Channel Carrying: A Novel Hando Scheme. for Mobile Cellular Networks. Purdue University, West Lafayette, IN 47907, U.S.A.

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1 Cannel Carryng: A Novel Hando Sceme for oble Cellular Networks Juny L Ness B. Sro y Edwn K.P. Cong Scool of Electrcal and Computer Engneerng Purdue Unversty, West Lafayette, IN 47907, U.S.A. E-mal: funy, sro, econgg@ecn.purdue.edu Abstract We present a new sceme tat addresses te call ando problem n moble cellular networks. Ecently solvng te ando problem s mportant for guaranteeng Qualty of Servce QoS) to already admtted calls n te network. Our sceme s based on a new concept called cannel carryng: wen a moble user moves from one cell to anoter, under certan moblty condtons, te user s allowed to carry ts current cannel. We propose a new cannel assgnment sceme to ensure tat ts movement of cannels wll not lead to any extra co-cannel nterference or cannel lockng. In our sceme, te moblty of cannels reles entrely on localzed nformaton, and no global coordnaton s requred. Terefore, te sceme s smple and easy to mplement. We furter develop a ybrd cannel carryng sceme tat allows us to maxmze performance under varous constrants. We provde numercal results comparng our sceme wt te tradtonal cannel reservaton types of tecnques. We nd tat our sceme outperforms te reservaton sceme over a broad range of trac parameters. 1 Introducton Te use of cellular systems s a popular means for enancng te capacty of wreless communcaton networks. In suc a system, te servce area s dvded nto cells, and cannels are reused among tose cells. A cannel can be tougt of as a generc network resource; for example, a frequency band n FDA, a tme-slot n TDA, or a specc spread spectrum code n CDA. Ts denton s consstent wt tat n [4]. Cannels tat are used n one cell cannot be used n oter cells tat are closer tan te mnmum reuse dstance. Hando occurs wen a moble subscrber moves from one cell to anoter. A ando call may be blocked f tere s no free cannel n te new cell. However, studes ave sown tat blockng a ando Ts researc was supported n part by AT&T specal purpose grant , by NSF troug grants NCR , ECS , and ECS , and by te U.S. Army Researc Oce troug grant EL-FRI. y Please address all correspondence to ts autor, Tel. 317) , FAX. 317) call s less desrable tan blockng a new call. Terefore, specc scemes ave been developed to prortze ando calls. Two prortzaton scemes ave been commonly studed n te lterature [1]. Tey are: ) Cannel reservaton scemes: In ts type of scemes, a number of cannels are reserved solely for te use of ando, allowng bot ando and new calls to compete for te remanng cannels [5]. Speccally, n eac cell a tresold s set, and f te number of cannels currently used n te cell s below tat tresold, bot new and ando calls are accepted. However, f te number of cannels used exceeds ts tresold, an ncomng new call s blocked and only ando calls are admtted. ) Queueng scemes: In ts type of scemes ando requests are queued, and may be later admtted nto te network n case cannels free up []. Te above two scemes can also be ntegrated togeter to mprove te ando blockng probablty and te overall cannel utlzaton. Te sceme we propose n ts paper s also readly ntegrated wt te queueng scemes. Terefore, we compare our sceme only wt te reservaton sceme. Our metod for treatng te ando problem stems from te followng smple dea. A user requestng a ando always occupes a cannel n ts current cell. Terefore, f tat cannel could be carred nto te new cell, te ando request would not be blocked. From a practcal pont of vew ts s not dcult to aceve. For example, n an FDA based system, suppose a user requestng ando to some cell A communcates over a frequency band x tat cell A s not allowed to use. Now, f normal ando s not possble te user or ts current base-staton) could sgnal cell A gvng t permsson to communcate over cannel x wt t. In a smlar way, cannels can be carred n CDA and TDA systems. However, wen a cannel s allowed to move nto anoter cell, t sortens te reuse dstance and may volate te mnmum reuse dstance requrement [1, 3]. To solve ts problem, we propose a new cannel assgnment metod tat allows cannels to be \carred" nto a negborng cell. Furtermore, wt an a pror agreement on cannel movement, cannel coordnaton can be aceved locally. Ts elps to sgncantly

