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"/> <!--[if gte mso 9]><xml> <o:DocumentProperties> <o:Author>Ziny Flikop</o:Author> <o:Template>Normal</o:Template> <o:LastAuthor>Ziny Flikop</o:LastAuthor> <o:Revision>2</o:Revision> <o:TotalTime>10</o:TotalTime> <o:Created>2004-01-14T20:51:00Z</o:Created> <o:LastSaved>2004-01-14T20:51:00Z</o:LastSaved> <o:Pages>1</o:Pages> <o:Words>2615</o:Words> <o:Characters>14911</o:Characters> <o:Company> self</o:Company> <o:Lines>124</o:Lines> <o:Paragraphs>34</o:Paragraphs> <o:CharactersWithSpaces>17492</o:CharactersWithSpaces> <o:Version>10.4219</o:Version> </o:DocumentProperties> </xml><![endif]--><!--[if gte mso 9]><xml> <w:WordDocument> <w:SpellingState>Clean</w:SpellingState> <w:GrammarState>Clean</w:GrammarState> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if !mso]><object classid=3D"clsid:38481807-CA0E-42D2-BF39-B33AF135CC4D" id=3Dieooui></objec= t> <style> st1\:*{behavior:url(#ieooui) } </style> <![endif]--> <style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} span.SpellE {mso-style-name:""; mso-spl-e:yes;} span.GramE {mso-style-name:""; mso-gram-e:yes;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} /* List Definitions */ @list l0 {mso-list-id:1517696795; mso-list-type:hybrid; mso-list-template-ids:1369050762 67698703 67698713 67698715 67698703 67698= 713 67698715 67698703 67698713 67698715;} @list l0:level1 {mso-level-tab-stop:.5in; mso-level-number-position:left; text-indent:-.25in;} @list l1 {mso-list-id:1791707182; mso-list-type:hybrid; mso-list-template-ids:2051184220 67698703 67698713 67698715 67698703 67698= 713 67698715 67698703 67698713 67698715;} @list l1:level1 {mso-level-tab-stop:.5in; mso-level-number-position:left; text-indent:-.25in;} @list l2 {mso-list-id:1957907022; 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The system is intended to analyze and optimize cellular network performance.<span style=3D'mso-spacerun:yes'>  </span>Networks are considered as loosely coupled heterogeneous distributed nonstationary nonli= near statistics systems. Fuzzy sets terminology is used for the network analysis= .</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></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'><b style=3D'mso-bidi-font-weight:normal'>Introduc= tion<o:p></o:p></b></li> </ol> <p class=3DMsoNormal style=3D'text-align:justify'>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<span class=3DGramE>,2</span>]. Publication of such articles continues. For examp= le, <span class=3DGramE>see[</span>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>Optimal design and measur= ement of the cellular radio network is a very complicated <span class=3DSpellE>tesk<= /span>. This complexity is caused by a number of different factors. Major of which = are:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></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'><span style=3D'mso-spacerun:yes'> </span>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<span class=3DGramE>, <span style=3D'mso-spacerun:yes'> </span>car</span> 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'><span style=3D'mso-spacerun:yes'> </span>Cha= nnel assignment <span class=3DGramE>and <span style=3D'mso-spacerun:yes'> </span>= hand</span>-off algorithms are designed to provide improved and <span style=3D'mso-spacerun:yes'> </span>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> <p class=3DMsoNormal style=3D'text-align:justify'>7. <span style=3D'mso-spacerun:yes'> </span>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'>8.<span style=3D'mso-spacerun:yes'>  </span><span style=3D'mso-spacerun:yes'> </span>Linear increments of the control attributes produce non-linear affects.</p> <p class=3DMsoNormal style=3D'text-align:justify'>9. <span style=3D'mso-spacerun:yes'> </span>Cellular network is loosely couplet= distributed system. Of <span class=3DSpellE>of</span> this unwise is shows that only co= mpany hence if management system that considers all the above.</p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span></p> <p class=3DMsoNormal style=3D'text-align:justify'>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> <p class=3DMsoNormal style=3D'margin-left:.25in;text-align:justify'><o:p>&n= bsp;</o:p></p> <p class=3DMsoNormal style=3D'margin-left:.5in;text-align:justify;text-inde= nt:-.5in; mso-list:l1 level1 lfo1;tab-stops:list .25in'><![if !supportLists]><b style=3D'mso-bidi-font-weight:normal'><span style=3D'mso-list:Ignore'>2.<sp= an style=3D'font:7.0pt "Times New Roman"'>      </spa= n></span></b><![endif]><b style=3D'mso-bidi-font-weight:normal'>Decision Support System<o:p></o:p></b= ></p> <p class=3DMsoNormal style=3D'text-align:justify'>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'>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. <span style=3D'mso-spacerun:yes'> </span>As a result models, proposed in the literature are inadequate to actual management tasks.</p> <p class=3DMsoNormal style=3D'text-align:justify'>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.</p> <p class=3DMsoNormal style=3D'margin-left:.25in;text-align:justify'><o:p>&n= bsp;</o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>For the following discuss= ion, let’s introduce some definitions.<o:p></o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'>      </span></p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>By sell side controlled attributes = we mean attributes that can be changed by an <span style=3D'mso-spacerun:yes'>       </span= >operator. They are, for example, access and hand-off thresholds, neighbor lists and t= ransmitted power levels.</p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>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. <span style=3D'mso-spacerun:yes'> </span>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>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. <span style=3D'mso-spacerun:yes'> </span>(An example of disturbance is a cel= l site equipment failure.)