A Comparison of the Performance of Two-Tier Cellular Networks Based on Queuing Handoff Calls

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1 Iteratoal Joural of Appled Matemats ad Computer Sees 2;2 Sprg 2006 A Comparso of te erformae of Two-Ter Cellular Networks Based o Queug Hadoff Calls Tara Sal ad Kemal Fdaboylu Abstrat Two-ter ellular etworks provde a eaed use of te etworks' resoures for bot g ad low speed users. However, tey ause a rease te umber of adoffs betwee ells due to avg smaller ell szes te mroell ter. A effetve approa used to prevet te droppg of ogog alls a etwork s delayg tese alls a queue utl a ael beomes avalable. I ts paper, we propose a ew Markov model for a two-ter ellular etwork avg a FIFO queue te mroell ter. Te performae of te model s te ompared wt tose of a prevously proposed model avg a queue te maroell ter ad te effet of avg a queue te mroell or maroell o bot g ad low speed users s observed. Keywords Blokg probablty, FIFO queue, Markov as, Two-ter ellular etworks. T I. INTRODUCTION o desg a effetve ellular system, t s requred to determe te Qualty of Serve (QoS). A ommo measure of te QoS s te adoff all blokg probablty, w s te probablty tat a ogog all s dropped due to te uavalablty of free aels te ellular etwork. Wreless ellular etworks osst of a umber of ells w ter szes deped prmarly o te populato ad te geograpal area. For g-populated areas, ells wt smaller szes are more preferable ta larger szes to aommodate te large umber of moble users. However, ts auses more blokg probablty for g speed users (.e. a ar) beause of te frequet adoff from oe ell to aoter. A sgle-ter ellular etwork a redue te adoff all blokg probablty by reservg aels te ell exlusvely for adoff alls or gvg ger prorty to te adoff alls over te ew alls. Queug adoff alls s aoter way to mprove te system performae by delayg te all utl a free ael s avalable. Tese metods mprove te adoff all blokg probablty; owever, tey ause a rease te ew all blokg probablty. I addto to ts, te umber of aels avalable te etwork may ot be eoug to adle te large umber of moble users. A mult-ter ellular etwork a mprove te system performae by usg te above metods. I addto to ts, t a provde more aels to te etwork ad based o te moblty of te moble users, alls a be delvered to te approprate layers. Cell splttg mproves te ellular etwork apaty by reasg te umber of ells ad aels w a moble user a aess troug te etwork. However, avg smaller ells reases te ross rate of moble users betwee tese ells. Mult-ter ellular etworks redue te ross rates by avg larger ells overlayg te smaller ells, ad te g speed users are assged to te layer wt larger ell szes. May studes ave bee doe to develop wreless ellular etworks tat provde te best performae ad effey. Hadoff alls ave bee te ma fator evaluatg te performae of a ellular etwork. Some models su as tose metoed [1], [2], ad [3] used guard aels for adoff alls to derease te blokg probablty. Guard aels are aels exlusvely reserved for adoff alls. However, oter models su as, [4] ad [2], used queues to delay adoff alls utl a ael beomes avalable. A model wt a prorty queue te maroell ter was proposed [5]. Te g speed users adoff alls te queue ad ger prorty we a ael s released. I [6], a two-ter ellular etwork avg a FIFO te maroell ter was proposed. Te proposed etwork took to aout te ell sze, te ell dwellg tme ad te moblty of te users to obta te queue tme of ea type of user. Se te queue s te maroell ter, bot te g ad low speed user ave aess to te queue. Te performae of a two-ter ellular etwork wt a queue oe of ts ters depeds o te dstrbuto of te users te geograpal area of te etwork. I our paper, we propose a model of a two-ter ellular etwork wt a FIFO queue te mroell to study ts effet o te users. We ompare te results wt tose obtaed from te prevously proposed model avg a queue te maroell ter. I addto, we ompare our results wt tose of a twoter etwork avg o queue ay ter ad dsplay te mprovemet avg a queue te etwork. Mausrpt reeved Mar 23, Tara Sal s wt te Computer Egeerg Departmet at Fat Uversty, Istabul, Turkey (poe: ; fax: ; e-mal: tsal@fat.edu.tr). Kemal Fdaboylu s wt te Eletros Egeerg Departmet at Fat Uversty, Istabul, Turkey (emal: kfda@fat.edu.tr). 54 II. SYSTEM DESCRITION I ts paper, a two-ter ellular etwork wt a FIFO queue te mroell s proposed. Te proposed model s vald for etworks overg a large geograpal area. Te low ad g speed users are assged to te mroells ad te maroells, respetvely. Te radus of te mroell s

