif]> as a value = of a change of a controlled attribute j<= /i> of a cell site d (effect). We also= will consider <![if !vml]><img width=3D92 height=3D25 src=3D"CellularNetworks_files/image028.gif" v:shapes=3D"_x0000_i1041"><![en= dif]> as correspo= nding cause-and-effect membership functions. <o:p> </o:p> Because of looseness, eff= ects die out when they propagate. Let’s assume that <![if !vml]><img width=3D19 height=3D25 src=3D"CellularNetworks_files/image031.gif" v:shapes=3D"_x0000_i1042"><![en= dif]> is a tolera= ted threshold value of an attribute j</= i>. Then a subset <![if !vml]><img width=3D63 height=3D25 src=3D"CellularNetworks_files/image033.gif" v:shapes=3D"_x0000_i1043"><![en= dif]> of cell sit= es (<![if !vml]><img width=3D20 height=3D25 src=3D"CellularNetworks_files/image035.gif" v:shapes=3D"_x0000_i1044"><![en= dif]>- affected zone) producing effect j in response to the cause i created on z</= i>, can be defined as follows: <o:p> </o:p> <![if !vml]><img width=3D267 height=3D25 src=3D"CellularNetworks_files/image037.gif" v:shapes=3D"_x0000_i1045"><![en= dif]> = &nb= sp; = &nb= sp; = (6) <o:p> </o:p> where= <![if !vml]><img width=3D56 height=3D25 src=3D"CellularNetworks_files/image039.gif" v:shapes=3D"_x0000_i1046"><![en= dif]> is a member= ship function of an effect j generat= ed on d by cause I created on z. <o:p> </o:p> When one cause can genera= te multiple effects, then <![if !vml]><img width=3D16 height=3D24 src=3D"CellularNetworks_files/image041.gif" v:shapes=3D"_x0000_i1047"><![en= dif]>-affected zone is defined as <o:p> </o:p> <![if !vml]><img width=3D35 height=3D24 src=3D"CellularNetworks_files/image043.gif" v:shapes=3D"_x0000_i1048"><![en= dif]><![if !vml]><img width=3D51 height=3D39 src=3D"CellularNetworks_files/image045.gif" v:shapes=3D"_x0000_i1049"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = = </s= pan>(7) <o:p> </o:p> If a number of causes (<s= ub><![if !vml]><img width=3D45 height=3D23 src=3D"CellularNetworks_files/image047.gif" v:shapes=3D"_x0000_i1050"><![en= dif]> are generated simultaneously on z (system engineers of cellular networks often make multiple ch= anges) then z’-affected zone is:= <o:p> </o:p> <o:p> </o:p> <![if !vml]><img width=3D297 height=3D39 src=3D"CellularNetworks_files/image049.gif" v:shapes=3D"_x0000_i1051"><![en= dif]> = &nb= sp; = &nb= sp; (8) <o:p> </o:p> where <![if !vml]><img width=3D101 height=3D24 src=3D"CellularNetworks_files/image051.gif" v:shapes=3D"_x0000_i1052"><![en= dif]> is a second= order membership function of causes created simultaneously on z; <![if !vml]><img width=3D159 height=3D25 src=3D"CellularNetworks_files/image053.gif" v:shapes=3D"_x0000_i1053"><![en= dif]>is a set of membership functions of causes created simultaneously on z; <![if !vml]><img width=3D60 height=3D28 src=3D"CellularNetworks_files/image055.gif" v:shapes=3D"_x0000_i1054"><![en= dif]> is a member= ship function of j effect generated = on d by causes I’ and created on z. Both membership functions in (8) consider the fact, that since networks are non-linear, resulting j-type ef= fect can be equal to, more than or less than a sum of partial effects of j-type generated on d by different causes and are created on z. <o:p> </o:p> The maximal size of the a= ffected zone <![if !vml]><img width=3D19 height=3D23 src=3D"CellularNetworks_files/image057.gif" v:shapes=3D"_x0000_i1055"><![en= dif]> will be whe= n I’=3DI. In this case = &nb= sp; <![if !vml]><img width=3D51 height=3D24 src=3D"CellularNetworks_files/image059.gif" v:shapes=3D"_x0000_i1056"><![en= dif]> = &nb= sp; = = &nb= sp; = &nb= sp; = (9) <o:p> </o:p> To evaluate and optimize = network performance and also to organize adaptability properties for the management system, a soft criterion (“goodness”) for the affected zone is proposed. (We do not discuss an adaptability issue in this article.) <o:p> </o:p> Goodness value <![if !vml]><img width=3D25 height=3D25 src=3D"CellularNetworks_files/image061.gif" v:shapes=3D"_x0000_i1057"><![en= dif]> generated o= n cell site d by I’ causes created on z. is as follows: <o:p> </o:p> <![if !vml]><img width=3D208 height=3D35 src=3D"CellularNetworks_files/image063.gif" v:shapes=3D"_x0000_i1058"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (10) <o:p> </o:p> When <![if !vml]><img width=3D81 height=3D25 src=3D"CellularNetworks_files/image065.gif" v:shapes=3D"_x0000_i1059"><![en= dif]>is a weight coefficient of the j-th<= /span> parameter. = ; Coefficients of this kind are usually the result of surveys made in = cellular telephone company and they represent subjecti= ve of imprecise collective opinion of different company representatives. This fact also justifies use of soft methods in the network optimization. <o:p> </o:p> The affected zone goodness value th= at is gained via I</i= >’ causes created on z is:<o:p></o:p> <o:p> </o:p> <![if !vml]><img width=3D84 height=3D39 src=3D"CellularNetworks_files/image067.gif" v:shapes=3D"_x0000_i1060"><![en= dif]> = &nb= sp; = = &nb= sp; = &nb= sp; = &nb= sp; (11) <o:p> </o:p> A set of the affected con= trolled attributes contains all cellular service quality attributes. Part of them c= an be considered as constrains. <o:p> </o:p> The optimization task for= d when I’ controlled attributes are changing on z is formulated as: <![if !vml]><img