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>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. <span class=3DSpellE>Pankratz</span>. <span style=3D'mso-spacerun:yes'> </sp= an>In this model a one-hour-ahead forecast of a value of attribute <i style=3D'mso-bidi-font-style:normal'>z</i> at hour <i style=3D'mso-bidi-fon= t-style: normal'>t</i> is calculated as: </p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative= =3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" stroked=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum @0 0 1"/> <v:f eqn=3D"prod @6 1 2"/> <v:f eqn=3D"prod @7 21600 pixelWidth"/> <v:f eqn=3D"sum @8 21600 0"/> <v:f eqn=3D"prod @7 21600 pixelHeight"/> <v:f eqn=3D"sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok=3D"f" gradientshapeok=3D"t" o:connecttype=3D"rect"/> <o:lock v:ext=3D"edit" aspectratio=3D"t"/> </v:shapetype><v:shape id=3D"_x0000_i1025" type=3D"#_x0000_t75" style=3D'wi= dth:141pt; height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image001.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D188 height=3D24 src=3D"CellularNetworks_files/image002.gif" v:shapes=3D"_x0000_i1025"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1025" DrawAspect=3D"Content" ObjectID=3D"_1135600648"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;     </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;        </span>(1)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE>where= </span>:</p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1026" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:12p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image003.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D17 height=3D16 src=3D"CellularNetworks_files/image004.gif" v:shapes=3D"_x0000_i1026"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1026" DrawAspect=3D"Content" ObjectID=3D"_1135600649"> </o:OLEObject> </xml><![endif]--><span class=3DGramE>and</span> <sub><!--[if gte vml 1]><v= :shape id=3D"_x0000_i1027" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:14.= 25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image005.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D17 height=3D19 src=3D"CellularNetworks_files/image006.gif" v:shapes=3D"_x0000_i1027"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1027" DrawAspect=3D"Content" ObjectID=3D"_1135600650"> </o:OLEObject> </xml><![endif]-->are weight coefficients.<span style=3D'mso-spacerun:yes'>=   </span>They are recalculated each time when new data are received. Calculat= ions are made via an optimization procedure aimed to minimize</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1028" type=3D"#_x0000_t75" style=3D'width:48.75pt;height:33.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image007.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D65 height=3D45 src=3D"CellularNetworks_files/image008.gif" v:shapes=3D"_x0000_i1028"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1028" DrawAspect=3D"Content" ObjectID=3D"_1135600651"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;       </span>(2)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>One-step-ahead backward f= orecasts</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1029" type=3D"#_x0000_t75" style=3D'width:126pt;height:18pt'= o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image009.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D168 height=3D24 src=3D"CellularNetworks_files/image010.gif" v:shapes=3D"_x0000_i1029"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1029" DrawAspect=3D"Content" ObjectID=3D"_1135600652"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =    </span>(3)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>One-step-ahead forward er= rors</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1030" type=3D"#_x0000_t75" style=3D'width:128.25pt;height:18= pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image011.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D171 height=3D24 src=3D"CellularNetworks_files/image012.gif" v:shapes=3D"_x0000_i1030"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1030" DrawAspect=3D"Content" ObjectID=3D"_1135600653"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =   </span>(4)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>One-step-ahead backward e= rrors</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1031" type=3D"#_x0000_t75" style=3D'width:126pt;height:18pt'= o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image013.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D168 height=3D24 src=3D"CellularNetworks_files/image014.gif" v:shapes=3D"_x0000_i1031"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1031" DrawAspect=3D"Content" ObjectID=3D"_1135600654"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =    </span>(5)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>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].</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>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= <i style=3D'mso-bidi-font-style:normal'>decomposition</i> problem. Assume <i style=3D'mso-bidi-font-style:normal'>S</i> is a set of all cell sites in the network; <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1032" type=3D"#_x00= 00_t75" style=3D'width:18.75pt;height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image015.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D25 height=3D24 src=3D"CellularNetworks_files/image016.gif" v:shapes=3D"_x0000_i1032"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1032" DrawAspect=3D"Content" ObjectID=3D"_1135600655"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>is a value = of a control attribute <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1033" type= =3D"#_x0000_t75" style=3D'width:36.75pt;height:15.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image017.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D49 height=3D21 src=3D"CellularNetworks_files/image018.gif" v:shapes=3D"_x0000_i1033"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1033" DrawAspect=3D"Content" ObjectID=3D"_1135600656"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>of cell sit= e<sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1034" type=3D"#_x0000_t75" style=3D'width:29.25pt;height:14.= 25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image019.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D39 height=3D19 src=3D"CellularNetworks_files/image020.gif" v:shapes=3D"_x0000_i1034"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1034" DrawAspect=3D"Content" ObjectID=3D"_1135600657"> </o:OLEObject> </xml><![endif]-->; <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1035" ty= pe=3D"#_x0000_t75" style=3D'width:17.