WITH the rapid growth of multiservice mobile wireless

Transcription

1 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER Bandwidth Reallocation for Bandwidth Ayetry Wirele Network Baed on Ditributed Multiervice Adiion Control Xun Yang, Meber, IEEE Coputer Society, and Gang Feng, Senior Meber, IEEE Abtract Thi paper addree when and how to adjut bandwidth allocation on uplink and downlink in a ultiervice obile wirele network under dynaic traffic load condition. Our deign objective i to iprove yte bandwidth utilization while atifying call level QoS requireent of variou call clae. We develop a new threhold-baed ultiervice adiion control chee (DMS-AC) a a tudy bae for bandwidth reallocation. When the traffic load brought by oe pecific clae under dynaic traffic condition in a yte exceed the control range of DMS-AC, the QoS of oe call clae ay not be guaranteed. In uch a ituation, bandwidth reallocation proce i activated and the adiion control chee will try to eet the QoS requireent under the adjuted bandwidth allocation. We explore the relationhip between adiion threhold and bandwidth allocation by identifying certain contraint for verifying the feaibility of the adjuted bandwidth allocation. We conduct extenive iulation experient to validate the effectivene of the propoed bandwidth reallocation chee. Nuerical reult how that when traffic pattern with certain bandwidth ayetry between uplink and downlink change, the yte can reallocate the bandwidth on uplink and downlink adaptively. With the deigned bandwidth reallocation chee in conjunction with the ditributed adiion control chee, the QoS requireent of variou call clae can be guaranteed under dynaic traffic condition, and in the eantie, the yte bandwidth utilization i iproved ignificantly. Index Ter Multiervice obile network, traffic ayetry, ditributed adiion control, bandwidth reallocation. Ç 1 INTRODUCTION WITH the rapid growth of ultiervice obile wirele network, any application that are popular in wired network are upported in obile environent. Since oe data application, uch a web browing and file downloading, ay bring higher traffic load on downlink than on uplink, next generation ultiervice wirele network are expected to preent ditinctive traffic ayetry between uplink and downlink [1], [2], [3], [4]. In uch network, if identical aount of bandwidth i allocated to downlink and uplink, oe yte reource ay be wated [3], [5], [6], [7]. In order to atch the ayetric traffic load, it i neceary to allocate different bandwidth to uplink and downlink. For deterinitic traffic paraeter and obility characteritic, fixed bandwidth allocation i able to provide an optial olution for the reource allocation proble in wirele network with bandwidth ayetry [3], [5]. However, any eerging application and ervice with burty and variable bandwidth requireent call for new treatent of network reource anageent, in order to atify application need and iprove network reource. X. Yang i with Beijing Jiaotong Univerity, TA2-704#, Beijing , P.R. China. E-ail: yangxun@pail.ntu.edu.g, yangxun_cn@hotail.co.. G. Feng i with the National Key Laboratory of Counication, Univerity of Electronic Science and Technology of China, Chengdu , P.R. China. E-ail: fenggang@uetc.edu.cn. Manucript received 12 Dec. 2006; revied 25 Sept. 2007; accepted 13 Mar. 2008; publihed online 1 Apr For inforation on obtaining reprint of thi article, pleae end e-ail to: tc@coputer.org, and reference IEEECS Log Nuber TMC Digital Object Identifier no /TMC utilization. Furtherore, in ultiervice obile wirele network, the traffic generated by oe application i tie dependent. For exaple, bandwidth ayetry caued by oe data application could be ignificantly higher than uual during peak hour in oe particular cell. In addition, due to obility, oe uer with certain application ay handoff fro one cell to another cauing the change of traffic load ayetry in that cell. Therefore, it i iperative to develop a dynaic bandwidth allocation chee that can adapt to the changing traffic condition in ultiervice obile wirele network with bandwidth ayetry. In [8], the author proved that the yte with different tie-lot allocation for different cell alway outperfor that with the ae tie-lot allocation, if the tie lot on uplink and downlink are properly allocated. However, there i only little known work in the literature, which addree how to properly allocate bandwidth on uplink and downlink. On the other hand, ince bandwidth reallocation on uplink and downlink ay affect all ongoing call in the yte [3], we hould liit bandwidth reallocation frequency and perfor bandwidth reallocation when it i neceary. Although it i uggeted that a yte hould allocate bandwidth to uplink and downlink according to the traffic load [3], [9], we till do not know when the yte need to adjut the bandwidth allocation on uplink and downlink. In thi paper, we explore when and how to adjut bandwidth allocation properly in a ultiervice obile wirele network. A one of the critical Quality of Service (QoS) proviioning trategie, call adiion control (CAC) i alway ued to guarantee the QoS of different call clae in ultiervice /08/$25.00 ß 2008 IEEE Publihed by the IEEE CS, CASS, CoSoc, IES, & SPS