2 r r+1 A B A B Cannel Cannel Set I Set II Cannel Set I Fgure 1: Lnear Cellular System r Fgure 3: r + 1)-Cannel Assgnment r+1 Cannel Cannel Set 1 Set Cannel Cannel Set 1 Set Fgure : r?cannel Assgnment Left Cannel Set I Rgt cannel 1 cannel m+1 cannel cannel m+ Left Cannel Set I Rgt cannel 1 cannel m+1 cannel cannel m+ smplfy te mplementaton. Te new ando sceme proposed n ts paper s called cannel carryng. We next descrbe ow te cannels are assgned for te cannel carryng sceme, and ten present our basc ando algortm. Cannel Assgnment For smplcty, we descrbe our cannel carryng sceme usng a lnear cellular system model. In ts system, cells or base statons) are arranged n a lnear conguraton, as sown n Fgure 1. Let N denote te total number of dstnct cannels tat are avalable n te cellular system. Two cells can use te same set of cannels as long as tey are at least r cells apart. Ts dstance r s called te mnmum reuse dstance or reuse factor. In te conventonal xed cannel assgnment sceme, te cannels are assgned suc tat te same cannels are reused exactly r cells apart, as sown n Fgure. Terefore, te total number of dstnct cannels avalable to eac cell s N=r. We refer to ts cannel assgnment as r-cannel assgnment. In our cannel carryng sceme, we allevate blockng due to ando by allowng calls to \carry" cannels from one cell to anoter. However, usng r- cannel assgnment, a call tat carres a cannel to an adacent cell may volate te mnmum reuse dstance requrement. For example, n Fgure 1, cells A and A 0 use te same set of cannels. Suppose a call n cell A uses a cannel y, and carres t to cell B. Now, f a user arrves n cell A 0 and uses cannel y, ten te two y cannels are only a dstance of r? 1 cells apart, tus volatng te mnmum reuse dstance requrement. One way to overcome ts problem s to ave global coordnaton algortms tat use cannel lockng [3] to ensure tat suc stuatons do not occur. However, suc scemes are computatonally expensve and terefore dcult to mplement [3]. oreover, cannel lockng also degrades ecency. To ensure tat te mnmum reuse dstance requrement s not volated, we use an r + 1)-cannel assgnment sceme. In oter words, te same cannels are reused exactly r + 1 cells apart, as sown n Fgure 3. In ts case, te total number of dstnct cannels avalable to eac cell s N=r + 1). To ensure tat te same cannels do not get closer tan r cells apart due to cannel carryng), we restrct cannel movement n te followng way. Eac cannel s allowed to be carred n only one drecton, left or rgt. Ts restrcton tus dvdes te cannels assgned to eac cannel m cannel n cannel m cannel n Fgure 4: Cannel Dvson n te r + 1)-Cannel Assgnment Sceme cell nto two types. Furter, as sown n Fgure 4, exactly te same dvson s used n cells tat are a dstance r + 1 apart. Usng ts r + 1)-cannel assgnment sceme, and te cannel carryng algortm descrbed n te next secton, we ensure tat tere s no co-cannel nterference due to cannel movement, wle avodng te need for global coordnaton. 3 Hando Algortm 3.1 Algortm Descrpton To descrbe our ando algortm, we rst focus our attenton on a partcular arbtrary) cell, wc we call te local cell. Te adacent cells to te left and rgt of te local cell are called foregn cells. Te cannels tat ave been assgned to te local cell are called local cannels, and are dvded nto two types: local-left LL) and local-rgt LR) cannels as sown n Fgure 4. An LL LR) cannel s one tat can be carred to te left rgt) cell durng ando. In oter words, an LL LR) cannel can be used by a call n te local cell as well as n te foregn cell to te left rgt). A cannel from a foregn cell tat s beng used n te local cell s called a foregn cannel. Foregn cannels from te left cell are called foregnleft FL) cannels