2 Iteratoal Joural of Appled Matemats ad Computer Sees 2;2 Sprg 2006 smaller ta te maroell, ad a teger umber of mroells are overed by oe maroell. We ave assumed tat oe a low speed user all s overflowed to te maroell, t aot retur bak to te mroell ad we a low speed user beomes a g speed user te all s overflowed to te maroell. Calls overflow from te mroell to te maroell also we te low speed user s ew or adoff all aot fd a free ael te mroell. A ael s released uder two odtos: we a user volutarly termates te ogog all ad we a adoff all ompletes eter wt suess or falure. A adoff all s bloked we t aot fd a free ael te desred ell. Ts appes due to erta fators, su as, te queue s full or te queue tme assged to te users s too sort for te all to wat for a ael to be released. A ew all s bloked we t aot fd a free ael te ell. A. Model parameters We assume tat te ells are rular sape. Table 1 sows te parameters we ave used for modelg te ellular etwork. TABLE I MODEL ARAMETERS AND DESCRITIONS Symbol Desrpto Number of aels ea ell. N Number of mroells tat are overlad by oe maroell Q Sze of FIFO queue. 1 Arrval rate of ew alls for low speed users. Arrval rate of ew alls for g speed users. l Arrval rate of adoff alls for low speed users. Arrval rate of adoff all for g speed users. 1/ Mea average oldg tme for bot types of users. 1/ dl Mea ell dwellg tme for low speed users. 1/ d Mea ell dwellg tme for g speed users. 1/ ql Mea queue tme for low speed users. 1/ q Mea queue tme for g speed users. Te arrval rates of ew alls ad adoff alls for bot low ad g speed users are assumed to be osso proesses. Te ell dwellg tme s te tme a moble user speds a ell before t s aded off to aoter ell. It depeds o te speed of te moble user ad te sze of te ell. Te ell dwellg tme a be alulated as sow [1] as follows: 1 r v (1) d 2 were r s te radus of te ell ad v s te speed of te moble user. Te queue tme s te tme te adoff all remas te queue. I [5], t s sow tat te mea queue tme depeds o two parameters (a) Te mea ell dwellg tme. (b) Te maxmum ross-dstae M, over te overlappg zoe betwee two ells. Hee, queue tme = ( M /100) x ell dwellg tme. Te average oldg tme, te mea ell dwellg tme ad te mea queue tme for bot low ad g speed users are assumed to be egatvely expoetally dstrbuted. B. Aalyss of te mroell ter Te frst part of te aalyss orrespods to te mroell ter represeted by a Markov a wt a FIFO queue ad s aalyzed as [7] ad [8]. Fg. 1 sows te state s(), were deotes te umber of low speed users te mroell. We assume tat te umber of aels,, equals 3 ad te queue sze, Q, equals 2 as sow Fg. 1. Fg. 1. State trasto dagram for a mroell wt 3 aels ad a queue sze of 2. I te above trasto dagram, m ad q are gve by m dl ad q ql, respetvely. By solvg te Markov as, we fd tat te state probablty () s smlar to te results obtaed [8] as follows: l l 0! dl l l l 0! dl j dl j 1 ql (2) Se 1 0 Q l 0 l 1 1! 1, te (0) a be expressed as dl! l dl dl j ql j1 Te blokg probablty for ew alls, q Te blokg probablty for adoff alls, l l, s gve by 1 (3) (4), s gve by (5) Q Te overflow traff for low speed ew alls, adoff alls, ol followg equatos ol ad are alulated, as [1], usg te N (6) ol ol C. Aalyss of te maroell ter l l N (7) Te seod part of te aalyss orrespods to te maroell ter wtout a queue. Te system s aalyzed usg a Markov a tat otas te state s(,, were ad j are te umbers of low ad g speed users te system, respetvely. Te Markov a model wt 3 aels s sow Fg