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image021.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image022.gif" v:shapes=3D"_x0000_i1035"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1035" DrawAspect=3D"Content" ObjectID=3D"_1135600658"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>- is a valu= e of a controlled attribute <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1036" t= ype=3D"#_x0000_t75" style=3D'width:44.25pt;height:15.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image023.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D59 height=3D21 src=3D"CellularNetworks_files/image024.gif" v:shapes=3D"_x0000_i1036"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1036" DrawAspect=3D"Content" ObjectID=3D"_1135600659"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>of a cell s= ite<sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1037" type=3D"#_x0000_t75" style=3D'width:30.75pt;height:14.= 25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image025.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D41 height=3D19 src=3D"CellularNetworks_files/image026.gif" v:shapes=3D"_x0000_i1037"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1037" DrawAspect=3D"Content" ObjectID=3D"_1135600660"> </o:OLEObject> </xml><![endif]-->; and <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1038" type=3D"#_x0000_t75" style=3D'width:69pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image027.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D92 height=3D25 src=3D"CellularNetworks_files/image028.gif" v:shapes=3D"_x0000_i1038"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1038" DrawAspect=3D"Content" ObjectID=3D"_1135600661"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>are corresp= onding membership functions. (Using membership functions instead of precise values will provide the necessary “softness” in our studies.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>Decomposition can be base= d on the concept of an <i style=3D'mso-bidi-font-style:normal'>affected</i> zone. For simplicity, let’s from now on consider <sub><!--[if gte vml 1]><v:sha= pe id=3D"_x0000_i1039" type=3D"#_x0000_t75" style=3D'width:18.75pt;height:18p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image029.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D25 height=3D24 src=3D"CellularNetworks_files/image016.gif" v:shapes=3D"_x0000_i1039"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1039" DrawAspect=3D"Content" ObjectID=3D"_1135600662"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>as a value = of a change of a control attribute <i style=3D'mso-bidi-font-style:normal'>I</i>= of cell site <i style=3D'mso-bidi-font-style:normal'>z</i> (it is a cause) and= <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1040" type=3D"#_x0000_t75" style=3D'width:17.25pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image021.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image022.gif" v:shapes=3D"_x0000_i1040"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1040" DrawAspect=3D"Content" ObjectID=3D"_1135600663"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>as a value = of a change of a controlled attribute <i style=3D'mso-bidi-font-style:normal'>j<= /i> of a cell site <i style=3D'mso-bidi-font-style:normal'>d</i> (effect). We also= will consider <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1041" type=3D"#_x00= 00_t75" style=3D'width:69pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image027.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D92 height=3D25 src=3D"CellularNetworks_files/image028.gif" v:shapes=3D"_x0000_i1041"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1041" DrawAspect=3D"Content" ObjectID=3D"_1135600664"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>as correspo= nding cause-and-effect membership functions.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>Because of looseness, eff= ects die out when they propagate. Let’s assume that <sub><!--[if gte vml 1]><v= :shape id=3D"_x0000_i1042" type=3D"#_x0000_t75" style=3D'width:14.25pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image030.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D19 height=3D25 src=3D"CellularNetworks_files/image031.gif" v:shapes=3D"_x0000_i1042"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1042" DrawAspect=3D"Content" ObjectID=3D"_1135600665"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>is a tolera= ted threshold value of an attribute <i style=3D'mso-bidi-font-style:normal'>j</= i>. Then a subset <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1043" type=3D"= #_x0000_t75" style=3D'width:47.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image032.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D63 height=3D25 src=3D"CellularNetworks_files/image033.gif" v:shapes=3D"_x0000_i1043"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1043" DrawAspect=3D"Content" ObjectID=3D"_1135600666"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>of cell sit= es (<sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1044" type=3D"#_x0000_t75" style=3D'width:15pt;height:18.75p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image034.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D25 src=3D"CellularNetworks_files/image035.gif" v:shapes=3D"_x0000_i1044"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1044" DrawAspect=3D"Content" ObjectID=3D"_1135600667"> </o:OLEObject> </xml><![endif]-->- affected zone) producing effect <i style=3D'mso-bidi-fo= nt-style: normal'>j</i> in response to the cause <span class=3DSpellE><i style=3D'mso= -bidi-font-style: normal'>i</i></span> created on <i style=3D'mso-bidi-font-style:normal'>z</= i>, can be defined as follows:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1045" type=3D"#_x0000_t75" style=3D'width:200.25pt;height:18= .75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image036.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D267 height=3D25 src=3D"CellularNetworks_files/image037.gif" v:shapes=3D"_x0000_i1045"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1045" DrawAspect=3D"Content" ObjectID=3D"_1135600669"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =        </span>(6)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE>where= </span> <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1046" type=3D"#_x0000_t75" style=3D'width:42pt;height:18.75p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image038.