and foregn cannels from te rgt cell are called foregn-rgt FR) cannels. Our algortm can be descrbed n ve man parts, correspondng to ve derent possble scenaros: arrval of a new call, ando from a foregn cell, ando to a foregn cell, termnaton of a call, and wen a local cannel becomes dle Arrval of a new call Wen a new call arrves, we ceck f tere are any dle unused) local cannels. If tere are, te new call s accepted and assgned te dle cannel; oterwse, te call s reected blocked) Hando request from a foregn cell Wen a ando call request s receved from a foregn left or rgt) cell, we ceck f tere are any dle lo-

3 cal cannels avalable. If tere are, te ando call s accepted and assgned te dle cannel; oterwse, te foregn cell s noted tat tere are no dle local cannels Hando to a foregn cell For smplcty, suppose a user U n te local cell wants to move to te left foregn cell. Te ando operaton s attempted accordng to te followng order: 1. If user U s currently usng a foregn-left FL) cannel, ten t smply carres t back to te left cell; oterwse, step s ntated.. We ceck f tere s an FL cannel beng used by some oter user V n te local cell. If so, user U excanges ts cannel wt user V and ten executes step 1 above; f not, we perform step We send a ando request to te left foregn cell. Te foregn cell ten executes te procedure n Secton If te ando s accepted, user U moves to te left cell and releases ts own cannel; f not, step 4 s ntated. 4. If user U s currently usng a local-left LL) cannel, ten t carres t to te left cell; oterwse, step 5 s ntated. 5. We ceck f tere s an dle LL cannel currently n te local cell. If so, U releases ts own cannel, grabs te dle LL cannel, and carres t to te left cell; oterwse step 6 s ntated. 6. We ceck f tere s an LL cannel beng used by some oter user W n te local cell. If so, user U excanges ts cannel wt user W, and executes step 4 above. 7. If all te above condtons do not old, ten te ando cannot be accomplsed. Normally, ts would result n te ando call beng blocked. A smlar procedure would be appled f a user n te local cell wanted to move to te rgt foregn cell Termnaton of a call Wen a call U s termnated eter due to te normal end of te call, or due to ando blockng), we rst ceck f te cannel beng used by U s a foregn cannel. If so, we release te foregn cannel and return t to ts orgnally assgned cell. Oterwse, U s usng a local cannel te call s ten termnated and te cannel becomes dle Local cannel becomes dle Ts scenaro arses n te followng stuatons: 1. Termnaton of a call n te local cell.. Hando from te local cell to a foregn cell wtout carryng. 3. Return of an dle local cannel from a foregn cell wen a local cannel s released n te foregn cell and returned to te local cell). Wen a local cannel becomes newly dle, we ceck f tere s a user V usng a foregn cannel n te local cell. If so, user V s assgned te newly dle local cannel, and te foregn cannel s released and returned to ts orgnally assgned cell. 3. Salent Features of te Algortm Te followng are some of te sgncant features of our algortm. Agan, for smplcty, we focus only on ando from te local cell to te left foregn cell. ) An mportant feature of our algortm s tat no global coordnaton s necessary, tus facltatng mplementaton. At te same tme, te algortm ensures tat tere s no co-cannel nterference due to cannel movement. ) In our algortm, ando calls ave access to a larger porton of te system capacty tan new ncomng calls. To see ts, note tat a new call s blocked f and only f tere s no dle local) cannel n te local cell. On te oter and, a ando request to te left) foregn cell s blocked f and only f all te left-local LL) cannels are beng used n te foregn cell. Ts occurrence s relatvely rare because t requres tat all tree of te followng condtons are smultaneously true: a) All te FL cannels are beng used by users n te left foregn cell. b) All te cannels n te left foregn cell are beng used. c) All te LL cannels ave been prevously carred to te left foregn cell. It s terefore apparent tat n our cannel