2 1312 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 obile wirele network. In our work, we tudy the bandwidth reallocation proble baed on a CAC chee ince it provide a good reference for bandwidth allocation in a obile wirele network. Our objective i to deign a dynaic bandwidth allocation chee baed on CAC to provide the deired QoS requireent of different call clae and, in the eantie, to utilize the bandwidth reource in the bet way. At call level, new call blocking probability ðp n Þ and handoff call dropping probability ðp h Þ are two ajor QoS paraeter in the deign of CAC chee. Since it i ore undeirable to dirupt an ongoing call, there i trict upper bound for P h. In order to guarantee P h of different call clae under certain contraint, there i a tradeoff between the adiion of handoff call and new call. However, it i unacceptable to acrifice the new call too uch, which ay reult in low yte bandwidth utilization. How to iniize new call blocking probability a well a guarantee the handoff call dropping probabilitie of different call clae under predefined criteria (MINBlock proble) i an open quetion challenging the exiting CAC chee in ultiervice obile wirele network. In thi paper, we firt propoe a Ditributed Multiervice Adiion Control (DMS-AC) chee to handle the MIN- Block proble in ultiervice obile wirele network. Then, DMS-AC i ued to provide a tudy bae for invetigating bandwidth reallocation proble. By identifying certain adiion condition, DMS-AC trie to find proper threhold for different call clae according to certain traffic pattern. The threhold i ued to liit the adiion of the new call of a pecific call cla to guarantee yte QoS. If the feaible threhold of oe call clae cannot be found or the blocking probabilitie of the new call exceed certain upper bound, it indicate the QoS of handoff/new call of oe call clae cannot be guaranteed. In uch a ituation, the bandwidth reallocation proce i activated and the yte ay adjut the bandwidth allocation on uplink and downlink and recopute the call adiion threhold until the proper threhold are deterined for each call cla in the cell. By tudying the bandwidth reallocation proble baed on the propoed DMS-AC, we find that the bandwidth allocated to uplink and downlink hould not only be proportional to the traffic load a that uggeted in [3] but alo need to atify oe contraint, which are obtained fro the derivation of the threhold in DMS-AC. By uing thee contraint to verify the feaibility of a bandwidth allocation, DMS-AC collaborate with bandwidth reallocation to iprove yte perforance ignificantly and, at the ae tie, anwer the quetion when and how to adjut the bandwidth allocation in a ultiervice obile wirele network. The ret of thi paper i organized a follow: We review oe exiting CAC and bandwidth allocation chee in Section 2. In Section 3, we decribe the yte odel and the propoed DMS-AC chee. In Section 4, we tudy the bandwidth reallocation proble baed on the propoed adiion control chee. In thi ection, we addre when and how to adjut the bandwidth allocation in a bandwidth ayetry network. The propoed bandwidth reallocation chee i alo preented in thi ection. Nuerical reult and analyi are given in Section 5. At lat, we conclude thi paper in Section 6. 2 RELATED WORK ON ADMISSION CONTROL AND BANDWIDTH ALLOCATION Bandwidth reallocation i a relatively new reearch topic in recent year ince the bandwidth allocation i alway yetric in traditional onoervice obile network. A bandwidth adjutable CDMA/TDD yte ha been propoed for traffic unbalance network in [3] and [10] to iprove yte utilization of obile wirele network with traffic ayetry. In the propoed yte of Jeong and Jeon [3], the nuber of uplink tie lot in a TDD frae differ fro that of downlink. Moreover, the difference can be reet by the network operator according to the traffic pattern. In [8], the author copared two different tie-lot allocation trategie, ae tie-lot allocation (SA) and different tie-lot allocation (DA), in CDMA/TDD yte. SA trategy require all cell within a ervice area have the ae tie-lot allocation. In DA trategy, the tie-lot allocation ay be different fro cell to cell according to the level of traffic ayetry in a cell. In ultiervice obile wirele network, the level of traffic ayetry ay be ignificantly divere fro cell to cell. In thi cae, the lot allocation hould be varied cell by cell to axiize the frequency utilization. However, DA trategy ay reult in croed-lot interference between two adjacent cell. To the bet of our knowledge, current reearch work of bandwidth reallocation (tie-lot reallocation) coonly focue on croed-lot interference proble of DA trategy [11], [12], [13]. Little exiting work invetigate when and how to adjut bandwidth allocation a well a the effect on call level perforance. Since our tudy of bandwidth reallocation i baed on adiion control, we next briefly review oe exiting CAC chee. In the pat two decade, CAC ha been extenively tudied in both wired and wirele network. In the deign of CAC in obile wirele network, handoff call dropping probability and new call blocking probability are two ajor QoS eaureent. In onoervice obile network, Guard Channel (GC) chee [14] i propoed to reduce handoff call dropping probability by reerving certain guard channel for handoff call excluively. Since reerving channel affect the adiion of new call, the nuber of guard channel hould be deterined carefully. However, the author did not illutrate how to find the proper nuber of guard channel. In [15], the author proved that the GC chee i optial to iniize a linear objective function, which i the weighted u of handoff and new call blocking probabilitie. They alo proved that the propoed Liited Fractional Guard Channel (LFGC) policy i optial for the MINBlock proble, which i defined a iniizing the new call blocking probability ubject to a hard contraint on the handoff dropping probability. Siilar to the GC chee, LFGC reerve C T channel out of a total of C channel for handoff call while T channel can be ued by both new and handoff call. When the nuber of ued channel i equal to T, a new call i accepted with probability. When