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D56 height=3D25 src=3D"CellularNetworks_files/image039.gif" v:shapes=3D"_x0000_i1046"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1046" DrawAspect=3D"Content" ObjectID=3D"_1135600670"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>is a member= ship function of an effect <i style=3D'mso-bidi-font-style:normal'>j</i> generat= ed on <i style=3D'mso-bidi-font-style:normal'>d</i> by cause <i style=3D'mso-bidi-fo= nt-style: normal'>I</i> created on <i style=3D'mso-bidi-font-style:normal'>z</i>.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>When one cause can genera= te multiple effects, then <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1047" type=3D"#_x0000_t75" style=3D'width:12pt;height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image040.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D16 height=3D24 src=3D"CellularNetworks_files/image041.gif" v:shapes=3D"_x0000_i1047"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1047" DrawAspect=3D"Content" ObjectID=3D"_1135600671"> </o:OLEObject> </xml><![endif]-->-affected zone is defined as</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1048" type=3D"#_x0000_t75" style=3D'width:26.25pt;height:18p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image042.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D35 height=3D24 src=3D"CellularNetworks_files/image043.gif" v:shapes=3D"_x0000_i1048"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1048" DrawAspect=3D"Content" ObjectID=3D"_1135600672"> </o:OLEObject> </xml><![endif]--><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1049" type= =3D"#_x0000_t75" style=3D'width:38.25pt;height:29.25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image044.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D51 height=3D39 src=3D"CellularNetworks_files/image045.gif" v:shapes=3D"_x0000_i1049"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1049" DrawAspect=3D"Content" ObjectID=3D"_1135600673"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =         </span><span style=3D'mso-spacerun:yes'>        =             </s= pan>(7)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>If a number of causes (<s= ub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1050" type=3D"#_x0000_t75" style=3D'width:33.75pt;height:17.= 25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image046.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D45 height=3D23 src=3D"CellularNetworks_files/image047.gif" v:shapes=3D"_x0000_i1050"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1050" DrawAspect=3D"Content" ObjectID=3D"_1135600674"> </o:OLEObject> </xml><![endif]--> are generated simultaneously on <i style=3D'mso-bidi-fon= t-style: normal'>z</i> (system engineers of cellular networks often make multiple ch= anges) then <i style=3D'mso-bidi-font-style:normal'>z</i>’-affected zone is:= </p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1051" type=3D"#_x0000_t75" style=3D'width:222.75pt;height:29= .25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image048.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D297 height=3D39 src=3D"CellularNetworks_files/image049.gif" v:shapes=3D"_x0000_i1051"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1051" DrawAspect=3D"Content" ObjectID=3D"_1135600675"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;          </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;      </span>(8)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>where <sub><!--[if gte vm= l 1]><v:shape id=3D"_x0000_i1052" type=3D"#_x0000_t75" style=3D'width:75.75pt;height:18p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image050.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D101 height=3D24 src=3D"CellularNetworks_files/image051.gif" v:shapes=3D"_x0000_i1052"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1052" DrawAspect=3D"Content" ObjectID=3D"_1135600676"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>is a second= order membership function of causes created simultaneously on <i style=3D'mso-bid= i-font-style: normal'>z</i>; <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1053" type=3D= "#_x0000_t75" style=3D'width:119.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image052.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D159 height=3D25 src=3D"CellularNetworks_files/image053.gif" v:shapes=3D"_x0000_i1053"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1053" DrawAspect=3D"Content" ObjectID=3D"_1135600677"> </o:OLEObject> </xml><![endif]-->is a set of membership functions of causes created simultaneously on <i style=3D'mso-bidi-font-style:normal'>z</i>; <sub><!--[= if gte vml 1]><v:shape id=3D"_x0000_i1054" type=3D"#_x0000_t75" style=3D'width:45pt;height:21pt' = o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image054.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D60 height=3D28 src=3D"CellularNetworks_files/image055.gif" v:shapes=3D"_x0000_i1054"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1054" DrawAspect=3D"Content" ObjectID=3D"_1135600678"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>is a member= ship function of <i style=3D'mso-bidi-font-style:normal'>j</i> effect generated = on <i style=3D'mso-bidi-font-style:normal'>d</i> by causes <i style=3D'mso-bidi-f= ont-style: normal'>I</i>’ and created on <i style=3D'mso-bidi-font-style:normal'= >z</i>. Both membership functions in (8) consider the fact, that since networks are non-linear, resulting <i style=3D'mso-bidi-font-style:normal'>j</i>-type ef= fect can be equal to, more than or less than a sum of partial effects of <i style=3D'mso-bidi-font-style:normal'>j</i>-type generated on d by different causes and are created on z.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>The maximal size of the a= ffected zone <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1055" type=3D"#_x0000_t= 75" style=3D'width:14.25pt;height:17.25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image056.