width=3D284 height=3D41 src=3D"CellularNetworks_files/image069.gif" v:shapes=3D"_x0000_i1061"><![en= dif]> = &nb= sp; = &nb= sp; = (12) The optimization of the a= ffected zone, which is made by varying the cell site z control attributes, is gover= ned by the following: <o:p> </o:p> <![if !vml]><img width=3D303 height=3D41 src=3D"CellularNetworks_files/image071.gif" v:shapes=3D"_x0000_i1062"><![en= dif]> = &nb= sp; = &nb= sp; = (13) <o:p> </o:p> Whole network decompositi= on can be achieved via a set M cell sites selected in such a way that: <o:p> </o:p> <![if !vml]><img width=3D225 height=3D36 src=3D"CellularNetworks_files/image073.gif" v:shapes=3D"_x0000_i1063"><![en= dif]> = = &nb= sp; = &nb= sp; = (14) <o:p> </o:p> When |M|=3D1 then decompo= sition is impossible. <o:p> </o:p> Total optimal network “goodness” value can be calculated as: <o:p> </o:p> opt&n= bsp; G =3D <![if !vml]><img width=3D33 height=3D36 src=3D"CellularNetworks_files/image075.gif" v:shapes=3D"_x0000_i1064"><![en= dif]>opt <![if !vml]><img width=3D21 height=3D23 src=3D"CellularNetworks_files/image077.gif" v:shapes=3D"_x0000_i1065"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; (15) <o:p> </o:p> It is possible that the n= etwork can be decomposed in several different ways. In this case we can define <su= b><![if !vml]><img width=3D41 height=3D17 src=3D"CellularNetworks_files/image079.gif" v:shapes=3D"_x0000_i1066"><![en= dif]>as an r-attem= pt of decomposition, <![if !vml]><img width=3D27 height=3D20 src=3D"CellularNetworks_files/image081.gif" v:shapes=3D"_x0000_i1067"><![en= dif]> as a set of= cell sites used in this attempt, and opt= <![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image083.gif" v:shapes=3D"_x0000_i1068"><![en= dif]> as correspo= nding total network “goodness” value. It is a logical to try to find<= /p> <o:p> </o:p> opt <![if !vml]><img width=3D17 height=3D23 src=3D"CellularNetworks_files/image085.gif" v:shapes=3D"_x0000_i1069"><![en= dif]>=3Dmax opt <s= ub><![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image083.gif" v:shapes=3D"_x0000_i1070"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; (16) <![if !vml]><img width=3D41 height=3D17 src=3D"CellularNetworks_files/image079.gif" v:shapes=3D"_x0000_i1071"><![en= dif]> where= opt <![if !vml]><img width=3D17 height=3D23 src=3D"CellularNetworks_files/image085.gif" v:shapes=3D"_x0000_i1072"><![en= dif]>is a best total network optimal “goodness” va= lue found during all decompositions. Because |D| can be significant, we shell limit our self to a reasonable number of attem= pts. <o:p> </o:p> Sometimes management task= is reduced to the adjustment of only one controlled attribute. Let’s consider th= is: to create an necessary effect <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image088.gif" v:shapes=3D"_x0000_i1073"><![en= dif]> on d (for example, to decrease a perc= ent of dropped calls on cell site) often a combination of changes made on a group = of cell sites <![if !vml]><img width=3D55 height=3D25 src=3D"CellularNetworks_files/image090.gif" v:shapes=3D"_x0000_i1074"><![en= dif]>is needed. We should consider that in this case quality attributes of cell sites that are outside of an affected zone can also be a= ffected. A set <![if !vml]><img width=3D25 height=3D25 src=3D"CellularNetworks_files/image092.gif" v:shapes=3D"_x0000_i1075"><![en= dif]> of possible solutions <![if !vml]><img width=3D91 height=3D27 src=3D"CellularNetworks_files/image094.gif" v:shapes=3D"_x0000_i1076"><![en= dif]>can be defined as: <o:p> </o:p> <![if !vml]><img width=3D444 height=3D29 src=3D"CellularNetworks_files/image096.gif" v:shapes=3D"_x0000_i1077"><![en= dif]> = &nb= sp; (17) = <![if !vml]><img width=3D33 height=3D25 src=3D"CellularNetworks_files/image098.gif" v:shapes=3D"_x0000_i1078"><![en= dif]> = &nb= sp; = <![if !vml]><img width=3D33 height=3D25 src=3D"CellularNetworks_files/image098.gif" v:shapes=3D"_x0000_i1079"><![en= dif]> <o:p> </o:p> where= <![if !vml]><img width=3D81 height=3D24 src=3D"CellularNetworks_files/image101.gif" v:shapes=3D"_x0000_i1080"><![en= dif]> is a third = order membership function of causes that are simultaneously created on cell sites= in the affected zone. This membership function shall reflect the non-linear na= ture of cellular networks; <![if !vml]><img width=3D59 height=3D25 src=3D"CellularNetworks_files/image103.gif" v:shapes=3D"_x0000_i1081"><![en= dif]>is a t constr= ain of a membership function of cell site <![if !vml]><img width=3D61 height=3D24 src=3D"CellularNetworks_files/image105.gif" v:shapes=3D"_x0000_i1082"><![en= dif]> is a tolera= nce threshold of quality attribute t</i= >. <o:p> </o:p> It is possible that<= !--[if gte vml 1]><v:shape id=3D"_x0000_i1083" type=3D"#_x0000_t75" style=3D'width:42.75pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image106.