3 YANG AND FENG: BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY WIRELESS NETWORKS BASED ON DISTRIBUTED the nuber of ued channel i greater than T, only handoff call can be accepted. One of the critical proble in the deign of LFGC i how to copute appropriate value of T and. Becaue of the relatively all tate pace in onoervice network, LFGC deterine the value of T and by uing biection earch. Naghhineh and Schwartz propoed Ditributed Adiion Control (DCA) in [16] baed on the inforation exchanged between different cell in a obile yte. DCA ue a threhold to liit the adiion of new call and thu reerve reource for handoff call and at the ae tie reduce the nuber of potential handoff call. The threhold can be obtained by uing a Gauian approxiation according to the hard contraint on handoff call dropping probability. Regardle of the nuber of guard channel in GC, T and in LFGC, or the value of the threhold in DCA, they can be coputed readily due to one-dienionality in onoervice obile network. However, the ituation becoe ore coplicated in ultiervice network, where different call clae hare certain yte bandwidth reource according to oe adiion condition. Thee call clae ay have different ean call arrival rate, ean ervice tie, required bandwidth, and QoS requireent. Kaufan invetigated a general odel of ultiervice reource haring network in [17]. A well-known product for olution i obtained to copute the call blocking probability for arbitrary reource haring policy. Furtherore, a iple 1D recurive algorith i propoed to copute the call blocking probabilitie of different call clae, which i applicable regardle of the dienionality of the underlying odel. Kaufan production olution iplifie the theoretical coputation of call blocking probability, epecially in a ultiervice network. However, it i ipractical to copute the paraeter optiizing yte perforance, uch a the nuber of reerved channel or the threhold of different call clae, fro the recurive proce. In [18], Ro and Tang abtracted ultiervice reource haring proble into tochatic knapack odel. They proved that the optial olution of revenue axiization proble i of threhold type when the nuber of call clae i two. Indeed, the GC chee i a pecial cae of thi general odel. Since the author focued on the tudy of the tructure of the optial policy, they did not dicu how to find proper threhold of different call clae in detail. In [19], the author propoed dynaic bandwidth reervation trategy for different call clae in ultiervice obile network. In the propoed reervation chee, the nuber of reerved channel ay be increaed or decreaed according to the eaureent of call blocking probabilitie of different call clae. However, they did not invetigate how any channel hould be increaed or decreaed to atify different QoS requireent of divere call clae. Chau et al. extended the LFGC chee to incorporate the ultiple traffic clae in [20]. Siulated annealing technique i eployed to obtain the optial control paraeter. Ni et al. propoed a general iterative coordinate earch algorith to find the appropriate threhold by conidering revenue axiization proble in [21]. Since the objective i to axiize a revenue function, the propoed threhold coputing ethod i not applicable for iniizing new call blocking probability with hard contraint on handoff dropping probability. In [7], Jeon and Jeong propoed a ultiervice CAC baed on bandwidth reervation for different call clae by conidering ayetric traffic load in a obile yte. Since the bandwidth reervation i totally baed on the etiation of call arrival rate, it ay not guarantee the QoS of handoff call in a dynaic traffic load network. 3 DISTRIBUTED MULTISERVICE ADMISSION CONTROL 3.1 Syte Model We conider a cellular network in which the bandwidth allocation on both uplink and downlink i adjutable in individual cell [3], [8]. The bandwidth allocated on uplink and downlink could be different in a cell, but the total bandwidth of a cell i fixed. Let there be M clae of call in the yte. The call of a particular cla have the ae bandwidth requireent, obility characteritic, and ean reource holding tie. We aue that new and handoff cla i ði 2½0;M 1ŠÞ call arrive according to Poion proce with ean rate i and i, repectively. Let i denote the highet tolerable dropping probability of the cla i handoff call. The deign goal of the propoed adiion control chee i to anage the handoff call dropping probability of cla i ð8i 2½0;M 1ŠÞ call, denoted by i, to be below i and at the ae tie try to keep the blocking probability of the new cla i call, denoted by i, under a pecific upper bound i. The propoed DMS-AC chee operate in a ditributed anner. The inforation of yte tate, uch a the nuber of call of the individual clae and o forth, i exchanged between adjacent cell periodically. The bae tation of a cell ake an adiion deciion baed on the tate inforation of the cell itelf (called oberving cell) and it neighboring cell. DMS-AC ue the adiion threhold of each call cla baed on the yte tate to liit the adiion of the new call. When the nuber of call of a pecific cla reache the threhold of thi cla, new arrival of thi cla are rejected. Since the fixed threhold ay not be able to guarantee the QoS requireent when the offered traffic pattern change, we deign a dynaic threhold chee and the threhold of a pecific call cla can be recoputed and reet periodically according to the change of traffic pattern of the yte. We define the interval between two threhold coputing procee a a control period, which lat T unit of tie, and the threhold of a pecific call cla i fixed in a control period. The duration of the control period hould be aociated with the dynaic of traffic load. Too long or too hort interval ay affect the behavior and perforance of the propoed chee. If the control interval i too hort, uch a a few inute, the chee ay be enitive to the traffic burt. On the other hand, if it i too long uch a everal hour, the chee ay not adjut the threhold proptly according to the traffic pattern. We have conducted