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D19 height=3D23 src=3D"CellularNetworks_files/image057.gif" v:shapes=3D"_x0000_i1055"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1055" DrawAspect=3D"Content" ObjectID=3D"_1135600679"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>will be whe= n <i style=3D'mso-bidi-font-style:normal'>I’=3DI</i>.</p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>In this case </p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'>        =             &nb= sp;        </span><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1056" type=3D"#_x0000= _t75" style=3D'width:38.25pt;height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image058.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D51 height=3D24 src=3D"CellularNetworks_files/image059.gif" v:shapes=3D"_x0000_i1056"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1056" DrawAspect=3D"Content" ObjectID=3D"_1135600680"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =  </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =    </span>(9)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>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.)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>Goodness value <sub><!--[if gte vml= 1]><v:shape id=3D"_x0000_i1057" type=3D"#_x0000_t75" style=3D'width:18.75pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image060.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D25 height=3D25 src=3D"CellularNetworks_files/image061.gif" v:shapes=3D"_x0000_i1057"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1057" DrawAspect=3D"Content" ObjectID=3D"_1135600681"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>generated o= n cell site <i style=3D'mso-bidi-font-style:normal'>d</i> by <i style=3D'mso-bidi-= font-style: normal'>I’</i> causes created on z. is as follows: </p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1058" type=3D"#_x0000_t75" style=3D'width:156pt;height:26.25= pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image062.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D208 height=3D35 src=3D"CellularNetworks_files/image063.gif" v:shapes=3D"_x0000_i1058"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1058" DrawAspect=3D"Content" ObjectID=3D"_1135600682"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp; </span><span style=3D'mso-spacerun:yes'>        =      </span>(10)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>When <sub><!--[if gte vml= 1]><v:shape id=3D"_x0000_i1059" type=3D"#_x0000_t75" style=3D'width:60.75pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image064.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D81 height=3D25 src=3D"CellularNetworks_files/image065.gif" v:shapes=3D"_x0000_i1059"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1059" DrawAspect=3D"Content" ObjectID=3D"_1135600683"> </o:OLEObject> </xml><![endif]-->is a weight coefficient of the j-<span class=3DSpellE>th<= /span> <span class=3DGramE>parameter.</span><span style=3D'mso-spacerun:yes'> = ;  </span>Coefficients of this kind are usually the result of surveys made in = <span class=3DGramE>cellular telephone company</span> 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.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>The affected zone goodness value th= at is gained via <span class=3DGramE><i style=3D'mso-bidi-font-style:normal'>I</i= ></span>’ causes created on z is:<o:p></o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1060" type=3D"#_x0000_t75" style=3D'width:63pt;height:29.25p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image066.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D84 height=3D39 src=3D"CellularNetworks_files/image067.gif" v:shapes=3D"_x0000_i1060"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1060" DrawAspect=3D"Content" ObjectID=3D"_1135600684"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =          </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;  </span>(11)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>A set of the affected con= trolled attributes contains all cellular service quality attributes. Part of them c= an be considered as constrains.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>The optimization task for= <i style=3D'mso-bidi-font-style:normal'>d</i> when <i style=3D'mso-bidi-font-s= tyle: normal'>I’</i> controlled attributes are changing on <i style=3D'mso-= bidi-font-style: normal'>z</i> is formulated as:</p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1061" type=3D"#_x0000_t75" style=3D'width:213pt;height:30.75= pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image068.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D284 height=3D41 src=3D"CellularNetworks_files/image069.gif" v:shapes=3D"_x0000_i1061"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1061" DrawAspect=3D"Content" ObjectID=3D"_1135600685"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =         </span>(12)</p> <p class=3DMsoNormal style=3D'text-align:justify'>The optimization of the a= ffected zone, which is made by varying the cell site z control attributes, is gover= ned by the following:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1062" type=3D"#_x0000_t75" style=3D'width:227.25pt;height:30= .75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image070.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D303 height=3D41 src=3D"CellularNetworks_files/image071.gif" v:shapes=3D"_x0000_i1062"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1062" DrawAspect=3D"Content" ObjectID=3D"_1135600686"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =    </span>(13)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>Whole network decompositi= on can be achieved via a set M cell sites selected in such a way that:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1063" type=3D"#_x0000_t75" style=3D'width:168.75pt;height:27= pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image072.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D225 height=3D36 src=3D"CellularNetworks_files/image073.gif" v:shapes=3D"_x0000_i1063"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1063" DrawAspect=3D"Content" ObjectID=3D"_1135600687"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =            </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =    </span>(14)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>When |M|=3D1 then decompo= sition is impossible.