Performance Evaluation of an Enhanced Distance-based Registration Scheme Using the Normal Distribution Approximation

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1 Peomance Evaluation o an Enhanced Ditance-baed Regitation Scheme Uing the Nomal Ditibution Appoimation Jang Hyun Bae * Jae Young Seo and Dougla C. Sice Depatment o Inomation Sytem Engineeing Chonbu National Univeity Koea Depatment o Compute Science Univeity o Coloado at Boulde USA SUMMARY Having an eicient location management cheme o mobile tation MS i vey impotant o optimiing the peomance o mobile cellula ytem. In thi tudy a ditance-baed egitation DBR cheme and an enhanced DBR cheme ae eamined. Accoding to compute imulation on the DBR cheme we how that mot MS tend to ditibute aound the cente o the location aea. Thi centaliing popety o the MS in the DBR cheme enable u to appoimate the ditibution o the MS in the location aea to a nomal ditibution. We analye the peomance o the DBR cheme accoding to the above appoimation and ou mobility model. We alo popoe a ditance-baed implicit egitation DIR cheme in ode to impove the peomance o the DBR cheme. We evaluate the peomance o the popoed cheme uing the nomal ditibution appoimation to compae to the peomance o the DBR cheme. The numeical eult how that the DIR cheme not only outpeom the DBR cheme in all the cae but alo outpeom the one-baed egitation ZBR cheme in mot cae. * Coepondence to: Jang Hyun Bae Depatment o Inomation Sytem Engineeing Chonbu National Univeity Koea jbae@chonbu.ac. Jang Hyun Bae i cuently at Univeity o Coloado at Boulde USA. Pat o thi wo wee peented on CIE coneence Cheju 004. Contact/gant pono: Koea Science and Engineeing Foundation; contact/gant numbe: R

2 . Intoduction In a mobile cellula ytem location egitation i the poce by which the mobile tation MS notiie the ytem o it location tatu and othe chaacteitic []. The MS inom the ytem o it location and tatu o that the ytem can eiciently page the MS when etablihing an MS-teminated call. Without egitation the ytem doe not now with which cell to aociate the MS and theeoe the ytem might have to page the MS in evey cell o the ytem. On the othe hand equent egitation allow the ytem to now the location o the MS with geat accuacy and theeoe the ytem page the MS in only a ew cell o the ytem. Howeve equent egitation place a high load on the acce channel and a modeate load on the paging channel. Thu a tade o i equied between the paging and egitation load in ode to optimie the ue o the adio channel and ytem equipment. Many cheme have been popoed in ode to minimie the location egitation cot [- 0]. In paticula nine dieent egitation cheme have been ecommended in CDMA mobile cellula ytem [] a hown in Table. Table. Regitation cheme in CDMA mobile cellula ytem In geneal the DBR cheme i evaluated to be upeio to a movement-baed egitation cheme in all the cae [-3]. Thi pape peent a new analyi o the DBR cheme and an enhanced DBR cheme. The DBR cheme caue an MS to egite it location when the ditance between the cuent bae tation and the bae tation at which it lat egiteed

3 3 it location eceed a pedetemined thehold. The MS detemine that it ha moved a pedetemined ditance by computing the meaued ditance baed on the dieence in latitude and longitude between the cuent bae tation and the bae tation whee the MS lat egiteed. I thi ditance meaue eceed the thehold value the mobile tation egite []. Some peviou wo analyed the ZBR cheme [4] and compae the peomance o the ZBR cheme with that o the DBR cheme [5-6]. The ZBR cheme how good peomance in geneal and ha been adopted by mot mobile cellula netwo. One o the main poblem o the ZBR cheme i that eceive location egitation occu when an MS igag between two neighboing location aea. On the othe hand thi ping-pong phenomenon doe not occu in the DBR cheme and the egitation load o the DBR cheme ditibute equally to all cell in the location aea. So the DBR cheme may need a malle egitation load than the ZBR cheme which wa decibed uing mathematical analyi by Bae et al. [5]. One o the main aumption in [5] i that the MS uniomly ditibute ove the cicula location aea. Howeve uch an aumption doe not coincide with eal ituation and o it undeetimate the peomance o the DBR cheme. Theeoe i popely etimated the DBR cheme may be upeio to the ZBR cheme in mot cae. In thi tudy ou compute imulation o the DBR cheme how that mot MS have a tendency to ditibute aound the cente o the location aea. Uing thi tendency o the MS we analye the peomance o the DBR cheme. We alo popoe a hybid egitation cheme called DIR ditance-baed egitation with an implicit egitation