4 1314 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 Fig. 1. Two-cell yte. extenive experient to tudy how the control interval affect the perforance of the propoed chee. The experient reult how that the control interval doe not affect the perforance of the propoed chee ignificantly. Due to the liitation of paper length, we do not how the experient reult here. In thi paper, we aue that T could take the value between 15 and 60 inute. In the reaining part of thi ection, we firt conider a iple yte, which i copoed of two cell, and then extend the propoed adiion control chee to a ulticell yte. 3.2 Ditributed Multiervice Adiion Control in a Two-Cell Syte The yte we conider firt i copoed of two cell, denoted by C r and C l, a hown in Fig. 1. In the ret of thi paper, we ue r and l in upercript or ubcript of notation to denote the right cell C r and the left cell C l, repectively. u and d in upercript or ubcript of notation are ued to denote uplink and downlink, repectively. B r u ðbl u Þ and B r d ðbl dþ unit of bandwidth are allocated to uplink and downlink of the cell C r ðc l Þ, repectively. The total bandwidth in C r ðc l Þ i denoted by B r ðb l Þ, where B r i equal to B r u þ Br d (B l i equal to B l u þ Bl d ). Without lo of generality, let C r be the current oberving cell and C l be regarded a the neighboring cell. Before we preent DMS-AC, we need to define the overload tate of a pecific call cla in the ultiervice yte. In a onoervice yte, the yte i at the overload tate when no ore call can be accepted. In ultiervice network, the et of overload tate of different call clae ay be different. We ue a iple exaple to illutrate thi. Suppoe that a cell ha 10 downlink channel and five uplink channel. Two call clae, cla 1 and cla 2, are upported. A cla 1 call require one channel on both uplink and downlink while a cla 2 call require one uplink channel and three downlink channel. We ue ðn 1 ;n 2 Þ to denote a yte tate, where n 1 and n 2 repreent the nuber of cla 1 call and cla 2 call in the yte, repectively. In Fig. 2, we how all poible tate with dot. Fro the figure, we find that when the yte i at tate (0, 3) and (2, 2), no cla 2 call can be accepted while cla 1 call are till adiible. Thu, thee two tate, (0, 3) and (2, 2), are the overload tate of cla 2 call (but not cla 1 call). The olid dot in Fig. 2a and 2b are ued to indicate the overload tate of cla 1 and cla 2 call, repectively. Fro thi exaple, we know that the et of overload tate of cla 1 call (Fig. 2a) i different fro that of cla 2 call (Fig. 2b). Generally, for the ultiervice network, the et of overload tate of variou call clae ay be different. Fig. 2. An exaple. (a) Overload tate of cla 1 call. (b) Overload tate of cla 2 call. We ue i to denote the probability that the yte i at any one of the overload tate of a pecific call cla i. i can alo be regarded a the handoff call dropping probability of call cla i, ince we do not conider threhold of handoff call in the propoed chee. During a control period, the adiion of a cla i ði 2 ½0;M 1ŠÞ new call in the oberving cell C r hould atify the following two condition according to the QoS requireent of that call cla: 1. The adiion of a new cla i ði 2½0;M 1ŠÞ call in C r cannot caue the call dropping probability of call cla j in C r, denoted by r j, to exceed j ð8j 2½0;M 1ŠÞ. 2. The adiion of a new cla i ði 2½0;M 1ŠÞ call in C r cannot caue the call dropping probability of call cla j in the neighboring cell C l, denoted by l j,to exceed j ð8j 2½0;M 1ŠÞ. The econd condition i ued to liit the nuber of handoff call fro C r to C l to avoid uperfluou handoff call of a pecific call cla fro overuing the reource in C l. The key of DMS-AC i to deterine the threhold of individual call clae in each cell. To thi end, we need to copute r j and l j ð8j 2½0;M 1ŠÞ. Aue that there are r i and l i cla i call in C r and C l at the beginning of the current control period, repectively. Our objective i to find the axiu value of r i, denoted by Th r i, a the threhold of the new call of cla i during the current control period. We aue that a cla i call in C r reain in the ae cell during the control period with probability P and ove to C l with probability Pl. Accordingly, P i;l denote the probability that a cla i call reain in C l and Pi;lr denote the probability of a cla i call oving to C r during the control period. P ðp i;l Þ and P l ðp i;lr Þ can be etiated according to uer oveent pattern uch a oving peed, oving direction, and o forth. Soe reearch tudie have been conducted to etiate thee probabilitie [22], [16], [23] and we do not dicu it further in thi paper. Let r i ðl i Þ and r i ðl iþ denote the ean new call and handoff call arrival rate of call cla i in C r ðc l Þ during the control period, repectively. Let u conider the firt adiion condition. During a control period, the probability that x i cla i call out of r i call tay in C r ha a binoial ditribution given by Bðx i ;r i ;P Þ¼ r i P xi rix i: x 1 P ð1þ i