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D57 height=3D25 src=3D"CellularNetworks_files/image107.gif" v:shapes=3D"_x0000_i1083"><![en= dif]>. However, if <![if !vml]><img width=3D57 height=3D25 src=3D"CellularNetworks_files/image109.gif" v:shapes=3D"_x0000_i1084"><![en= dif]> and it cont= ains more then one solution, then a “goodness” value for every solut= ion can be calculated as: <o:p> </o:p> <![if !vml]><img width=3D224 height=3D37 src=3D"CellularNetworks_files/image111.gif" v:shapes=3D"_x0000_i1085"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; (18) (For the simplicity in th= is a equation we use <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image113.gif" v:shapes=3D"_x0000_i1086"><![en= dif]>to present weight coefficient for that desired effects and constraints, and <![if !vml]><img width=3D59 height=3D25 src=3D"CellularNetworks_files/image115.gif" v:shapes=3D"_x0000_i1087"><![en= dif]>to represent membership functions for the desired effects= and constrains.) The solution that provides a maximum value of <![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image117.gif" v:shapes=3D"_x0000_i1088"><![en= dif]>is a candidate for implementation. <o:p> </o:p> We should note that multiple causes created on a set of cells sites represent a general case. When only one con= trol attribute of a cell site is changing, then formulas need to be modified, ca= use membership functions A’ and <![if !vml]><img width=3D20 height=3D24 src=3D"CellularNetworks_files/image119.gif" v:shapes=3D"_x0000_i1089"><![en= dif]> should be replaced by <![if !vml]><img width=3D47 height=3D24 src=3D"CellularNetworks_files/image121.gif" v:shapes=3D"_x0000_i1090"><![en= dif]>, and effect membership function should be represented by= <![if !vml]><img width=3D56 height=3D25 src=3D"CellularNetworks_files/image039.gif" v:shapes=3D"_x0000_i1091"><![en= dif]>. <o:p> </o:p> Causes that produced a de= sired result on the consider cell site or in the effected zone should be used for creating reasoning rule(s) in the Decision Support Subsystem. <o:p> </o:p> 3. Conclusion<o:p></o:p> <o:p> </o:p> The soft approach is emer= ging now as a most promising direction in analysis and development of complex and no= n-stationary systems. Designed soft methodologies often have a generic nature and can be reused for application in areas other then for which they were developed. T= he decomposition and decision-making methodology proposed in this article can = be used in such different system as data communications, electrical and oil pi= pe networks, car traffic flows in major cities and so on. <o:p> </o:p> 4.References <o:p></o:p> <o:p> </o:p> [1] D.C Cox, D.O. Reudink. Dynamic Channel Assignme= nt in High-Capasity <st1:place>Mobile</st1:place> Communications Systems. The <st1:City><st1:place><s= pan class=3DGramE>Bell</st= 1:place></st1:City> System Technical Jou= rnal, Vol. 50#6, 1971. <o:p> </o:p> [2] T.J. Kahwa, N.D. Georganas. A Hybrid Channel Assignment Sch= eme in Large-Scale, Cellular-Structured <st1:place>Mobile</st1:place> Communication Systems, <st1:City><st1:place>Lund<= /i></st1:place></st1:City> Institute of Technology. Tech.Rep.,1986= . <o:p> </o:p> [3] = J.Karisson. Supplementary to a Cellular Mobile Telephone System wit= h Load Sharing. Department of Communication Systems.</s= pan> <st1:City><st1:place>Lund</st= 1:place></st1:City> Institute of Technol= ogy. Tech.Rep.,1= 986. <o:p> </o:p> [4] = J.Karisson, B.Eklundh. A Cellular Mobile Telephone System with Load Sharing – an Enhancement of Direct Retry.<= /span> IEEE Transactio= ns on Communications, Vol.37#5, 1989. <o:p> </o:p> [5] <st1:City><st1:place>= L.A.</st1:place></st1:City> Zadeh. The Concept of a Lin= guistic Variable and its Application to Approximate Reasoning. Information Sciences, 8 pp.199-249, 301-357 and 9 pp.43-80, = 1975 <o:p> </o:p> <o:p> </o:p> <o:p> </o:p> <o:p> </o:p> </div> </body> </html> ------=_NextPart_01C3DAB6.4179A4E0 Content-Location: file:///C:/2FA955D3/CellularNetworks_files/image001.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBYIOjAxMAJYn30ZQQxmM8yMjAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgcmBYICgFZamz8DFIM/0GKGQSA/ANA1jIgThBkYHgGNIwbqoaHwTexJCOksiCV gSEBbPdvJoX/EBdOAFnKwMLEIBCSmZtarOCXWq4QlJ+bmMew/ejx8gNArHDgVDkDgwEDC1CdLlA1 B5A24nrAWCkAcpKRCYx/kReVP48LZLQhnB/FgcpfzgJRj8U9TEAoEFyZm5Sfw1DuABTYyMGVh909 jGD6A5K7PvKDjNCF26PPhcqXZ4HwIfY2/MNn7x8mLh1c4QCxlxFqbwPjNB6QEYEmMH4NN7K9DYxq 7CC+G5zPxgbia8P518Hxb4sRHowkxQ9meMwCh0cJ3P83OFH5J5hR+Z8ZIHz08GEkMZ2gh88FPpAJ iXD/3gOnh3I4XxHsjio434cBwueCpmIucEoHJ1doGhZgYAfz9oDzBiMTk1JwZXFJai6Ix8WgyNAF VgwivnwWYth58Hg5ehgxg/UDALmDnFKwAwAA ------=_NextPart_01C3DAB6.4179A4E0 Content-Location: file:///C:/2FA955D3/CellularNetworks_files/image002.gif 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MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C3DAB6.4179A4E0" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C3DAB6.4179A4E0 Content-Location: file:///C:/2FA955D3/CellularNetworks.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Uncertainty and Management of Cellular Telephone Networks</= title> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"country-region"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"place"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"address"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"Street"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"City"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"State"/> <o:SmartTagType namespaceuri=3D"urn:schemas-microsoft-com:office:smarttags" name=3D"PostalCode"/>  <style>  </style>  </head> <body lang=3DEN-US style=3D'tab-interval:.5in'> <div class=3DSection1> Proceedings of the International F= uzzy Engineering Symposium ’91 = 220;Fuzzy Engineering toward Human Friendly Systems”.Vol.2. <st1:pla= ce><st1:City>Yokohama</st1:City>, <st1:country-region>Japan</st1:country-region></st1:place> 1991, pp.929-94= 3 <o:p> </o:p> Uncertainty and Management of Cellular Telephone Networks<o:p></o:p> <o:p> </o:p> = &nb= sp; = Ziny = Flikop<o:p></o:p> NYNEX Science = & Technology, Inc. <st1:address><st1:Street>500 Westchester Ave.