3 Iteratoal Joural of Appled Matemats ad Computer Sees 2;2 Sprg 2006 probabltes for low speed users, respetvely. Te, tese probabltes a be wrtte as: b _ b (10) b _ b (11) b _ l b (12) b _ l b (13) Fg. 2. Markov model of te maroell wt 3 aels. Te parameters volved te Markov a are defed as follows L ol H ol M1 dl M 2 d L2 We defe te followg luso futos to fd te equlbrum equato of te state probabltes usg te approa preseted [9]. 1 j, q 0 1 0, q 0 1 j 0, q 0 III. NUMERICAL RESULTS AND COMARISIONS I ts seto, we sow omparsos of te umeral results for te proposed two-ter ellular etwork avg a queue te mroell wt tose preseted [6]. Furtermore, te same results are ompared wt tose obtaed for a two-ter ellular etwork wtout avg a queue. For te omputato of te umeral results, we ave assumed a omogeeous two-ter ellular etwork wt oe maroell overg 7 mroells ad ea ell otag 3 aels. We assumed tat te speed of te moble users s pre-alulated so tat oe a all s orgated te low speed users are assged to te mroell ter ad te g speed users are assged to te maroell ter. We used te same assumptos [6] to obta te results. Fg. 3 sows te effet of te ew arrval rate o te adoff all blokg probabltes of low speed users for te tree models. It s lear from te fgure tat te model wt a queue te mroell ter as a lower blokg probablty ta te oters beause te low speed users ave aess to te queue. I addto, te model wt a queue te maroell ter also as lower blokg probablty ta te model wt o queue. Ts s due to te fat tat te low speed users after beg overflowed ave aess to te queue alog wt te g speed users te maroell ter. Te equlbrum equato for te state oupay probabltes (,q) a be alulated as follows: ( (, ( L H ) (, M 1 (, jm 2) (, (, ( (, j 1)( j 1) M 2 ( 1, ( 1) M 1) (, ( 1, L (, (, j 1) H Te blokg probablty for ew alls, b, te maroell s gve by (, (9) b j Se te maroell does ot ave a queue, te blokg probablty for adoff alls,, te maroell a be alulated usg te same equato for b. Te blokg probabltes for te overall system are alulated, as [5]. Hee, let b _ ad b _ be te ew ad adoff all blokg probabltes for g speed user ad b _ l ad b _ l be te ew ad adoff all blokg b (8) Fg. 3. Hadoff all blokg probablty of low speed users for te tree dfferet two-ter etwork models wt dfferet arrval rates of ew alls. Te adoff all blokg probabltes for g speed users of te tree models are ompared Fg. 4 we te arrval rate of ew alls reases. Te results sow tat, te model wt te queue te maroell ter as a lower blokg probablty ta te oters beause te g speed users are able to aess te queue te maroell we o free aels are avalable. I addto, te results for te model wt o queue ad te model wt a queue te mroell ter ave te same blokg probabltes beause te g speed users ave o aess to te queue te 56

4 Iteratoal Joural of Appled Matemats ad Computer Sees 2;2 Sprg 2006 mroell ter. Hee, te all s ot queued ad terefore t s dropped. From tese results we a olude tat te low speed users ave better performae ta g speed users se te adoff alls ave aess to bot of te queues weter te queue s te mroell or te maroell. Te adoff all blokg probablty of g speed users versus te queue sze s llustrated Fg. 7. Te results obtaed ts fgure are smlar to tose obtaed Fg. 4. Fg. 6. New all blokg probablty of low speed users for te tree dfferet two-ter etwork models wt dfferet queue szes. Fg. 4. Hadoff all blokg probablty of g speed users for te tree dfferet two-ter etwork models wt dfferet arrval rates of ew alls. Fg. 5 llustrates te effet of te arrval rate of ew alls o te ew all blokg probablty for g speed users two dfferet ases: a queue te mroell ad a queue te maroell. I ts fgure, t s sow tat te model wt a queue te mroell as a slgtly lower blokg probablty ta te oter model. Ts results from avg a lower rate of overflow alls (ew ad adoff) to te maroell ter due to te queue ts ter. Te results for te ew alls of low speed users are smlar to tose of te g speed users we te arrval rate reases. Te ew all blokg probablty of low speed users versus te queue sze for te tree proposed models s sow Fg. 6. From ts fgure, t a be observed tat te ew all blokg probablty for low speed users s lower for te model wt a queue te mroell ta te oter models, beause more ew alls are able to overflow to te maroell wle te adoff alls are queued te mroell. Fg. 7. Hadoff all blokg probablty of g speed users for te tree dfferet two-ter etwork models wt dfferet queue szes. Te ew all blokg probablty of g speed users as a futo of te queue sze for te tree proposed models s sow Fg 8. From ts fgure, t a be observed tat te model wt a queue te maroell as a ger probablty ta te oter two models ad reases utl te queue sze reaes te umber of aels ad te t beomes ostat. O te oter ad, te blokg probabltes of te oter two models do ot age wt respet to te queue sze. Fg. 5. New all blokg probablty of g speed users for two-ter ellular etwork models for dfferet ew all arrval rates. Fg. 8. New all blokg probablty of g speed users for te tree dfferet two-ter etwork models wt dfferet queue szes. 57