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>Total optimal network “goodness” value can be calculated as:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE><i style=3D'mso-bidi-font-style:normal'>opt<span style=3D'mso-spacerun:yes'>&n= bsp; </span>G</i></span> =3D <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1064" type=3D"#_x0000_t75" style=3D'width:24.75pt;height:27pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image074.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D33 height=3D36 src=3D"CellularNetworks_files/image075.gif" v:shapes=3D"_x0000_i1064"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1064" DrawAspect=3D"Content" ObjectID=3D"_1135600688"> </o:OLEObject> </xml><![endif]--><i style=3D'mso-bidi-font-style:normal'>opt</i> <sub><!--= [if gte vml 1]><v:shape id=3D"_x0000_i1065" type=3D"#_x0000_t75" style=3D'width:15.75pt;height:17.= 25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image076.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D21 height=3D23 src=3D"CellularNetworks_files/image077.gif" v:shapes=3D"_x0000_i1065"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1065" DrawAspect=3D"Content" ObjectID=3D"_1135600689"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp; </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;         </span>(15)</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>It is possible that the n= etwork can be decomposed in several different ways. In this case we can define <su= b><!--[if gte vml 1]><v:shape id=3D"_x0000_i1066" type=3D"#_x0000_t75" style=3D'width:30.75pt;height:12.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image078.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D41 height=3D17 src=3D"CellularNetworks_files/image079.gif" v:shapes=3D"_x0000_i1066"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1066" DrawAspect=3D"Content" ObjectID=3D"_1135600690"> </o:OLEObject> </xml><![endif]-->as an <i style=3D'mso-bidi-font-style:normal'>r</i>-attem= pt of decomposition, <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1067" type=3D= "#_x0000_t75" style=3D'width:20.25pt;height:15pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image080.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D27 height=3D20 src=3D"CellularNetworks_files/image081.gif" v:shapes=3D"_x0000_i1067"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1067" DrawAspect=3D"Content" ObjectID=3D"_1135600691"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>as a set of= cell sites used in this attempt, and <i style=3D'mso-bidi-font-style:normal'>opt= </i> <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1068" type=3D"#_x0000_t75" style=3D'width:17.25pt;height:15.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image082.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image083.gif" v:shapes=3D"_x0000_i1068"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1068" DrawAspect=3D"Content" ObjectID=3D"_1135600692"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>as correspo= nding total network “goodness” value. It is a logical to try to find<= /p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE><i style=3D'mso-bidi-font-style:normal'>opt</i></span><i style=3D'mso-bidi-fon= t-style: normal'> </i><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1069" type=3D"#= _x0000_t75" style=3D'width:12.75pt;height:17.25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image084.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D17 height=3D23 src=3D"CellularNetworks_files/image085.gif" v:shapes=3D"_x0000_i1069"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1069" DrawAspect=3D"Content" ObjectID=3D"_1135600693"> </o:OLEObject> </xml><![endif]-->=3D<i style=3D'mso-bidi-font-style:normal'>max opt</i> <s= ub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1070" type=3D"#_x0000_t75" style=3D'width:17.25pt;height:15.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image082.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image083.gif" v:shapes=3D"_x0000_i1070"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1070" DrawAspect=3D"Content" ObjectID=3D"_1135600694"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;   </span><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;        </span>(16)</p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1071" type=3D"#_x0000_t75" style=3D'width:30.75pt;height:12.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image086.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D41 height=3D17 src=3D"CellularNetworks_files/image079.gif" v:shapes=3D"_x0000_i1071"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1071" DrawAspect=3D"Content" ObjectID=3D"_1135600695"> </o:OLEObject> </xml><![endif]--></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE>where= </span> <i style=3D'mso-bidi-font-style:normal'>opt</i> <sub><!--[if gte vml 1]><v:sha= pe id=3D"_x0000_i1072" type=3D"#_x0000_t75" style=3D'width:12.75pt;height:17.= 25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image084.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D17 height=3D23 src=3D"CellularNetworks_files/image085.gif" v:shapes=3D"_x0000_i1072"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1072" DrawAspect=3D"Content" ObjectID=3D"_1135600696"> </o:OLEObject> </xml><![endif]-->is a best total network optimal “goodness” va= lue found during all decompositions. Because |<i style=3D'mso-bidi-font-style:n= ormal'>D</i>| can be significant, we shell limit our self to a reasonable number of attem= pts.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>Sometimes management task= is reduced to the adjustment of only one controlled attribute. Let’s consider th= is: to create <span class=3DGramE>an</span> necessary effect <sub><!--[if gte v= ml 1]><v:shape id=3D"_x0000_i1073" type=3D"#_x0000_t75" style=3D'width:17.25pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image087.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image088.gif" v:shapes=3D"_x0000_i1073"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1073" DrawAspect=3D"Content" ObjectID=3D"_1135600697"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>on <i style=3D'mso-bidi-font-style:normal'>d</i> (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 <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1074" type=3D"#_x= 0000_t75" style=3D'width:41.