</st1:Street>, <st1:City>White Plai= ns</st1:City>, <st1:State>NY</st1:State> <st1:PostalCode>10604</st1:PostalCode></st1:addr= ess> <o:p></o:p> <o:p> </o:p> Abstract<o:p></o:p> <o:p> </= o:p> This article discusses so= me aspects of the development of the management system for the Cellular teleph= one networks. The system is intended to analyze and optimize cellular network performance. Networks are considered as loosely coupled heterogeneous distributed nonstationary nonli= near statistics systems. Fuzzy sets terminology is used for the network analysis= . <o:p> </o:p> <ol style=3D'margin-top:0in' start=3D1 type=3D1> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l1 level1 lfo1; tab-stops:list .5in'>Introduc= tion<o:p></o:p></li> </ol> The first articles addres= sing cellular network performance analysis and optimization were published long before ac= tual full-scale cellular networks were created. For instance see [1,2]. Publication of such articles continues. For examp= le, see[3,4] However, the cellular network management prob= lem is so complex that is still very far from resolution. This article does not pretend to answer all questions but shell tried to discuss some problems, directions and suggestions that can bring to us close to the solution. <o:p> </o:p> Optimal design and measur= ement of the cellular radio network is a very complicated tesk<= /span>. This complexity is caused by a number of different factors. Major of which = are: <o:p> </o:p> <ol style=3D'margin-top:0in' start=3D1 type=3D1> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>Traffic varies from region to region and depends = on the sizes and shapes of service zones, the covered roads and the densi= ty of car traffic on them, the penetration of the cellular service and so= on.</li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'> In = turn, the service zones of the cell sites depend on power levels of the transmitters, the terrain, access thresholds, and other parameters.</l= i> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>Telephone traffic in the same region can fluctuate widely, depending on the time of day the day, the day of the week, the seasons of the year, car traffic conditions,= unusual events and so forth.</li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'> Cha= nnel assignment and = hand-off algorithms are designed to provide improved and reliable service. However, they create such a complicated call migration pattern that a mathematical m= odel that is adequate to real cellular networks has not yet been developed.= </li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>Distribution of telephone traffic in the system depends not only on size and shape of the services zones, but also on = the values of the different network attributes, such as hand-off threshold= s, directed retry assignments, biases and so on.</li> <li class=3DMsoNormal style=3D'text-align:justify;mso-list:l0 level1 lfo2; tab-stops:list .5in'>The results of cellular network analysis are valid only for a short period of time because real networks are in state of constant change.</li> </ol> 7. Cause-and-effect trials that are ma= de at the same time but in different regions can show different relationships bet= ween the same parameters. 8. Linear increments of the control attributes produce non-linear affects. 9. Cellular network is loosely couplet= distributed system. Of of this unwise is shows that only co= mpany hence if management system that considers all the above. This analysis shows that = only comprehensive management system that considers all the above described feat= ures can provide efficient management. To create a classical control loop the management system should be composed of three interrelated subsystems Monitoring, Decision Support and Executive. However, in this article we will only discuss problems relevant to the Decision Support Subsystem design. </= p> <o:p>&n= bsp;</o:p> <![if !supportLists]>2.<sp= an style=3D'font:7.0pt "Times New Roman"'> </spa= n><![endif]>Decision Support System<o:p></o:p></b= > This subsystem is an inte= lligent module or the Management system. It should study cellular network behavior, analyze its performance and provide a system engineer with the information = and tools that are necessary for the decision making. The size and complexity o= f real cellular networks is the reason that neither adequate hard (precise) models= nor comprehensive hard management methodology based on precise methods have yet been developed. This situation exists because the traditional modeling appr= oach requires significant simplification of real networks to allow the use of av= ailable theories. As a result models, proposed in the literature are inadequate to actual management tasks. To resolve these difficul= ties and keep simplification to the minimum, we suggest the use of soft (imprecise) models and soft management methodologies hat mimic a human reasoning for st= udy, modeling, and optimization. As an object for study we intend to use real networks. To avoid analysis of whole network we shall try to create a netwo= rk decomposition technique that take advantage of network looseness. <o:p>&n= bsp;</o:p> For the following discuss= ion, let’s introduce some definitions.