4 4 cheme to impove the peomance o the DBR cheme. We evaluate the peomance o the DIR cheme and how that the DIR cheme i upeio to the DBR cheme in all the cae and bette than the ZBR cheme in mot cae. When a call occu in the DBR cheme the ytem can implicitly now the MS location without any additional egitation pocedue. In othe wod when a call aive at an MS o an MS oiginate a call the MS implicitly notiie the ytem o it location inomation by uing the call et up meage without an additional egitation meage. In [] thi type o poce i eeed to a implicit egitation. Hence i the DBR cheme incopoate implicit egitation then the netwo can now the MS location wheneve thee i an outgoing o incoming call to o om the MS without any eplicit egitation poce. The netwo et up a new location aea in which the MS location i the cente o the new location aea which educe the numbe o egitation. Note that implicit egitation doe not have any inluence on the numbe o egitation in the ZBR cheme. Following thi intoduction Section decibe the mobility model o the DBR cheme and the nomal ditibution appoimation o the DBR cheme. Section 3 decibe the popoed DIR cheme and the analytic model o the DIR cheme. The numeical eult ae hown in Section 4. Finally concluding ema ae given in Section 5.

5 5. Ditance-baed egitation and it peomance. Sytem deciption To analye and compae the peomance o egitation cheme equie a eaonable yet imple mobility model. Seveal mobility model have been popoed; a imple onedimenional model [] a andom wal model [3 7-8] a luid low model [9] the Bownian motion model [0] and a ou-diectional model [4-5]. Among them a imple onedimenional model i too imple to be applied o eact analyi. The andom wal model and the luid low model ae alo elatively imple and mae it eay to analye the peomance o one egitation cheme but diicult to analye othe cheme. Fo eample the andom wal model i good o analying the peomance o the movementbaed egitation cheme but it i not adequate to apply to the ZBR cheme [6]; and the luid low model i good o obtaining the peomance o the ZBR cheme but it cannot be applied to the DBR cheme. The Bownian motion model while pomiing i budened with the diiculty o deiving cloed omed olution. The ou-diectional mobility model can handle diection change o the ubcibe imply and ealitically which enable u to eectively analye the peomance o both o the DBR and ZBR cheme. Theeoe in thi pape we mae ue o the ou-diectional mobility model [4-5] to analye the DBR and DIR cheme. The ollowing ae aumed in the ou-diectional model [4-5]. An MS move in a taight line until it eache a tuning point. An MS change it coue in ou diection uch a ont ea ight and let.

6 6 When it eache the tuning point it can chooe any diection with equal pobability. The ditance between two conecutive tuning point i eponentially ditibuted. Fo the peomance evaluation the ollowing paamete and contant ae deined. X: the ditance between two conecutive tuning point K: the numbe o egitation between two conecutive tuning point N: the numbe o egitation pe ubcibe o an hou L: the ditance moved o an hou : the ditance om the lat tuning point to the bode o the location aea Figue. Mobility o a mobile ubcibe. Ditance-baed egitation The DBR cheme caue an MS to egite it location when the ditance between the cuent bae tation and the bae tation at which it lat egiteed eceed a pedetemined thehold. The MS detemine that it ha moved a cetain ditance by computing a meaued ditance baed on the dieence in latitude and longitude between the cuent bae tation and the bae tation whee the MS lat egiteed it location. I thi meaued ditance eceed the thehold value the MS egite it location []. Fom the deinition o the DBR cheme the location aea o the DBR cheme can be modeled a a cicle whoe adiu i equal to the thehold a hown in Figue. Bae et al.

7 7 [5] aumed that the ditance between two conecutive tuning point ollow an eponential ditibution. They alo aumed that the MS ditibute uniomly ove the cicula location aea and calculated the numbe o egitation to evaluate the peomance uing thoe aumption. I the MS ditibute uniomly ove the cicula location aea o the DBR cheme the pobability denity unction o the andom vaiable which i the ditance om the lat tuning point to the bode o the location aea can be omulated a ollow [5]: S = 0 < π.3 Centaliing tendency and nomal ditibution appoimation To eview the accuacy o Equation compute imulation wee peomed o vaiou cae. Accoding to the imulation eult it tuned out the aumption that the MS ditibute uniomly ove the cicula location aea o the DBR cheme wa inadequate and the MS ha a tendency to ditibute intenively aound the cente o the location aea. In othe wod in the DBR cheme an MS will ditibute mainly nea the cente o the location aea but aely nea the bode o the location aea. We call thi tendency the centaliing popety o the MS in the DBR cheme. The eaon why the MS ditibution doe not ollow a uniom ditibution but athe a nomal ditibution may be tongly elated to the act that the hape o the location aea o the DBR cheme i a cicle and that the MS tat to move om the cente o the new location aea at evey egitation.