carryng sceme, ando call requests are favored over new call requests. eanwle, we do not requre cannels to be reserved a pror for ando calls. Ts elps ncrease te ecency of our sceme compared to reservaton scemes, as demonstrated n Sectons 4.3 and 5.. ) In our algortm, we prefer to use local cannels wenever possble. We refer to ts polcy as a return-as-soon-as-possble polcy. For example, wenever a cannel becomes dle, we always return te foregn cannel f any) nstead of keepng tat dle cannel watng for a potental call n te local cell. Te polcy serves to protect potental ando calls, because te accumulaton of foregn cannels may block furter ando requests from te foregn cell. 4 Performance Analyss 4.1 Cannel Carryng Sceme In ts secton we develop a arkov can model to analyze te performance of our ando algortm. Te QoS measures tat we are nterested n are: P bn, te steady state probablty of blockng a new call; and

4 k H H k l l H H 0 0 Average Handoff Rate cell A cell B a) cell A cell B b) Fgure 5: a) Lnear Cellular system wt varous traf- c parameters. b) Two-Cell model wt te correspondng trac parameters. P bh, te steady state probablty of blockng a ando call. Te system tat we are nterested n modelng s te lnear cellular system sown n Fgure 5a). Te traf- c s assumed to be symmetrcally dstrbuted over all te cells, for example, te new call arrval rate at every cell s n. Te ando rates between cells s assumed to be drectly proportonal to te number of users n tat cell, so f a cell as users te ando rate to ts negborng cell s H, as sown n Fgure 5a). Analyss of ts entre system s computatonally nfeasble. Terefore, te performance analyss of call ando scemes n wreless systems s typcally done by focusng on a sngle cell wc results n a one dmensonal arkov can. However, te one-cell model does not accurately capture te essence of our algortm. For example, suppose tat a user n te local cell wants to move to te left foregn cell. Weter or not t carres a cannel durng ando depends not only on te avalablty of FL and LL cannels n te local cell but also on weter tere s an dle cannel n te left foregn cell. Hence, te avalablty of cannels n adacent cells s coupled. To allevate dcultes wt a one-cell model we consder a two-cell model, as sown n Fgure 5b). We assume tat n eac cell A and B, new call requests arrve accordng to Posson processes wt rate n. Te tme t takes for eac call n a cell to request a ando to te oter cell s assumed to be exponentally dstrbuted wt mean 1= H. Call andos arrve from outsde te two-cell subsystem accordng to a Posson process wt rate. Te tme untl a call termnates s assumed to be exponentally dstrbuted wt mean 1= 0. Terefore te tme untl a call leaves te two-cell system eter due to ando or call termnaton) s exponentally dstrbuted wt mean 1= = 1= 0 + H ). Now, assumng tat all of te above mentoned processes new arrval, call ando request, and call termnaton) are mutually ndependent, we can analyze our two-cell system usng a arkov Can. Recall tat te total number of local cannels n eac cell s = N=r + 1). To furter smplfy te,, 0-1,, 0 -,, 0 +1) + 3 H H + H + n -1, -1, 0 -, -1, 0, -1, 0 +1) 3 +1) +) +1) +1) +) + +1) H -, -, 0 ++1) +1) +1) +m) +1) 0 -, -, 0 -,, 0 0,, 0 0, -1, 0, -, 0, -, 0 +) +1) +1) 1 1 0, -, +1) 0, -m, m +1) +) -1) -1) +) +) +m) k-) +m) +1) k-m) k-+1) k-) H k-m+1) 0, -k, 0, -k, m -1) -, -, 0 +m) H ++1) +) -1) +1) -1) k-m+1) ++1) k-+1) -1) +) n 0, 1, 0 1, 1, 0 -m) +m) -) -1) -m+1) H -) -+1) -1) +1) + +1) n + Fgure 6: arkov Can for te Cannel Carryng Sceme usng te Two-Cell model. Note tat m = =, and = N=r + 1). model, we assume tat te total number of local cannels,, s dvded nto an equal number, m = =, of local left LL) and local rgt LR) cannels. Our arkov can model s sown n Fgure 6. To descrbe te model, let N A f0; : : :; g and N B f0; : : :; g represent te number of dle local cannels n cell A and cell B, respectvely. Next, let N B!A f? ; : : :; 0; : : :; g represent te followng. If N B!A 0, t denotes te number of for- egn cannels from cell B tat are beng used n cell A. On te oter and, f N B!A 0, t denotes te number of foregn cannels from cell A tat are beng used n cell B. Hence, N B!A t) can take values from? to. Te trple N A; N B ; N B!A ) represents te state of te arkov can. Altoug tere are tree components n eac state, te state trans- 0, 0, m 0, 0, 1 0, 0, 0, 0, 0 +1) +m) H ++1) +) +)