<o:p></o:p> By sell side controlled attributes = we mean attributes that can be changed by an </span= >operator. They are, for example, access and hand-off thresholds, neighbor lists and t= ransmitted power levels. Attributes that that changing as a = result of changes made to control attributes, we will call sell site (network) con= trolled attributes. This attributes are: percent of successfully processed calls, blocking ratio, percent of dropped calls, percent of covered area with sufficient SNR, and so on. We should consider that the change = of the control attribute can produce changes of more than one controlled attribute= s. The same change of controlled attribute can be a result of changes of different= control attributes. To achieve a desi= red change of a controlled attribute sometimes a set of control attributes of a number= of cell sites have to be changed. For the network modeling, decomposi= tion, management and optimization we need to know how changes of control attribut= es are mapped to changes of controlled attributes. This mapping reflects all t= he complexities and uncertainties cellular network behavior and constitute a m= ajor problem in the whole management task. As a possible solution to the problem= of mapping analysis we propose to use a cause-and-effect approach. It can be executed = either via preplanned changes of control attributes in the real network or by a mo= nitoring disturbances created in network by external sources with simultaneous evaluation of hollow controlled attribute became affected. (An example of disturbance is a cel= l site equipment failure.) <o:p> </o:p> Measurement of controlled attributes is a difficult task sense they are non-0stationery and noisy. For the filtration of a noise, we can recommend using seasonal time series anal= ysis forecasting algorithm because variations of majority of attributes contain a periodical component of the. In this approach, noise can be a partially filtered when real data are substituted with forecasted values. Good results can be achieved via model developed in corporation with Dr. A. Pankratz. </sp= an>In this model a one-hour-ahead forecast of a value of attribute z at hour t is calculated as: <o:p> </o:p> <![if !vml]><img width=3D188 height=3D24 src=3D"CellularNetworks_files/image002.gif" v:shapes=3D"_x0000_i1025"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; (1) <o:p> </o:p> where= : <![if !vml]><img width=3D17 height=3D16 src=3D"CellularNetworks_files/image004.gif" v:shapes=3D"_x0000_i1026"><![en= dif]>and <![if !vml]><img width=3D17 height=3D19 src=3D"CellularNetworks_files/image006.gif" v:shapes=3D"_x0000_i1027"><![en= dif]>are weight coefficients.= They are recalculated each time when new data are received. Calculat= ions are made via an optimization procedure aimed to minimize <o:p> </o:p> <![if !vml]><img width=3D65 height=3D45 src=3D"CellularNetworks_files/image008.gif" v:shapes=3D"_x0000_i1028"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; (2) <o:p> </o:p> One-step-ahead backward f= orecasts <o:p> </o:p> <![if !vml]><img width=3D168 height=3D24 src=3D"CellularNetworks_files/image010.gif" v:shapes=3D"_x0000_i1029"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (3) <o:p> </o:p> One-step-ahead forward er= rors <o:p> </o:p> <![if !vml]><img width=3D171 height=3D24 src=3D"CellularNetworks_files/image012.gif" v:shapes=3D"_x0000_i1030"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (4) <o:p> </o:p> One-step-ahead backward e= rrors <o:p> </o:p> <![if !vml]><img width=3D168 height=3D24 src=3D"CellularNetworks_files/image014.gif" v:shapes=3D"_x0000_i1031"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (5) <o:p> </o:p> Our experience shows ther= e for forecasting, a history of constantly moving 240 hours values can be conside= red sufficient. Even though some noise can be filtrated, the results of measurements of controlled attributes will still be uncertain. Mapping and measuring problems are a justification (from our point of view) for using s= oft methods for network analysis. As a descriptive and analytical tool we have chosen a Fuzzy Sets theory [5]. <o:p> </o:p> Network studies should st= art with preliminary self-educational phase, during which sufficient cause-and-effect data have been accumulated. After this phase we can start our analysis with= decomposition problem. Assume S is a set of all cell sites in the network; <![if !vml]><img width=3D25 height=3D24 src=3D"CellularNetworks_files/image016.gif" v:shapes=3D"_x0000_i1032"><![en= dif]> is a value = of a control attribute <![if !vml]><img width=3D49 height=3D21 src=3D"CellularNetworks_files/image018.gif" v:shapes=3D"_x0000_i1033"><![en= dif]> of cell sit= e<![if !vml]><img width=3D39 height=3D19 src=3D"CellularNetworks_files/image020.gif" v:shapes=3D"_x0000_i1034"><![en= dif]>; <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image022.gif" v:shapes=3D"_x0000_i1035"><![en= dif]> - is a valu= e of a controlled attribute <![if !vml]><img width=3D59 height=3D21 src=3D"CellularNetworks_files/image024.gif" v:shapes=3D"_x0000_i1036"><![en= dif]> of a cell s= ite<![if !vml]><img width=3D41 height=3D19 src=3D"CellularNetworks_files/image026.gif" v:shapes=3D"_x0000_i1037"><![en= dif]>; and <![if !vml]><img width=3D92 height=3D25 src=3D"CellularNetworks_files/image028.gif" v:shapes=3D"_x0000_i1038"><![en= dif]> are corresp= onding membership functions. (Using membership functions instead of precise values will provide the necessary “softness” in our studies. <o:p> </o:p> Decomposition can be base= d on the concept of an affected zone. For simplicity, let’s from now on consider <![if !vml]><img width=3D25 height=3D24 src=3D"CellularNetworks_files/image016.gif" v:shapes=3D"_x0000_i1039"><![en= dif]> as a value = of a change of a control attribute I= of cell site z (it is a cause) and= <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image022.gif" v:shapes=3D"_x0000_i1040"><![en= dif]> as a value = of a change of a controlled attribute j<= /i> of a cell site d (effect). We also= will consider <![if !vml]><img width=3D92 height=3D25 src=3D"CellularNetworks_files/image028.gif" v:shapes=3D"_x0000_i1041"><![en= dif]> as correspo= nding cause-and-effect membership functions. <o:p> </o:p> Because of looseness, eff= ects die out when they propagate. Let’s assume that <![if !vml]><img width=3D19 height=3D25 src=3D"CellularNetworks_files/image031.gif" v:shapes=3D"_x0000_i1042"><![en= dif]> is a tolera= ted threshold value of an attribute j</= i>. Then a subset <![if !vml]><img width=3D63 height=3D25 src=3D"CellularNetworks_files/image033.gif" v:shapes=3D"_x0000_i1043"><![en= dif]> of cell sit= es (<![if !vml]><img width=3D20 height=3D25 src=3D"CellularNetworks_files/image035.gif" v:shapes=3D"_x0000_i1044"><![en= dif]>- affected zone) producing effect j in response to the cause i created on z</= i>, can be defined as follows: <o:p> </o:p> <![if !vml]><img width=3D267 height=3D25 src=3D"CellularNetworks_files/image037.gif" v:shapes=3D"_x0000_i1045"><![en= dif]> = &nb= sp; = &nb= sp; = (6) <o:p> </o:p> where= <![if !vml]><img width=3D56 height=3D25 src=3D"CellularNetworks_files/image039.gif" v:shapes=3D"_x0000_i1046"><![en= dif]> is a member= ship function of an effect j generat= ed on d by cause I created on z. <o:p> </o:p> When one cause can genera= te multiple effects, then <![if !vml]><img width=3D16 height=3D24 src=3D"CellularNetworks_files/image041.gif" v:shapes=3D"_x0000_i1047"><![en= dif]>-affected zone is defined as <o:p> </o:p> <![if !vml]><img width=3D35 height=3D24 src=3D"CellularNetworks_files/image043.gif" v:shapes=3D"_x0000_i1048"><![en= dif]><![if !vml]><img width=3D51 height=3D39 src=3D"CellularNetworks_files/image045.gif" v:shapes=3D"_x0000_i1049"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = = </s= pan>(7) <o:p> </o:p> If a number of causes (<s= ub><![if !vml]><img width=3D45 height=3D23 src=3D"CellularNetworks_files/image047.gif" v:shapes=3D"_x0000_i1050"><![en= dif]> are generated simultaneously on z (system engineers of cellular networks often make multiple ch= anges) then z’-affected zone is:= <o:p> </o:p> <o:p> </o:p> <![if !vml]><img width=3D297 height=3D39 src=3D"CellularNetworks_files/image049.gif" v:shapes=3D"_x0000_i1051"><![en= dif]> = &nb= sp; = &nb= sp; (8) <o:p> </o:p> where <![if !vml]><img width=3D101 height=3D24 src=3D"CellularNetworks_files/image051.gif" v:shapes=3D"_x0000_i1052"><![en= dif]> is a second= order membership function of causes created simultaneously on z; <![if !vml]><img width=3D159 height=3D25 src=3D"CellularNetworks_files/image053.gif" v:shapes=3D"_x0000_i1053"><![en= dif]>is a set of membership functions of causes created simultaneously on z; <![if !vml]><img width=3D60 height=3D28 src=3D"CellularNetworks_files/image055.gif" v:shapes=3D"_x0000_i1054"><![en= dif]> is a member= ship function of j effect generated = on d by causes I’ and created on z. Both membership functions in (8) consider the fact, that since networks are non-linear, resulting j-type ef= fect can be equal to, more than or less than a sum of partial effects of j-type generated on d by different causes and are created on z. <o:p> </o:p> The maximal size of the a= ffected zone <![if !vml]><img width=3D19 height=3D23 src=3D"CellularNetworks_files/image057.gif" v:shapes=3D"_x0000_i1055"><![en= dif]> will be whe= n I’=3DI. In this case = &nb= sp; <![if !vml]><img width=3D51 height=3D24 src=3D"CellularNetworks_files/image059.gif" v:shapes=3D"_x0000_i1056"><![en= dif]> = &nb= sp; = = &nb= sp; = &nb= sp; = (9) <o:p> </o:p> To evaluate and optimize = network performance and also to organize adaptability properties for the management system, a soft criterion (“goodness”) for the affected zone is proposed. (We do not discuss an adaptability issue in this article.) <o:p> </o:p> Goodness value <![if !vml]><img width=3D25 height=3D25 src=3D"CellularNetworks_files/image061.gif" v:shapes=3D"_x0000_i1057"><![en= dif]> generated o= n cell site d by I’ causes created on z. is as follows: <o:p> </o:p> <![if !vml]><img width=3D208 height=3D35 src=3D"CellularNetworks_files/image063.gif" v:shapes=3D"_x0000_i1058"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = (10) <o:p> </o:p> When <![if !vml]><img width=3D81 height=3D25 