5 YANG AND FENG: BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY WIRELESS NETWORKS BASED ON DISTRIBUTED Siilarly, the probability that y i cla i call handoff to C r fro C l during a control period i B y i ; l i ;P i;lr ¼ Pi;lr yi l 1 Pi;lr i y i; ð2þ l i y i where l i i expreed a l i þð^ i l þ ^ l iþt. Since the new arrival in C l during the current control period, which include both new and handoff call, ay alo handoff to C r, we ue l i intead of l i in (2). The nuber of the handoff and new call that will be aditted during the control period i repreented a ð^ i l þ ^ l i ÞT, where ^l i and ^ l i are equal to ð1 l i Þl i and ð1 l i Þl i, repectively. We ue l i and l i to denote the handoff dropping probability and new call blocking probability of call cla i in C l during the current control period, repectively. The controller of C l ay copute l i and l i given certain bandwidth allocation and threhold value. The adiion controller of C r can obtain the value of l i and l i by exchanging inforation with C l. Let P r ðn i Þ denote the probability that there are n i cla i call in C r during T unit of tie, where n i ¼ x i þ y i. Thu, P r ðn i Þ i the convolution u of two binoial ditribution Bðx i ;r i ;P Þ and Bðy i; l i ;P i;lr Þ, where x i and y i hould atify 0 x i r i and 0 y i l i, repectively. Since CAC i eployed in a heavy traffic load yte, we could approxiate the binoial ditribution Bði; n; pþ by a Gauian ditribution p Gð; Þ with ean ¼ np and variance ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi npð1 pþ [24]. Thu, the nuber of cla i call in C r during the control period alo ha a Gauian ditribution given by P r ðn i Þ¼B x i ;r i ;P B y i ; l i ;P i;lr rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G r i P þ l i P i;lr ; r i P þ l i P : 1P i;lr 1P i;lr We know that a yte tay in a feaible tate at any tie, which ean that a tate, ¼ðn 0 ;n 2 ;...;n M1 Þ, hould atify P M1 i¼0 n i b u i B u and P M1 i¼0 n i b d i B d. n i ði 2½0;M 1ŠÞ i the nuber of cla i call in the yte. b u i and b d i are the bandwidth required by a cla i call on uplink and downlink, repectively. B u and B d are the bandwidth allocated to uplink and downlink, repectively. Let S denote the et of feaible tate of a cell. Since the reource in the yte are liited, the nuber of feaible tate of the yte i alo liited. Let there be total q feaible tate and S can be expreed a n 1 0 ;n1 1 ; 3...;n1 M1.. S ¼ k ¼ n k ;nk 1 ;...;nk M1 ; ð4þ q n q 0 ;nq 1 ;...;nq M1 where k, k ¼ðn k 0 ;nk 1 ;...;nk M1Þ, i the kth tate of S, and n k i i the nuber of cla i call in the yte when the yte tate i k, which atifie P M1 i¼0 n k i bu i B u and P M1 i¼0 n k i bd i B d. We define S i;j ðs i;j SÞ to be the et of tate of cla j, uch that for a yte at a tate k 2 S i;j, it can reach the ð3þ Fig. 3. Illutration of S i;j. overload tate of cla j with the increae of the nuber of cla i call in the yte. We continue the exaple ued previouly to explain the eaning of S i;j. Fro Fig. 2, we find that when n 1 ¼ 0 or n 1 ¼ 2 the yte cannot reach the overload tate of call cla 1 by only increaing the nuber of cla 2 call. When the yte i at tate (0, 3) or (2, 2), cla 1 call till can be accepted although no cla 2 call can be accepted. On the other hand, when n 1 ¼ 1; 3; 4; or 5 the yte can reach the overload tate of call cla 1 by increaing n 2. Thu, S 2;1 i repreented, a hown in Fig. 3. When the yte i at a tate in S 2;1, the yte can reach the overload tate of call cla 1 by only increaing the nuber of cla 2 call in the yte. We alo define N i;j ð k Þð k 2 S i;j Þ to be the iniu nuber of cla i call that let the yte enter the overload tate of call cla j when the yte i at tate k. For exaple, we know that N 1;2 ð0; 2Þ i equal to 2 fro Fig. 3. Let r i;j denote the probability that the cell C r i at one of the overload tate of call cla j, which reult due to the adiion of cla i call. For the firt adiion condition, the blocking probability of cla j call in C r expreed a and r i;j ¼ X 8 r k 2Sr i;j can be r j ¼ XM1 r i;j ð5þ i¼0 P r ¼ r X k P r ðn i Þj r ¼ r k ; ð6þ n in i;jð r k Þ where r i a rando variable, which denote the yte tate of C r, and r k i a pecific yte tate. Next, we conider the econd adiion condition, which tate that the call dropping probability of cla j in C l incurred by the handoff cla i call fro C r ut be aller than or equal to j. Aue that there are r i and l i cla i call in C r and C l at the beginning of a control period, repectively. Siilar to that in the dicuion of the firt adiion condition, the probability that x i cla i call out of r i call handoff fro C r to C l during the control period ha a binoial ditribution given by Bðx i ;r i ;Pl Þ and the probability that y i cla i call out of l i tay in C l during the control period i Bðy i ; l i ;P i;lþ. Thu, the probability ditribution of having n i cla i call in C l during the control period, denoted by P l ðn i Þ, i given by the convolution u of two binoial ditribution Bðx i ;r i ;Pl Þ and Bðy i; l i ;P i;l Þ, where x i þ y i i equal to n i ð0 x i r i ; 0 y i l iþ. We approxiate the binoial ditribution by a Gauian