5 ton dagram of te arkov can can be represented n a planar fason. To see ts, recall tat a foregn cannel wll move nto a cell only wen tere s no dle local cannel n tat cell. Also, wenever servce s termnated, te foregn cannel wtn te local cell wll be returned mmedately. Tus, f we neglect te addtonal tme t would take to return or carry a cannel, t follows tat N B!A > 0 ) N A = 0, and N B!A < 0 ) N B = 0. Tese equatons elp restrct one degree of freedom tereby resultng n te planar or two-dmensonal arkov can sown n Fgure 6. Note tat, because of te symmetrc nature of te arkov can,.e., P fn A = ; N B = ; N B!A = kg = P fn A = ; N B = ; N B!A =?kg, only alf of te arkov can s sown n te gure. Let P ;;k = P fn A = ; N B = ; N B!A = kg denote te steady state probablty of te state fn A = ; N B = ; N B!A = kg. We obtan tese probabltes by explotng te above mentoned symmetry and by applyng standard numercal arkov can tecnques. Now observe Fgures 5a) and 5b) agan. In Fgure 5b) we ave focussed only on cells A and B of Fgure 5a). Let te cells to te rgt of cell B and to te left of cell A be called external cells. Te ando rate n te two-cell model of Fgure 5a) s actually te average of te state dependent ando rate from ter negborng external cells. Averagng over all te states, s gven by X =? ) H X mx P ;;k ; 1) =0 =0 k=?m were m = =. Snce depends on P ;;k, we teratvely solve te arkov can. Havng determned P ;;k, we calculate P bn, and P bh as follows: P bn = mx X?k k=0 =0 P 0;;k ; P bh = X?m?1 =0 P 0;;m ; ) 4. Cannel Sceme In ts secton we develop a arkov can model, sown n Fgure 7, to analyze te system performance usng te tradtonal cannel reservaton sceme. As n te cannel carryng sceme, we focus on te two-cell model sown n Fgure 5. Te parameters, n, H, and are dened as before. Snce no cannel movement s allowed, te par N A ; N B ), N A f0; : : :; 0 g, N B f0; : : :; 0 g, suces to caracterze te state of te two-cell system. Here, 0 = N=r s te total number of dstnct cannels avalable to eac cell, and N A N B ) s te total number of dle cannels n cell A cell B). Te resultng arkov can s sown n Fgure 7. Agan, because of te symmetrc nature of te arkov can,.e., P fn A = ; N B = g = P fn A = ; N B = g, only alf of te arkov can s sown n Fgure 7. Let 4 P = P fna = ; N B = g denote te steady state probablty of te state fn A = ; N B = g. Ten, as n te cannel carryng sceme,, te average external ando arrval rate, s gven by:, -1, -, -K, 0, 3 K K+1) + 3 H H K + H H + n + -1, -1 -, -1 0, H n -, K+1) H 0, - -K, - K+1) K +1) +1) K +1) +1) Fgure 7: arkov Can for te Cannel Sceme usng te Two-Cell model. Note: 0 = N=r. = X 0 =0 K K K K+1) 0, -K -K, -K K+1) X0 0? ) H K+1) K+1) =0-1) -1) -1) 1, 1 0, 1 P ; : 3) Snce depends on P ;, we teratvely solve te arkov can n Fgure 7. Now P bn and P bh are gven by P bn = X 0?K =0 X 0 =0 P ; ; P bh = X 0 =0 0, 0 P 0; 4) It s nstructve to compare te state transton dagrams n Fgures 6 and 7. Te number of local cannels n eac cell s 0 = N=r n te reservaton sceme Fgure 6) nstead of = N=r + 1) n te carryng sceme Fgure 7). Te derence s d = 0? = N, wc s te cost we pay rr+1) for cannel moblty. Clearly, wen te reuse factor r s large, ts derence s margnal. Also, because of cannel reservaton, new calls ave to be blocked wen te number of occuped local cannels exceeds a tresold K n Fgure 7. Ten, te arrval rate s reduced from n + to, wc s a dsadvantage of te reservaton sceme compared to te cannel carryng sceme. 4.3 Numercal Results In ts secton, we provde numercal results to compare te performance of te cannel carryng sceme and te reservaton sceme. We use our arkov can model for computng te performance measures P bn and P bh and also smulate te system under te carryng and reservaton scemes. Our smulaton conssts of a 10 cell lnear