8 8 Thi centaliing popety o the DBR cheme mae ou new analyi o the DBR cheme quite dieent om the peviou appoach. Fit the pobability denity unction o the andom vaiable which i the ditance om the lat tuning point to the bode o the location aea hould be deived again o it can agee with the centaliing popety. Thi centaliing popety o the MS in the DBR cheme enable u to appoimate the ditibution o the ditance to the bode o the location aea to a nomal ditibution. Theeoe the andom vaiable hould have a bell-haped and ymmetic pobability denity unction with the median and mean o being the ame. In ode to tatitically eamine whethe ollow a nomal ditibution we peomed a goodne-o-it tet o the data om the imulation. In the imulation it i aumed that the ditance between two conecutive tuning point X ollow an eponential ditibution a peviouly decibed and that the adiu o the location aea i 5 m. We then ued the Andeon-Daling tet A-D [] to eamine the goodne-o-it o ou appoimation. In the Andeon-Daling tet it i nown that the data can be aid to ollow a nomal ditibution i the p-value i lage than 0.05 []. Table how the p-value o the Andeon-Daling tet o each imulation eult. Fom the table it i hown that andom vaiable ollow a nomal ditibution a the epected ditance between two tuning point EX inceae. Howeve it i alo obeved that when EX i vey mall it i omewhat diicult to ay that andom vaiable ollow a nomal ditibution. Baed on numeou imulation eult o vaiou ituation it i concluded that andom vaiable appoimately ollow a nomal ditibution. In Table it i hown that andom vaiable ollow a nomal ditibution accuately o lage EX and appoimately o mall EX.

9 9 Figue. An eample o the p-value o A-D tet EX= Table. EX v. p-value o the A-D tet =5 Table 3. EX v. the mean value µ and tandad deviation σ =5 Net let u etimate mean and tandad deviation o two paamete o a nomal ditibution. In ode to ind the elation between andom vaiable and EX we ue the imulation eult o vaiou ituation. Some o thee imulation eult ae hown in Table 3. Fom the table it i hown that the mean value o tend to deceae linealy a EX inceae. Conideing thi elation between andom vaiable and EX the genealied omula o the mean value o can be deived a a unction o EX. Similaly the tandad deviation can be deived a a pogeion o dieence with a geometic atio o 0.. Equation how the inal omula o the mean and tandad deviation o a a unction o EX. Thi equation enable u to epe andom vaiable a a unction o EX and get the mean and tandad deviation without peoming complicated and timeconuming compute imulation. S θ = N θ i= whee θ = E X i 0. Uing the pobability denity unction o the epected numbe o egitation between two conecutive tuning point EK can be deived a ollow []:

10 0 E K = = 0 e θ θ S dd 3 Finally the epected numbe o egitation pe ubcibe pe hou EN can be deived a ollow: E L E N = E K E X E L = θ = 0 e θ θ S dd 4 3. Ditance-baed egitation with an Implicit Regitation and it peomance Accoding to CDMA technical equiement [] the BS can ine the MS location when an MS ucceully end an Oigination Meage o Page Repone Meage. Thi poce i called implicit egitation. In othe wod when an outgoing call om an MS ucceully complete o an incoming call to an MS ucceully complete the BS can ine the location o the MS om the inomation in Oigination Meage o Page Repone Meage epectively without an additional egitation meage. Hence i the DBR cheme incopoate implicit egitation in a mobile cellula netwo then the netwo can detemine the MS location wheneve thee i an outgoing o incoming call to o om the MS without any additional egitation poce. The netwo et up a new location aea in which the MS location i the cente o the new location aea which educe the numbe o egitation.