6 1316 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 ditribution with appropriate ean and variance. A a reult, P l ðn i Þ i given a P l ðn i Þ¼B x i ;r i ;Pl B y i ; l i ;P i;l rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G r i Pl þl i P i;l ; r i Pl 1Pl þ l i P i;l 1Pi;l : For the econd adiion condition, the blocking probability of cla j call in C l i expreed a and l i;j ¼ X 8 l k 2Sl i;j ð7þ l j ¼ XM1 l i;j ð8þ i¼0 X P l ¼ l k P l ðn i Þj l ¼ l k ; ð9þ n in i;j ð Þ where l i a rando variable, which denote the yte tate of C l, and l k i a pecific yte tate. 3.3 Derivation of Adiion Threhold In the following, we derive the threhold for the propoed DMS-AC. Let u conider the firt adiion condition, where r j i required to be aller than or equal to j ðj 2½0;M 1ŠÞ. Fro (5), we know that r j can be expreed a the uation of r i;j ð8i 2½0;M 1ŠÞ, which reult due to the arrival of cla i call. Thu, we can require r i;j r i þ r i P M1 k¼0 r k þ j ð10þ r k ð8i; j2½0;m1šþ. r i;j can be expreed a that hown in (6). However, it i difficult to copute the threhold of each call cla fro (6) directly. We ue an indirect ethod to copute the threhold. Fro (6) and (9), we know that the overload probabilitie of the pecific feaible tate r k and l k can be expreed a X r i;j r k ¼ P r ðn i Þj r ¼ r k n in i;j ð r kþ 0 1 N i;j r k ri P þ l i P i;lr ð11þ A r i P 1 P þ l i P i;lr 1 Pi;lr and X ¼ P l ðn i Þj l ¼ l k n in i;j ð l kþ 0 1 N i;j l k ri Pl þ l i P i;l A ; r i Pl 1 Pl þ l i P i;l 1 Pi;l l i;j l k l k ð12þ repectively. QðÞ i the integral over the tail of a Gauian ditribution, which can be expreed in ter of the error function [8], [24]. We conider a conervative way to copute threhold by requiring the overload probability of the pecific tate ( r i;j ðr k Þ or r i;j ðr k Þ)tobe aller than certain contraint and thu obtain the lower bound of threhold. Then, the threhold will be tuned according to the call blocking probability a illutrated in Section 3.5. When we require that r i;j ðr k Þ r i þr i P M1 j, we can k¼0 ðr k þr k find a value, ay a r Þ i;j, uch that r i þ r i P M1 k¼0 r k þ j ¼ Q a r r i;j : ð13þ k Thu, we have N i;j r k ri P þ l i P i;lr rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð14þ a r i;j r i P 1 P þ l i P i;lr 1 Pi;lr ¼ 0: By anipulating (14), we can obtain a value of r i, which i regarded a the threhold of cla i call that atifie (13) when the yte i at a pecific tate r k. We ue Th1 i;j ðr k Þ to repreent thi value a Th 1 1 i;j r k ¼ 2P 2N i;j r k 2 l i Pi;lr þ ar i;j 2 1 P h a r i;j 4N i;j r 2 k 1 P þ a r i;j 2þ4 i 1=2 1 P l i Pi;lr P P i;lr : ð15þ Following the iilar way, we can obtain the threhold Th 2 i;j ðl kþ that atify the econd adiion condition a Th i;j l k ¼ 2Pl 2N i;j l k 2 l i Pi;l þ al i;j 1 P l h a l i;j 4N i;j l 2 k 1 P l þ a l i;j 2þ 1 Pl 4 l i Pi;l Pl P i;l i 1=2 : ð16þ Fro (15) and (16), we can obtain a erie value of Th 1 i;j ðr k Þ and Th2 i;j ðl k Þ for pecific tate r k and l k in C r and C l, repectively. Thu, the adiion threhold of cla i call in C r to atify the two adiion condition are given by and Th 1 i;j ¼ Th 2 i;j ¼ X 8 r k 2Sr i;j X 8 l k 2Sl i;j P r k Th 1 i;j r k ð17þ P l k Th 2 i;j l k : ð18þ Fro (17) and (18), we can obtain a erie value of the threhold of cla i call to atify different QoS requireent of all call clae in the yte. Let Th 1 i and Th 2 i denote the threhold of cla i call that atifie the firt and the econd adiion condition, repectively. Thu, Th 1 i and Th 2 i can be expreed a

7 YANG AND FENG: BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY WIRELESS NETWORKS BASED ON DISTRIBUTED variance. The probability that there are n i ðn i ¼ x i þ P 6 h¼1 y j;hþ cla i call in C 0 during the control period i Fig. 4. Seven-cell yte. and Th 1 i ¼ Th 2 i ¼ in 8j2½0;M1Š in 8j2½0;M1Š Th 1 i;j Th 2 i;j ð19þ : ð20þ The final adiion threhold of cla i call in C r, which atifie all adiion condition, i given by Th r i ¼ inðth1 i ;Th2 i Þ. 3.4 Extenion to Multicell Syte In thi ection, we extend the above DMS-AC chee of a two-cell yte to a ulticell yte. We conider a yte with even hexagonal cell (denoted by C 0 ;C 1 ;...; and C 7 ), a hown in Fig. 4. Without lo of generality, let C 0 be the current oberving cell and C 1 to C 6 be the neighboring cell. During a control period, the adiion of a cla i ði 2 ½0;M 1ŠÞ call in C 0 hould atify: 1. The adiion of a new cla i ði 2½0;M 1ŠÞ call in C 0 cannot caue the call dropping probability of call cla j in C 0, 0 j, to exceed j ð8j 2½0;M 1ŠÞ. 2. The adiion of a new cla i ði 2½0;M 1ŠÞ call in C 0 cannot caue the call dropping probability of call cla j in the neighboring cell to exceed j ð8j 2½0;M 1ŠÞ. The procedure for coputing the threhold of cla i call i iilar to that in the two-cell yte. Let u conider the firt adiion condition. At the beginning of a control period, there are w i;h cla i call in cell C h, where h could be 0;...; 6. Let i;h ðh ¼ 1;...; 6Þ denote the nuber of call in cell C h ðh ¼ 1;...; 6Þ during the control period and it i defined a i;h ¼ w i;h þð^ i h þ ^ h i ÞT. The nuber of the handoff and new call that will be aditted during the control period i repreented a ð^ i h þ ^ h i ÞT, where ^h i and ^ h i are equal to ð1 h i Þh i and ð1 h i Þh i, repectively. We ue h i and h i to denote the handoff dropping probability and new call blocking probability of call cla i in C h during the current control period, repectively. The probability that a cla i call tay in C 0 during the control period i denoted by Pi;0 and the probability that a cla i call hand-off to C 0 fro C 1 ;...;C 6 i repreented by Pi;h0 ðh ¼ 1;...; 6Þ. Thu, the probability ditribution of the nuber of cla i call in the cell C 0 during the control period i given by a convolution u of even binoial ditribution Bðx i ;w i;0 ;Pi;0 Þ and Bðy i;h; i;h ;Pi;h0 Þ, where h could be 1;...; 6. We approxiate the binoial ditribution by Gauian ditribution with appropriate ean and repreented a P C0 ðn i Þ G n i;0 Pi;0 þ X6 h i;h Pi;h0 n i;0 Pi;0 1 P i;0 h¼1 þ X6 i 1=2 i;h Pi;h0 1 P i;h0 : h¼1 0 k ð21þ Then, the overload probability of cla j call in C 0 i j ¼ XM1 B X P 0 ¼ 0 k P C0 ðn i Þj 0 ¼ 0 k C A; i¼0 8 0 k 2S0 i;j n i N i;j ð Þ ð22þ where S 0 i;j i the et of tate of cla j in C 0, uch that for the yte at a tate k 2 S 0 i;j, it can reach the overload tate of cla j with the increae of the nuber of cla i call in C 0. 