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image089.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D55 height=3D25 src=3D"CellularNetworks_files/image090.gif" v:shapes=3D"_x0000_i1074"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1074" DrawAspect=3D"Content" ObjectID=3D"_1135600698"> </o:OLEObject> </xml><![endif]-->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 <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1075" type=3D"#_x0000_= t75" style=3D'width:18.75pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image091.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D25 height=3D25 src=3D"CellularNetworks_files/image092.gif" v:shapes=3D"_x0000_i1075"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1075" DrawAspect=3D"Content" ObjectID=3D"_1135600699"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>of possible solutions <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1076" type=3D"#_x0= 000_t75" style=3D'width:68.25pt;height:20.25pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image093.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D91 height=3D27 src=3D"CellularNetworks_files/image094.gif" v:shapes=3D"_x0000_i1076"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1076" DrawAspect=3D"Content" ObjectID=3D"_1135600700"> </o:OLEObject> </xml><![endif]-->can be defined as:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1077" type=3D"#_x0000_t75" style=3D'width:333pt;height:21.75= pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image095.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D444 height=3D29 src=3D"CellularNetworks_files/image096.gif" v:shapes=3D"_x0000_i1077"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1077" DrawAspect=3D"Content" ObjectID=3D"_1135600701"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;    </span>(17)</p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'>        =              </span><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1078" type=3D"#_x0000= _t75" style=3D'width:24.75pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image097.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D33 height=3D25 src=3D"CellularNetworks_files/image098.gif" v:shapes=3D"_x0000_i1078"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1078" DrawAspect=3D"Content" ObjectID=3D"_1135600702"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =      </span><sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1079" type=3D"#_x0000_t75" style=3D'width:24.75pt;height:18.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image099.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D33 height=3D25 src=3D"CellularNetworks_files/image098.gif" v:shapes=3D"_x0000_i1079"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1079" DrawAspect=3D"Content" ObjectID=3D"_1135600703"> </o:OLEObject> </xml><![endif]--></p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE>where= </span> <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1080" type=3D"#_x0000_t75" style=3D'width:60.75pt;height:18p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image100.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D81 height=3D24 src=3D"CellularNetworks_files/image101.gif" v:shapes=3D"_x0000_i1080"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1080" DrawAspect=3D"Content" ObjectID=3D"_1135600704"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>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; <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1081" type=3D"#_x0000_t75" style=3D'width:44.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image102.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D59 height=3D25 src=3D"CellularNetworks_files/image103.gif" v:shapes=3D"_x0000_i1081"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1081" DrawAspect=3D"Content" ObjectID=3D"_1135600705"> </o:OLEObject> </xml><![endif]-->is a <i style=3D'mso-bidi-font-style:normal'>t</i> constr= ain of a membership function of cell site <sub><!--[if gte vml 1]><v:shape id=3D"_= x0000_i1082" type=3D"#_x0000_t75" style=3D'width:45.75pt;height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image104.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D61 height=3D24 src=3D"CellularNetworks_files/image105.gif" v:shapes=3D"_x0000_i1082"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1082" DrawAspect=3D"Content" ObjectID=3D"_1135600706"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>is a tolera= nce threshold of quality attribute <i style=3D'mso-bidi-font-style:normal'>t</i= >.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>It is possible that<sub><= !--[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]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1083" DrawAspect=3D"Content" ObjectID=3D"_1135600707"> </o:OLEObject> </xml><![endif]-->. However, if <sub><!--[if gte vml 1]><v:shape id=3D"_x00= 00_i1084" type=3D"#_x0000_t75" style=3D'width:42.75pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image108.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D57 height=3D25 src=3D"CellularNetworks_files/image109.gif" v:shapes=3D"_x0000_i1084"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1084" DrawAspect=3D"Content" ObjectID=3D"_1135600708"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>and it cont= ains more then one solution, then a “goodness” value for every solut= ion can be calculated as:</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><sub><!--[if gte vml 1]><= v:shape id=3D"_x0000_i1085" type=3D"#_x0000_t75" style=3D'width:168pt;height:27.75= pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image110.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D224 height=3D37 src=3D"CellularNetworks_files/image111.gif" v:shapes=3D"_x0000_i1085"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1085" DrawAspect=3D"Content" ObjectID=3D"_1135600709"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'>        =             &nb= sp;            =             &nb= sp;            =             &nb= sp;       </span>(18)</p> <p class=3DMsoNormal style=3D'text-align:justify'>(For the simplicity in th= is <span class=3DGramE>a</span> equation we use <sub><!--[if gte vml 1]><v:shape id= =3D"_x0000_i1086" type=3D"#_x0000_t75" style=3D'width:17.