11 Figue 3. Location egitation pocedue in the DIR cheme A hown in Figue 3 the DBR cheme can be impoved in a numbe o egitation by combining with an implicit egitation and the peomance o thi hybid cheme become bette a the numbe o call geneated by the MS inceae. In thi tudy a hybid cheme that combine a ditance-baed egitation with an implicit egitation DIR cheme i popoed. Futhemoe the peomance o the DIR cheme i evaluated uing the nomal ditibution appoimation in ode to compae it with that o the DBR cheme. In ode to evaluate the peomance o the DIR cheme it i aumed that the ditance between two conecutive call geneation point denoted by a new andom vaiable i eponentially ditibuted with mean λ. Concening call geneation thee poible cae detemined by and hould be conideed in the DIR cheme. Then the pobability that the MS egite it location time o an hou i epeed a ollow []: P[ MS egite time ] = P[ MS egite time ate a call geneation P[ MS egite time without call geneation time ] j= MS egite j= P[ MS egite j time ate a call geneation j time ] = P[ < < 0 < < ] P[ < < < ] Acall geneate without egitati on P[ j < < j j < < j ] No call geneate beoe MS egite Acall geneate ate ] 5

12 Uing Equation and 5 the epected numbe o egitation between two conecutive tuning point EK can be calculated a ollow: ] [ e e whee ddd ddd ddd K E S j j j j j θ λ θ λ = = = = 6 Finally uing Equation 4 the epected numbe o egitation pe ubcibe pe hou can be calculated a ollow: }] { [ e e whee ddd ddd ddd L E N E S j j j j j θ λ θ λ θ = = = = 7 4. Numeical eult Fo the numeical analyi and peomance compaion the ollowing ae aumed. - Radiu o the location aea: 5m - Ditance moved o an hou L: 0m - Mean ditance between two conecutive call geneation point E: 4m

13 3 The peomance o the DBR and DIR cheme ae evaluated uing the nomal ditibution appoimation and the peomance o the DIR cheme i compaed with that o the ZBR cheme. Figue 4. EX v. numbe o egitation in the DBR cheme and imulation eult Figue 4 how that ou appoach i cloe to the imulation eult than the peviou model [5]. Fom thi igue it i hown that the popoed model coincide vey cloely with the imulation eult a the mean ditance between two conecutive tuning point EX inceae. Howeve thee i a mall gap between the imulation eult and ou calculation when EX i vey mall. In concluion it i hown that andom vaiable eactly ollow a nomal ditibution o lage EX and appoimately ollow a nomal ditibution o mall EX. Figue 5. EX v. numbe o egitation in the DIR DBR and ZBR cheme E=4 In Figue 5 the DIR cheme i compaed with the DBR and ZBR cheme. Fo the ae o aine it i aumed that the ie o the quadangula location aea in the ZBR cheme i the ame a that o the cicula location aea in the DBR cheme i.e. d=8.86 ince π = 5π=d whee d i the length o a ide o the quadangula location aea in the ZBR cheme. The imultaneou paging cheme i alo aumed. When the imultaneou paging i

14 4 aumed we do not need to conide the paging cot becaue evey cheme ha the ame paging cot i each cheme ha the ame location aea ie. Figue 5 how that the DIR cheme outpeom the DBR cheme o evey EX. When the mean ditance between conecutive tuning point EX i malle than the adiu o the location aea 5m the DIR cheme how a bette peomance than the ZBR cheme. On the othe hand i EX i lage than the adiu the ZBR cheme how a bette peomance than the DIR cheme. Howeve uch a lage value o EX aely occu in eal ituation. Theeoe we can conclude that the DIR cheme peom bette than the DBR cheme in evey cae and bette than the ZBR cheme in mot cae. Figue 6. E v. numbe o egitation in the DIR and ZBR cheme EX=4 Figue 6 how the numbe o egitation a E vaie given that EX i 3m. Note that a mall E mean a high call geneation ate and the ZBR cheme i not aected by call geneation at all. Figue 6 how that the high call geneation ate inluence the DIR cheme to educe location egitation and outpeom the ZBR cheme. In concluion we can ay that the DIR cheme outpeom the ZBR cheme in mot cae a E inceae. 5. Concluion In thi tudy the DBR cheme and an enhanced DBR cheme wee eamined. The DBR cheme caue a mobile tation to egite it location when the ditance between the cuent bae tation and the bae tation at which it lat egiteed it location eceed a