src=3D"CellularNetworks_files/image065.gif" v:shapes=3D"_x0000_i1059"><![en= dif]>is a weight coefficient of the j-th<= /span> parameter. = ; Coefficients of this kind are usually the result of surveys made in = cellular telephone company and they represent subjecti= ve of imprecise collective opinion of different company representatives. This fact also justifies use of soft methods in the network optimization. <o:p> </o:p> The affected zone goodness value th= at is gained via I</i= >’ causes created on z is:<o:p></o:p> <o:p> </o:p> <![if !vml]><img width=3D84 height=3D39 src=3D"CellularNetworks_files/image067.gif" v:shapes=3D"_x0000_i1060"><![en= dif]> = &nb= sp; = = &nb= sp; = &nb= sp; = &nb= sp; (11) <o:p> </o:p> A set of the affected con= trolled attributes contains all cellular service quality attributes. Part of them c= an be considered as constrains. <o:p> </o:p> The optimization task for= d when I’ controlled attributes are changing on z is formulated as: <![if !vml]><img width=3D284 height=3D41 src=3D"CellularNetworks_files/image069.gif" v:shapes=3D"_x0000_i1061"><![en= dif]> = &nb= sp; = &nb= sp; = (12) The optimization of the a= ffected zone, which is made by varying the cell site z control attributes, is gover= ned by the following: <o:p> </o:p> <![if !vml]><img width=3D303 height=3D41 src=3D"CellularNetworks_files/image071.gif" v:shapes=3D"_x0000_i1062"><![en= dif]> = &nb= sp; = &nb= sp; = (13) <o:p> </o:p> Whole network decompositi= on can be achieved via a set M cell sites selected in such a way that: <o:p> </o:p> <![if !vml]><img width=3D225 height=3D36 src=3D"CellularNetworks_files/image073.gif" v:shapes=3D"_x0000_i1063"><![en= dif]> = = &nb= sp; = &nb= sp; = (14) <o:p> </o:p> When |M|=3D1 then decompo= sition is impossible. <o:p> </o:p> Total optimal network “goodness” value can be calculated as: <o:p> </o:p> opt&n= bsp; G =3D <![if !vml]><img width=3D33 height=3D36 src=3D"CellularNetworks_files/image075.gif" v:shapes=3D"_x0000_i1064"><![en= dif]>opt <![if !vml]><img width=3D21 height=3D23 src=3D"CellularNetworks_files/image077.gif" v:shapes=3D"_x0000_i1065"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; (15) <o:p> </o:p> It is possible that the n= etwork can be decomposed in several different ways. In this case we can define <su= b><![if !vml]><img width=3D41 height=3D17 src=3D"CellularNetworks_files/image079.gif" v:shapes=3D"_x0000_i1066"><![en= dif]>as an r-attem= pt of decomposition, <![if !vml]><img width=3D27 height=3D20 src=3D"CellularNetworks_files/image081.gif" v:shapes=3D"_x0000_i1067"><![en= dif]> as a set of= cell sites used in this attempt, and opt= <![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image083.gif" v:shapes=3D"_x0000_i1068"><![en= dif]> as correspo= nding total network “goodness” value. It is a logical to try to find<= /p> <o:p> </o:p> opt <![if !vml]><img width=3D17 height=3D23 src=3D"CellularNetworks_files/image085.gif" v:shapes=3D"_x0000_i1069"><![en= dif]>=3Dmax opt <s= ub><![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image083.gif" v:shapes=3D"_x0000_i1070"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; = &nb= sp; (16) <![if !vml]><img width=3D41 height=3D17 src=3D"CellularNetworks_files/image079.gif" v:shapes=3D"_x0000_i1071"><![en= dif]> where= opt <![if !vml]><img width=3D17 height=3D23 src=3D"CellularNetworks_files/image085.gif" v:shapes=3D"_x0000_i1072"><![en= dif]>is a best total network optimal “goodness” va= lue found during all decompositions. Because |D| can be significant, we shell limit our self to a reasonable number of attem= pts. <o:p> </o:p> Sometimes management task= is reduced to the adjustment of only one controlled attribute. Let’s consider th= is: to create an necessary effect <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image088.gif" v:shapes=3D"_x0000_i1073"><![en= dif]> on d (for example, to decrease a perc= ent of dropped calls on cell site) often a combination of changes made on a group = of cell sites <![if !vml]><img width=3D55 height=3D25 src=3D"CellularNetworks_files/image090.gif" v:shapes=3D"_x0000_i1074"><![en= dif]>is needed. We should consider that in this case quality attributes of cell sites that are outside of an affected zone can also be a= ffected. A set <![if !vml]><img width=3D25 height=3D25 src=3D"CellularNetworks_files/image092.gif" v:shapes=3D"_x0000_i1075"><![en= dif]> of possible solutions <![if !vml]><img width=3D91 height=3D27 src=3D"CellularNetworks_files/image094.gif" v:shapes=3D"_x0000_i1076"><![en= dif]>can be defined as: <o:p> </o:p> <![if !vml]><img width=3D444 height=3D29 src=3D"CellularNetworks_files/image096.gif" v:shapes=3D"_x0000_i1077"><![en= dif]> = &nb= sp; (17) = <![if !vml]><img width=3D33 height=3D25 src=3D"CellularNetworks_files/image098.gif" v:shapes=3D"_x0000_i1078"><![en= dif]> = &nb= sp; = <![if !vml]><img width=3D33 height=3D25 src=3D"CellularNetworks_files/image098.gif" v:shapes=3D"_x0000_i1079"><![en= dif]> <o:p> </o:p> where= <![if !vml]><img width=3D81 height=3D24 src=3D"CellularNetworks_files/image101.gif" v:shapes=3D"_x0000_i1080"><![en= dif]> is a third = order membership function of causes that are simultaneously created on cell sites= in the affected zone. This membership function shall reflect the non-linear na= ture of cellular networks; <![if !vml]><img width=3D59 height=3D25 src=3D"CellularNetworks_files/image103.gif" v:shapes=3D"_x0000_i1081"><![en= dif]>is a t constr= ain of a membership function of cell site <![if !vml]><img width=3D61 height=3D24 src=3D"CellularNetworks_files/image105.gif" v:shapes=3D"_x0000_i1082"><![en= dif]> is a tolera= nce threshold of quality attribute t</i= >. <o:p> </o:p> It is possible that<= !