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image112.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D25 src=3D"CellularNetworks_files/image113.gif" v:shapes=3D"_x0000_i1086"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1086" DrawAspect=3D"Content" ObjectID=3D"_1135600710"> </o:OLEObject> </xml><![endif]-->to present weight coefficient for that desired effects and constraints, and <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1087" type= =3D"#_x0000_t75" style=3D'width:44.25pt;height:18.75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image114.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D59 height=3D25 src=3D"CellularNetworks_files/image115.gif" v:shapes=3D"_x0000_i1087"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1087" DrawAspect=3D"Content" ObjectID=3D"_1135600711"> </o:OLEObject> </xml><![endif]-->to represent membership functions for the desired effects= and constrains.) The solution that provides a maximum value of <sub><!--[if gte= vml 1]><v:shape id=3D"_x0000_i1088" type=3D"#_x0000_t75" style=3D'width:17.25pt;height:15.= 75pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image116.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D23 height=3D21 src=3D"CellularNetworks_files/image117.gif" v:shapes=3D"_x0000_i1088"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1088" DrawAspect=3D"Content" ObjectID=3D"_1135600712"> </o:OLEObject> </xml><![endif]-->is a candidate for implementation.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span style=3D'mso-spacerun:yes'> </span>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 <sub><!--[if gte vml 1]><v:shape id=3D"_x= 0000_i1089" type=3D"#_x0000_t75" style=3D'width:15pt;height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image118.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D20 height=3D24 src=3D"CellularNetworks_files/image119.gif" v:shapes=3D"_x0000_i1089"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1089" DrawAspect=3D"Content" ObjectID=3D"_1135600713"> </o:OLEObject> </xml><![endif]--><span style=3D'mso-spacerun:yes'> </span>should be replaced <span class=3DGramE>by </span><sub><!--[if gte vml 1]><v:shape id= =3D"_x0000_i1090" type=3D"#_x0000_t75" style=3D'width:35.25pt;height:18pt' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image120.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D47 height=3D24 src=3D"CellularNetworks_files/image121.gif" v:shapes=3D"_x0000_i1090"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1090" DrawAspect=3D"Content" ObjectID=3D"_1135600714"> </o:OLEObject> </xml><![endif]-->, and effect membership function should be represented by= <sub><!--[if gte vml 1]><v:shape id=3D"_x0000_i1091" type=3D"#_x0000_t75" style=3D'width:42pt;height:18.75p= t' o:ole=3D""> <v:imagedata src=3D"CellularNetworks_files/image038.wmz" o:title=3D""/> </v:shape><![endif]--><![if !vml]><img width=3D56 height=3D25 src=3D"CellularNetworks_files/image039.gif" v:shapes=3D"_x0000_i1091"><![en= dif]></sub><!--[if gte mso 9]><xml> <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i1091" DrawAspect=3D"Content" ObjectID=3D"_1135600715"> </o:OLEObject> </xml><![endif]-->.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font= -weight: normal'>3. Conclusion<o:p></o:p></b></p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>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.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'><span class=3DGramE>4.<b style=3D'mso-bidi-font-weight:normal'>References</b></span><b style=3D'mso-= bidi-font-weight: normal'> <o:p></o:p></b></p> <p class=3DMsoNormal style=3D'text-align:justify'><b style=3D'mso-bidi-font= -weight: normal'><o:p> </o:p></b></p> <p class=3DMsoNormal style=3D'text-align:justify'>[1] D.C Cox, D.O. <span class=3DSpellE>Reudink</span>. <span class=3DGramE>Dynamic Channel Assignme= nt in High-<span class=3DSpellE>Capasity</span> </span><st1:place><span class=3DG= ramE>Mobile</span></st1:place><span class=3DGramE> Communications Systems.</span> <span class=3DGramE><i style=3D'mso-bidi-font-style:normal'>The </i></span><st1:City><st1:place><s= pan class=3DGramE><i style=3D'mso-bidi-font-style:normal'>Bell</i></span></st= 1:place></st1:City><span class=3DGramE><i style=3D'mso-bidi-font-style:normal'> System Technical Jou= rnal</i>, Vol. 50#6, 1971.</span></p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>[2] T.J. <span class=3DSp= ellE>Kahwa</span>, N.D. <span class=3DSpellE>Georganas</span>. A Hybrid Channel Assignment Sch= eme in Large-Scale, Cellular-Structured <st1:place>Mobile</st1:place> Communication Systems, <st1:City><st1:place><i style=3D'mso-bidi-font-style:normal'>Lund<= /i></st1:place></st1:City><i style=3D'mso-bidi-font-style:normal'> Institute of Technology</i>. <i style=3D'mso-bidi-font-style:normal'>Tech.Rep</i>.<span class=3DGramE>,1986= </span>.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>[3] <span class=3DSpellE>= J.Karisson</span>. <span class=3DGramE>Supplementary to a Cellular Mobile Telephone System wit= h Load Sharing.</span> <span class=3DGramE>Department of Communication Systems.</s= pan> <st1:City><st1:place><span class=3DGramE><i style=3D'mso-bidi-font-style:normal'>Lund</i></span></st= 1:place></st1:City><span class=3DGramE><i style=3D'mso-bidi-font-style:normal'> Institute of Technol= ogy</i>.</span> <i style=3D'mso-bidi-font-style:normal'>Tech.Rep</i>.<span class=3DGramE>,1= 986</span>.</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>[4] <span class=3DSpellE>= J.Karisson</span>, <span class=3DSpellE>B.Eklundh</span>. <span class=3DGramE>A Cellular Mobile Telephone System with Load Sharing – an Enhancement of Direct Retry.<= /span> <span class=3DGramE><i style=3D'mso-bidi-font-style:normal'>IEEE Transactio= ns on Communications</i>, Vol.37#5, 1989.</span></p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal style=3D'text-align:justify'>[5] <st1:City><st1:place>= L.A.</st1:place></st1:City> <span class=3DSpellE>Zadeh</span>. <span class=3DGramE>The Concept of a Lin= guistic Variable and its Application to Approximate Reasoning.</span> Information Sciences, <span class=3DGramE>8 pp.199-249,</span> 301-357 and 9 pp.43-80, = 1975</p> <p class=3DMsoNormal style=3D'text-align:justify'><o:p> </o:p></p> <p class=3DMsoNormal 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