5 Iteratoal Joural of Appled Matemats ad Computer Sees 2;2 Sprg 2006 III. CONCLUSION Mult-ter ellular etworks mprove te performae of te system by addg addtoal aels tat aomodate more users. A mult-ter ellular etwork wt a queue oe of ts ters allow te adoff alls to wat te queue for a lmted amout of tme utl a ael s released. I ts paper, we proposed a ew markov model for a mult-ter ellular etwork wt a queue te mroell. We ompared te performae of ts model wt tose preseted [6]. From te results obtaed, we olude tat te blokg probabltes of te g ad low speed users are dfferet ea model based o ter dstrbuto te etwork, ter moblty ad te geograpal area of te etwork. He joed Drexel Uversty, Eletral Egeerg Departmet as a Vstg Assoate rofessor 1987 ad was appoted as te Assoate Dretor of Fber Opts ad otos Maufaturg Egeerg Ceter. I September 2000, e joed Fat Uversty, Eletros Egeerg Departmet. I May 2001, e establsed te IEEE Fat Uversty Studet Bra. Betwee Jue 2001 ad Mar 2002, e served as te Dretor of Graduate Isttute of Egeerg ad Sees ad betwee Jauary 2002 ad Aprl 2004 e served as te Ve Retor for Aadem Affars. He s urretly servg as te Atg Carma of te Computer Egeerg Departmet. Hs resear terests are wreless ommuatos, eletro ruts ad fber opts. REFERENCES [1] E. Ek ad C.Ersoy, Mult-ter etwork dmesog, Wreless Networks 7, 2001, pp [2] C. Cag, C. H. Cag ad K. R. Lo, Aalyss of a eraral ellular system wt reegg ad droppg for watg ew ad adoff alls, IEEE Trasatos o Veular Teology, vol. 48, o. 4, July [3] M. Olver ad J. Borras, erformae evaluato of varable reservato poles for ad-off protzato moble etworks, Ifoom 99 roeedg of IEEE, 1999, vol. 3, pp [4] S. Tekay ad B. Jabbar, A measuremet-based prortzato seme for adovers moble ellular etworks, IEEE Joural o Seleted Areas Commuatos, vol. 10, o. 8., Otober [5] X. Wu, Supportg qualty of serve (QoS) overlad wreless etworks,.d tess, Uversty of Calfora Davs, USA, [6] T. Sal ad K. M. Fdaboylu, erformae aalyss ad modelg of two-ter ellular etworks wt queug adoff alls, Egt IEEE Iteratoal Symposum o Computers ad Commuatos (ISCC 2003) Turkey, 2003, vol. 1, pp [7] D. Hog ad S. S. Rappaport, Traff model ad performae aalyss for ellular moble rado telepoe systems wt prortzed ad oprortzed adoff proedures, IEEE Trasatos o Veular Teology, vol. 35, o. 3, pp , Aug [8] Y. B. L, S. Moa ad A. Noerpel, Modelg te ael assgmet strateges for ad-off ad tal aess for a ps etwork, IEEE Trasatos o Veular Teology, vol. 43 o..3, pp , [9] M. Cu ad M. A. Basso, redtve semes for adoff prortzato ellular etworks based o moble postog, IEEE o Seleted Areas Commuatos, vol. 18, o. 3, Mar Tara Sal reeved er BS degree Computer See ad Egeerg from Al-Isra Uversty Se reeved er MS degree Computer Egeerg from Fat Uversty Se worked as a resear assstat te Computer Egeerg Departmet betwee Otober 2000 ad September Se was appoted as a Istrutor te same departmet Otober Her resear terests are wreless moble etworkg ad 2G/3G wreless ommuato systems (GSM ad UMTS). Kemal Fdaboylu reeved s B.S. degrees bot Eletral Egeerg ad Matemats ad M.S. degree Eletral Egeerg from Uversty of etroleum ad Merals 1985 ad 1987, respetvely. He reeved s.d. degree Eletral Egeerg from Vrga olyte Isttute ad State Uversty He worked as a resear assstat te Eletral Egeerg Departmet at Uversty of etroleum ad Merals betwee 1985 ad He also worked as a resear assstat ad te as a Vstg Assstat rofessor te Eletral Egeerg Departmet at Vrga olyte Isttute ad State Uversty from 1987 to 1991 ad from 1991 to 1992, respetvely. I 1992, e joed te Computer Egeerg Departmet at Marmara Uversty. He establsed te Eletros Egeerg Departmet at te same uvesty 1993 ad was appoted as te Ve Dea of Aadem Affars ad te Dretor of Computer Trag Certfate rogram