15 5 pedetemined thehold. Accoding to compute imulation on the DBR cheme we howed that mot MS tend to ditibute aound the cente o the location aea. Thi centaliing popety o the MS in the DBR cheme allow u to appoimate the ditibution o the MS in the location aea to a nomal ditibution. Uing the above appoimation and ou mobility model the peomance o the DBR cheme wa then analyed. Thi tudy alo popoed ditance-baed egitation with an implicit egitation DIR cheme to impove the peomance o the DBR cheme and evaluated the peomance o the DIR cheme uing the nomal ditibution appoimation. The numeical eult howed that the DIR cheme outpeom not only the DBR cheme in evey cae but alo the one-baed egitation cheme in mot cae. Acnowledgment Thi wo wa uppoted by the Koea Science & Engineeing Foundation R Reeence [] EIA/TIA/IS-95-B MS-BS Compatibility Standad o Wideband Spead Spectum Cellula Sytem 999. [] Ba-Noy A Kele I Sidi M Mobile ue: to update o not to update? Wiele Netwo 995; : [3] Ryu BH Ahn JH Bae JH Compaative peomance evaluation o movement-baed

16 6 egitation and ditance-baed egitation IEICE T. on Communication 003; E86- B3: [4] Bae JH. Ryu BH Lim SK Kim KS Mobility model and peomance analyi o one-baed egitation in CDMA mobile communication ytem Telecommunication Sytem 000; 4:3-9. [5] Bae JH Lie CH Peomance analyi o location egitation method: one-baed egitation and ditance-baed egitation Jounal o the Koean Intitute o Indutial Enginee 997; 3: [6] Kim KH Bae JH Falouto M Modeling and Peomance Analyi o Zone-Baed Regitation o Mobile Communication Netwo IEICE T. on Communication ubmitted. [7] Li J Kameda H Li K Optimal dynamic mobility management o PCS netwo IEEE/ACM T. on Netwoing 000; 83: [8] Bae JH Ryu BH An Impoved Movement-Baed Location Update and Selective Paging o PCS Netwo IEICE T. on Communication 000; E83-B7: [9] Xie H Tabbane S Goodman DJ Dynamic location aea management and peomance analyi Intenational Coneence on Vehicula Technology 993. [0] Roe C Yate R Location uncetainty in mobile netwo: a theoetical amewo IEEE Communication Magaine 997; 35:94-0. [] Cave RH Cave MR Doing data analyi with Minitab 4 Dubuy Pe 003. [] Ro S Stochatic Pocee Wiley 996.

17 7 Table. Regitation cheme in CDMA mobile cellula ytem Regitation cheme Zone-Baed Regitation Ditance-Baed Regitation Implicit Regitation Powe-up Regitation Powe-down Regitation Paamete-change Regitation Odeed Regitation Time-baed Regitation Taic channel Regitation Deciption when to egite When the MS ente a new one When the MS move moe than a cetain ditance When the MS oiginate a call o epond to paging When the MS powe on When the MS powe o When the paamete o the MS change At the equet o the bae tation When a time epie While it i aigned a taic channel diectional tuning point egitation point Figue. Mobility o a mobile ubcibe

18 8 Nomal Pobability Plot Pobability Aveage: StDev: N: S Andeon-Daling Nomality Tet A-Squaed: P-Value: Figue. An eample o the p-value o A-D tet EX= Table. EX v. p-value o the A-D tet =5 EX Reult Reult Reult

19 9 Table 3. EX v. the mean value µ and tandad deviation σ =5 EX Tet Tet Tet µ = 4.86 µ = µ = 4.78 σ =.759 σ =.956 σ =.909 µ = 4.6 µ = 4.87 µ = 4.8 σ =.809 σ =.95 σ =.835 µ = µ = µ = 4.79 σ =.854 σ =.953 σ =.945 µ = µ = µ = 4.54 σ =.986 σ =.854 σ =.45 µ = 4.5 µ = 4.66 µ = σ =.09 σ =.978 σ =.997 diectional tuning point egitation point call geneated point Figue 3. Location egitation pocedue in the DIR cheme

20 No. o egitation/h DBR Simulat ion DBR with uniom ditibution M ean ditance between two ucceive tuning point E X Figue 4. EX v. numbe o egitation in the DBR cheme and imulation eult No. o egitation/h DIR DBR ZBR Mean ditance between two ucceive tuning point E X Figue 5. EX v. numbe o egitation in the DIR DBR and ZBR cheme E=4

21 .5 No. o egitation/h DIR ZBR Mean ditance between ucceive call E Figue 6. E v. numbe o egitation in the DIR and ZBR cheme EX=4