6 P bn P bh Analyss Results: Carryng r= Smulaton Results: Carryng r= Fgure 8: Plot of P bn versus n Analyss Results: Carryng r= Smulaton Results: Carryng r= Fgure 9: Plot of P bh versus n. cellular system, suc as te one sown n Fgure 5a). Snce we are nterested n te performance of a typcal cell, te statstcs are averaged over all cells. Trougout te paper, we nd tat te smulaton and analytcal results matc qute well, wc ndcates tat te two-cell model works well n caracterzng te beavor of te algortm n a lnear cellular system. In Fgure 8 we plot P bn, and n Fgure 9, we plot P bh for bot te cannel carryng and te reservaton sceme under derent trac loads n, rangng from 4 calls to 13 calls per unt tme. Te call ando rate s H = 1 call per unt tme, and te call termnaton rate s 0 = 1 call per unt tme. For te cannel carryng case, two values for te reuse dstance are consdered: r =, te mnmum possble reuse dstance, and r = 4, a more typcal value for te reuse dstance. Furter, n bot gures, 0 = N=r = 15; ence, N = 30 wen r =, and N = 60 wen r = 4. Note, tat n te cannel reservaton sceme, for a gven arrval rate, we can vary te tresold K to gve us derent values of P bn and P bh. We nd tat f we coose K = = N=r + 1), ten te values of P bn for te reservaton sceme are close to tose for te carryng sceme. Te reason for ts s tat f te number of occuped local cannels n a cell reaces K or ), any new call n te reservaton or carryng, respectvely) sceme s now blocked. For r =, we coose K = = 10, and we can observe n Fgure 8 tat te new call blockng probablty P bn ) curves for te reservaton and carryng scemes are n fact very close. However, for te same parameters, te call ando blockng probablty P bh ) as sown n Fgure 9 s at least about one order of magntude lower n te carryng sceme tan n te reservaton sceme. Wen te value of te reuse dstance s ncreased to r = 4, and we set K = 10, te carryng sceme sgncantly outperforms te reservaton sceme n terms of bot P bn and P bh. Ts result can be observed n Fgure 8, were te P bn curve n te carryng case s up to one order of magntude lower tan n te reservaton sceme, and n Fgure 9, were te P bh curve n te carryng sceme s up to tree orders of magntude lower tan n te reservaton sceme. We next develop a ybrd cannel carryng sceme wc attempts to maxmze performance, under varous constrants, by allowng us to vary te number of cannels tat can be carred. 5 Hybrd Cannel Carryng Sceme 5.1 Descrpton In te numercal examples of te prevous secton, we observe tat te cannel carryng sceme results n a large derence between te values of P bh and P bn. In partcular, wen te load s g, te value of P bn s muc ger tan tat of P bh. For example, for n = 13 and r = 4, te value of P bh s only about 10?5 wle tat of P bn s greater tan 10?1. Ts observaton suggests tat our cannel carryng sceme excessvely favors ando requests over new calls. We next present a ybrd sceme tat allows tradng o potental ando blockng for avalablty of dle cannels for new calls. Recall tat n te r + 1)-cannel assgnment sceme, te number of cannels assgned to eac cell s = N=r + 1), and every cannel can be carred eter to te left or to te rgt. On te oter and, n te r-cannel assgnment sceme, te number of cannels assgned to eac cell s N=r, but none of te cannels can be carred to foregn cells. In our ybrd sceme, we dvde te total number of cannels N nto two dstnct groups of sze N 1 and N, suc tat N = N 1 + N : Te N 1 cannels are assgned accordng to te r-cannel assgnment sceme, and cannot be carred to foregn cannels. Te N cannels, owever, are assgned accordng to te r + 1)-cannel assgnment sceme, and can be carred eter to te left or to te rgt, ust as n te prevous cannel carryng sceme. Terefore, n te ybrd sceme, eac cell s assgned ybrd = N 1 r + N r + 1 5) cannels, were te two terms n te sum corresponds to te two groups of cannels. As before, te N =r + 1) cannels of te second type are temselves dvded nto two types: left and rgt. Te ybrd sceme above denes a famly of cannel assgnments tat encompasses bot te pure r-