0 i a rando variable repreenting the yte tate while 0 k i the kth tate in C 0. N i;j ð 0 kþ repreent the iniu nuber of cla i call that let the yte enter the overload tate of call cla j when C 0 i at 0 k. By applying a iilar ethod ued in (14), (15), and (17), we could find the threhold Th 0 i;c 0 for cla i ði 2½0;M 1ŠÞ call in C 0 that atifie the firt adiion condition. Then, we conider the econd adiion condition. Let Th 0 i;c h be the call adiion threhold of cla i call in C 0 to atify the econd adiion condition for cell C h, where h ¼ð1;...; 6Þ. We how how to calculate Th 0 i;c 1 a an exaple and Th 0 i;c 2 ;...;Th 0 i;c 6 can be coputed in the iilar anner. Fro Fig. 4, we know that the neighboring cell of C 1 are C 0, C 2, and C 6. Following the iilar way ued in the two-cell yte, let P C1 ðn i Þ denote the probability ditribution of the nuber of cla i call in C 1 during the control period, and it i given by P C1 ðn i Þ¼B y i;1 ; i;1 ;Pi;1 B x i ;w i;0 ;Pi;01 B y i;2 ; i;2 ;Pi;21 B y i;6 ; i;6 ;Pi;61 : ð23þ Bðy i;1 ; i;1 ;Pi;1 Þ denote the probability that y i;1 cla i call out of i;1 cla i call reain in C 1 during the control period, where Pi;1 repreent the probability that a cla i call tay in C 1 during the control period. Bðx i ;w i;0 ;Pi;01 Þ i the probability that x i call out of w i;0 cla i call ove fro C 0 to C 1 during the control period and Pi;01 i the probability that a cla i call hand-off fro C 0 to C 1 during the control period. Bðy i;h ; i;h ;Pi;h1 Þ i the probability that y i;h cla i call out of i;h cla i call handoff fro C h to C 1, where Pi;h1 i the probability of a cla i call hand-off fro C h to C 1 during the control period, where h i 2 or 6. Thu, we could obtain P C1 ðn i Þ and the overload probability by approxiating the binoial ditribution with Gauian ditribution with appropriate ean and variance. By applying iilar technical ethod a that ued in (16) and (18), we could obtain Th 0 i;c 1 for cla i call in C 0 to atify certain QoS liitation in C 1. Siilarly, we could obtain Th 0 i;c h, where h could be 2;...; 6. Finally, the threhold of cla i call in C 0, Th 0 i,ith0 i ¼ in6 h¼0 ðth0 i;c h Þ.

8 1318 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 Fig. 5. Peudocode of the proce for tuning the threhold. 3.5 Threhold-Baed Adiion Control Schee So far, we have decribed how to copute the threhold of different call clae. In the above threhold coputing proce, r i;j ðr k Þ and l i;j ðl kþ are et to be aller than the criteria for each pecific tate in C r and C l. Indeed, thi ethod i too conervative ince it i not neceary to require r i;j ðr k Þ and l i;j ðl kþ to be aller than the criteria for every poible tate, which ay caue oe new call to be blocked unnecearily. In the propoed adiion control chee, we ue the coputed threhold a the lower bound and carefully tune the threhold value by increaing the until one or ore of the following condition are violated (we conider C r a an exaple and the iilar condition can be applied to C l ): 1. ^ r i i and ^ l i i ð8i 2½0;M 1ŠÞ; 2. ^r i > i ; 3. ^r j j ð8j 2½0;i 1ŠÞ; 4. ^r i i ð8i 2½0;M 1ŠÞ; 5. Th r i r i, where ^ i and ^ i are the coputed handoff and new cla i call blocking probabilitie, repectively. r i i the axiu nuber of cla i call that can be aditted in C r under a given bandwidth allocation. Without lo of generality, we ort the call clae according to the value of upper bound of the new call blocking probabilitie of different call clae in acending order fro 0 to M 1. In other word, the cla 0 ha the lowet upper bound of new call blocking probability. The peudocode of the tuning proce of the threhold i hown in Fig. 5. After we obtain Th r i ð8i 2½0;M 1ŠÞ, we need to check whether condition 1 can be atified or not for all call clae in the cell ðc r Þ and it neighboring cell ðc l Þ.If condition 1 i atified, Th r i increae continually until the blocking probability of cla i call i aller than the predefined upper bound or Th r i reache the axiu value. If Th r i doe not reach the axiu value, Th r i till can be increaed repeatedly until condition 1 and 4 cannot be atified. By eploying threhold tuning proce, we can decreae the new call blocking probability and avoid acrificing other call clae too uch (e.g., let the new call blocking probability exceed the upper bound). After obtaining Th i of cla i call, whether a new cla i call can be accepted i deterined by the nuber of the cla i call in the yte. If the nuber reache the threhold, no ore new cla i call can be accepted. 