--[if gte vml 1]><v:shape id=3D"_x0000_i1083" type=3D"#_x0000_t75" style=3D'width:42.75pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image106.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D57 height=3D25 src=3D"CellularNetworks_files/image107.gif" v:shapes=3D"_x0000_i1083"><![en= dif]>. However, if <![if !vml]><img width=3D57 height=3D25 src=3D"CellularNetworks_files/image109.gif" v:shapes=3D"_x0000_i1084"><![en= dif]> and it cont= ains more then one solution, then a “goodness” value for every solut= ion can be calculated as: <o:p> </o:p> <![if !vml]><img width=3D224 height=3D37 src=3D"CellularNetworks_files/image111.gif" v:shapes=3D"_x0000_i1085"><![en= dif]> = &nb= sp; = &nb= sp; = &nb= sp; (18) (For the simplicity in th= is a equation we use <![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image113.gif" v:shapes=3D"_x0000_i1086"><![en= dif]>to present weight coefficient for that desired effects and constraints, and <![if !vml]><img width=3D59 height=3D25 src=3D"CellularNetworks_files/image115.gif" v:shapes=3D"_x0000_i1087"><![en= dif]>to represent membership functions for the desired effects= and constrains.) The solution that provides a maximum value of <![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image117.gif" v:shapes=3D"_x0000_i1088"><![en= dif]>is a candidate for implementation. <o:p> </o:p> We should note that multiple causes created on a set of cells sites represent a general case. When only one con= trol attribute of a cell site is changing, then formulas need to be modified, ca= use membership functions A’ and <![if !vml]><img width=3D20 height=3D24 src=3D"CellularNetworks_files/image119.gif" v:shapes=3D"_x0000_i1089"><![en= dif]> should be replaced by <![if !vml]><img width=3D47 height=3D24 src=3D"CellularNetworks_files/image121.gif" v:shapes=3D"_x0000_i1090"><![en= dif]>, and effect membership function should be represented by= <![if !vml]><img width=3D56 height=3D25 src=3D"CellularNetworks_files/image039.gif" v:shapes=3D"_x0000_i1091"><![en= dif]>. <o:p> </o:p> Causes that produced a de= sired result on the consider cell site or in the effected zone should be used for creating reasoning rule(s) in the Decision Support Subsystem. <o:p> </o:p> 3. Conclusion<o:p></o:p> <o:p> </o:p> The soft approach is emer= ging now as a most promising direction in analysis and development of complex and no= n-stationary systems. Designed soft methodologies often have a generic nature and can be reused for application in areas other then for which they were developed. T= he decomposition and decision-making methodology proposed in this article can = be used in such different system as data communications, electrical and oil pi= pe networks, car traffic flows in major cities and so on. <o:p> </o:p> 4.References <o:p></o:p> <o:p> </o:p> [1] D.C Cox, D.O. Reudink. Dynamic Channel Assignme= nt in High-Capasity <st1:place>Mobile</st1:place> Communications Systems. The <st1:City><st1:place><s= pan class=3DGramE>Bell</st= 1:place></st1:City> System Technical Jou= rnal, Vol. 50#6, 1971. <o:p> </o:p> [2] T.J. Kahwa, N.D. Georganas. A Hybrid Channel Assignment Sch= eme in Large-Scale, Cellular-Structured <st1:place>Mobile</st1:place> Communication Systems, <st1:City><st1:place>Lund<= /i></st1:place></st1:City> Institute of Technology. Tech.Rep.,1986= . <o:p> </o:p> [3] = J.Karisson. Supplementary to a Cellular Mobile Telephone System wit= h Load Sharing. Department of Communication Systems.</s= pan> <st1:City><st1:place>Lund</st= 1:place></st1:City> Institute of Technol= ogy. Tech.Rep.,1= 986. <o:p> </o:p> [4] = J.Karisson, B.Eklundh. A Cellular Mobile Telephone System with Load Sharing – an Enhancement of Direct Retry.<= /span> IEEE Transactio= ns on Communications, Vol.37#5, 1989. <o:p> </o:p> [5] <st1:City><st1:place>= L.A.</st1:place></st1:City> Zadeh. The Concept of a Lin= guistic Variable and its Application to Approximate Reasoning. Information Sciences, 8 pp.199-249, 301-357 and 9 pp.43-80, = 1975 <o:p> </o:p> <o:p> </o:p> <o:p> </o:p> <o:p> </o:p> </div> </body> </html> ------=_NextPart_01C3DAB6.4179A4E0 Content-Location: file:///C:/2FA955D3/CellularNetworks_files/image001.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBYIOjAxMAJYn30ZQQxmM8yMjAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgcmBYICgFZamz8DFIM/0GKGQSA/ANA1jIgThBkYHgGNIwbqoaHwTexJCOksiCV gSEBbPdvJoX/EBdOAFnKwMLEIBCSmZtarOCXWq4QlJ+bmMew/ejx8gNArHDgVDkDgwEDC1CdLlA1 B5A24nrAWCkAcpKRCYx/kReVP48LZLQhnB/FgcpfzgJRj8U9TEAoEFyZm5Sfw1DuABTYyMGVh909 jGD6A5K7PvKDjNCF26PPhcqXZ4HwIfY2/MNn7x8mLh1c4QCxlxFqbwPjNB6QEYEmMH4NN7K9DYxq 7CC+G5zPxgbia8P518Hxb4sRHowkxQ9meMwCh0cJ3P83OFH5J5hR+Z8ZIHz08GEkMZ2gh88FPpAJ iXD/3gOnh3I4XxHsjio434cBwueCpmIucEoHJ1doGhZgYAfz9oDzBiMTk1JwZXFJai6Ix8WgyNAF VgwivnwWYth58Hg5ehgxg/UDALmDnFKwAwAA ------=_NextPart_01C3DAB6.4179A4E0 Content-Location: file:///C:/2FA955D3/CellularNetworks_files/image002.gif 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