7 and r + 1)-cannel assgnment scemes. Speccally, N 1 = 0 corresponds to te r + 1)-cannel assgnment sceme, wle N = 0 leads to te r-cannel assgnment sceme. Te N cannels allow us to trade o te ablty to carry and ence avod ando blockng) wt a reduced number of cannels avalable to eac cell. In partcular, te number of cannels tat we sacrce n usng r +1)-cannel assgnment nstead of r-cannels assgnment s d ybrd = N r? N r + 1 = 1 r N r + 1 : 6) P bn Analyss Results: Carryng r= 10 4 Smulaton Results: Carryng r= Tus, d ybrd serves as a desgn parameter tat we can adust to balance te requrements of te performance measures P bn and P bh, analogous to te tresold parameter K n te cannel reservaton sceme. Te larger te value of d ybrd n te ybrd sceme, te more we favor ando calls because tere are more movable cannels. Hence, as d ybrd ncreases, we expect P bh to decrease and P bn to ncrease. A smlar observaton olds for te desgn parameter K n te reservaton sceme. Also note tat, as n te orgnal cannel carryng case, for a xed number of cannels N tat are allowed to move, te prce we pay for te r+1)-cannel assgnment sceme n terms of d ybrd ) decreases wt ncreasng r. 5. Numercal Results For te purpose of performance evaluaton, we adopt te two-cell model and make te same assumptons ere as we dd n Secton 4.3. Te resultng arkov can as exactly te same structure as n Fgure 6, te only derence beng tat we substtute m ybrd = N n place of m. We can ten solve r+1) for te steady state probabltes n te arkov cans for te ybrd and reservaton scemes, and compute P bh and P bn as before. Also, as n Secton 4.3, for our smulatons we use a 10-cell lnear cellular system. We now provde plots of P bn under varyng load condtons for te ybrd and reservaton scemes. Te performance measures depend on te parameters d ybrd and K n te ybrd and reservaton scemes, respectvely. To meanngfully compare our ybrd sceme wt te reservaton sceme, we determne te optmal values of P bn for te two scemes, gven a constrant on P bh. Terefore, n te ybrd sceme, to approprately coose d ybrd, we consder te followng optmzaton problem: mnmze d ybrd P bn ; subect to P bh H max ; 7) were H max denotes a prespeced maxmum level for P bh. A smlar optmzaton problem can be dened for te reservaton sceme, were te decson varable d ybrd above s replaced wt te tresold parameter K. For a far comparson of our ybrd sceme wt te reservaton sceme, we calculate te optmal values of P bn for te two scemes, gven te same H max. Te optmal values can be computed numercally usng te arkov cans n Fgures 6 and 7. Fgure 10 Fgure 10: Plot of optmal P bn versus n for te problem dened n Equaton 7) Analyss Results: Carryng r= Smulaton Results: Carryng r= Fgure 11: Plot of optmal n versus P bh for te problem dened n Equaton 8). sows plots of te optmal values of P bn for te reservaton and ybrd scemes under varyng n. For ts gure we ave used te followng parameters: H = 1, 0 = 1, 0 = 15. Terefore, N = 30 for r =, and N = 60 for r = 4. For te constrant on P bh, we used H max = 10?4, a typcally desrable constrant for te ando blockng probablty. We can see tat te ybrd sceme aceves unformly lower values of P bn tan te reservaton sceme. As expected, ncreasng te value of r furter decreases P bn n te cannel carryng case. Next, n Fgure 11, we plot a grap n wc we compare te maxmum new call arrval rate n tat can be admtted by te carryng sceme and te reservaton sceme for varous ando blockng probabltes P bh. ore precsely we dene te followng optmzaton problem for te cannel carryng sceme: P bh maxmze d ybrd n ; subect to P bn N max ; P bh = H: 8) Here te constrant H for P bh s vared between 10?8 and 10? and te correspondng maxmum value of n s obtaned. A smlar optmzaton problem s dened for te reservaton sceme by replacng d ybrd by K. In Fgure 11 we plot te optmal values of n versus

8 γ Analyss Results: Carryng r= Smulaton Results: Carryng r= Fgure 1: Plot of optmal versus n for te problem dened n Equaton 9). P bh for te reservaton sceme and te cannel carryng sceme wt r = and r = 4. For ts gure we use te followng parameters: H = 1, 0 = 1, 0 = 15, N max = 10?. From Fgure 11 one can observe tat te ybrd carryng sceme allows a ger new call rate tan te reservaton sceme over all values of P bh. For large values of P bh all te scemes perform essentally te same snce t corresponds to te case wen no carryng s necessary n te ybrd case N = 0) and no reservaton s necessary K = N=r) n te reservaton sceme. However, for a typcal value of P bh = 10?4, te ybrd sceme wt r = 4 can admt approxmately 0% more calls nto te network tan te reservaton sceme. As s sown n te gure, for lower ando probablty constrants, ts derence s even larger. From a network provder's pont of vew, a more useful parameter of nterest s te normalzed cannel utlzaton,, dened as 4 = average number of users n one cell total number of avalable cannels n one cell ; were te total number of avalable cannels n one cell s 0 = N=r. Te parameter s drectly related to te revenue of a cellular network because t ncorporates bot new and ando calls. To plot te values of under varyng loads for te ybrd sceme, we dene te optmzaton problem maxmze d ybrd ; subect to P bh H max : 9) Once agan, we dene a smlar optmzaton problem for te reservaton sceme by replacng te decson varable d ybrd by K. In Fgure 1 we plot values of under varyng n. Te parameters used for ts gure are: H = 1, 0 = 1, 0 = 15, H max = 10?4. Te ybrd sceme aceves unformly ger values of under varous loads. Te derence between te ybrd and reservaton scemes s most apparent at g loads. At suc loads, a low value of K s requred n te reservaton sceme to mantan te QoS constrant on P bh, tus resultng n a low value of. On te oter and, due to te moblty of cannels n te ybrd sceme, te sacrce n te number of local cannels to mantan te QoS constrant on P bh s not as great. Wen r = 4, te cannel utlzaton for te cannel carryng sceme at g loads s over 50% more tan te reservaton sceme. Furter, ts advantage wll be even more sgncant as r ncreases. 6 Concluson We ave presented a novel cannel carryng sceme to address te problem of andos n moble cellular systems. Our basc dea s to allow moble users to carry ter current cannels nto new cells under certan condtons. We use te r+1)-cannel assgnment sceme to avod co-cannel nterference due to cannel movement. Ts aords us cannel moblty at te expense of some capacty. An attractve feature of te cannel carryng sceme s tat t does not requre complex power control tecnques or global cannel coordnaton, wc smples ts mplementaton. We develop a two-cell model to analyze our cannel carryng sceme and te tradtonal cannel reservaton tecnque. We nd troug numercal results tat even n te case of te mnmum possble reuse dstance, r =, te cannel carryng sceme outperforms te reservaton tecnque. We furter consder a renement to te cannel carryng sceme, wc provdes a useful desgn parameter tat allows us to optmze varous parameters of nterest. We agan nd tat our sceme sceme unformly and sgncantly mproves te system performance, n some cases resultng n over 50% better network utlzaton tan te cannel reservaton sceme. References [1] S. Teknay and B. Jabbar, \Handover and cannel assgnment n moble cellular networks," IEEE Communcatons agazne, vol.9, pp.4{ 46, Nov [] G.N. Senarat and D.H. Evertt, \Performance of andover prorty and queueng systems under derent andover request strateges for mcrocellular moble communcatons systems," Proc. IEEE Ve. Tecnol. Conf., pp.897{901, [3] H. Jang and S.S. Rappaport, \CBWL: a new cannel assgnment and sarng metod for cellular communcaton systems," IEEE Trans. Ve. Tecnol., vol.vt-43, pp.313{3, ay [4] E.D. Re, R. Fantacc and G. Gambene, \Handover and dynamc cannel allocaton tecnques n moble cellular networks," IEEE Trans. Ve. Tecnol., vol.vt-44, pp.9-37, ay [5] R. Ramee, R. Nagaraan and D. Towsley, \On optmal call admsson control n cellular networks," Proc. INFOCO., pp43{50, arc 1996.