4 BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY NETWORKS In Section 3, we have propoed a ditributed ultithrehold adiion control chee for ultiervice wirele network and derived the adiion threhold of each call cla to eet the QoS requireent. In thi ection, we preent a bandwidth reallocation chee baed on DMS-AC. Before dicuion, let u define the feaible threhold to be the threhold Th i for call cla i in a pecific cell with value between 0 and i, where i i the axiu nuber of cla i call that can be aditted in the cell under a given bandwidth allocation. If the coputed threhold i greater than i, we can et the value of that threhold to be i ince the threhold greater than i could guarantee the QoS requireent and thu the threhold, which i equal to i. On the other hand, if the derived threhold i aller than 0, it ean that we cannot find a feaible threhold value under current bandwidth allocation and the QoS requireent of one or ore call clae cannot be atified. When the yte i unable to deterine the feaible threhold of oe call clae, it iplie that the traffic load brought by oe call clae exceed the control range of the adiion control chee. The bandwidth reallocation function could be triggered to adjut the bandwidth allocation between uplink and downlink and then the call adiion threhold are recoputed until the feaible threhold are found. In thi paper, we aue that the feaible threhold can be found by adjuting bandwidth allocation between uplink and downlink of the cell if the traffic load exceed the control range of the eployed adiion control chee. If the threhold cannot be found under any poible bandwidth allocation in a cell, it ean that traffic load ha exceeded the utainable capacity of the cell. We do not conider uch ituation in thi paper a the bandwidth reallocation proble becoe trivial. On the other hand, the new call blocking probability cannot be acrificed too uch in order to guarantee the QoS of handoff call. Thu, there hould be oe upper bound of blocking probabilitie for the new call of different call clae. When the feaible threhold cannot be found or the new call blocking probability reache the predefined upper bound, the bandwidth reallocation proce i trigged. Next, we will dicu how to find the feaible bandwidth allocation for uplink and downlink. Since the baic procedure ued in the propoed adiion control chee in the two-cell yte and ulticell yte are iilar, we dicu the bandwidth allocation baed on the forer for eae of dicuion, and the obtained reult and algorith can be readily extended to the ultiple cell yte. Fro (15) and (16), we know that Th 1 i;j depend on the tate ð r k Þ of the oberving cell ðc rþ while Th 2 i;j depend on the tate ð l k Þ of the neighboring cell ðc lþ. There are two cae that ay reult in bandwidth reallocation. In cae 1, if we cannot find a feaible threhold fro (15) and (17) to atify the firt adiion condition, it iplie that the bandwidth allocation of C r hould be adjuted. In cae 2, if a proper threhold fro (16) and (18) cannot be found to atify the econd adiion condition, it ean that the QoS of oe call clae in C l ay be violated under the

9 YANG AND FENG: BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY WIRELESS NETWORKS BASED ON DISTRIBUTED current traffic condition and bandwidth reallocation hould be executed in C l. In the following, we dicu thee two cae in detail. 4.1 Cae 1 Let u exaine the firt cae. In the beginning of a control period, if the adiion control chee cannot find the feaible threhold of oe call clae, the yte need to reallocate the bandwidth on uplink and downlink of the cell. Fro (15), we can copute the threhold of cla i call for a given j, where i, j 2½0;M 1Š. We can rewrite (15) a ¼ Az 2 þ Bz þ C; ð24þ Th 1 i;j r k where z i h z ¼ 4N i;j r 2 2 k 1 P þ a r i;j 1 P i 1=2: ð25þ þ 4 l i P i;lr P P i;lr A ¼ 1 4P ð1p Þ, B ¼ ar i;j 2P and C ¼ 1 4P ða r i;j Þ2 ð1 P Þ 1 P ð1p Þ l i P i;lr ð1 P i;lr Þ. Fro (24), we can find that the threhold Th 1 i;j ðr k Þ i a function of z while z increae onotonouly with N i;j ð r k Þ a z i greater than 0. The value of N i;j ð r kþ could be 1; 2;...; r i. Thu, the value of z lie between ½z in;z ax Š, where z in and z ax are given, repectively, in h 2 2 z in ¼ 4 1 P þ a r i;j 1 P i 1=2; ð26þ þ 4 l i P i;lr P P i;lr h z ax ¼ P þ a r i;j 1 P i 1=2: ð27þ þ 4 l i P i;lr P P i;lr 4 r i We obtain z in and z ax by etting N i;j ð r k Þ to be 1 and r i, repectively. In order to obtain (24), P cannot be equal to 0 and 1. Since P i a tatitical variable ued to repreent the probability that cla i call reain in C r during T, iti reaonable that P 6¼ 0; 1 though the value of P ay be very cloe to 0 or 1. Siilarly, Pi;lr 6¼ 0; 1. Fro the definition of A, B, and C, we realize that B 2 4AC ¼ l i P i;lr ð1p i;lr Þ i greater than or equal to 0. When ðp ð1p ÞÞ2 ðb 2 4ACÞ > 0 ð l i 6¼ 0Þ, we can ketch the curve of Th1 i;j ðr k Þ a the function of z, a hown in Fig. 6. Regardle of whether C>0or C 0, we can obtain z 1;2 ¼ a r i;jð1 P qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Þ 2 l i P i;lr ð1 P i;lr Þ, which i the olution to the equation Az 2 þ Bz þ C ¼ 0. Obviouly, z in i between z 1 and qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi z ax, where z 1 can be expreed a z 1 ¼ a r i;jð1 P Þ2 l i P i;lr ð1 Pi;lr Þ. We are concerned about whether or not z ax i greater than z 2.If z ax i aller than z 2, the value of Th 1 i;j ðr kþ are negative. In fact, the negative threhold i infeaible, which ean Fig. 6. Th 1 i;j ðr k Þ a a function of z when l i 6¼ 0. that the QoS of oe call clae cannot be guaranteed although no cla i call can be aditted when the yte i at oe pecific tate. When z ax <z 2, we cannot find a feaible threhold of cla i call to atify the pecific QoS requireent j of call cla j no atter which tate the yte i at during the control period T. On the other hand, if there exit a feaible threhold, z ax ut be greater than z 2. Let z ax be greater than z 2 and we can obtain rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r i >l i P i;lr i;j l i P i;lr 1 Pi;lr ; ð28þ where r i ðr i ¼ inðbbr u b u i c; b Br dcþþ i the axiu nuber b d i of cla i call that can be aditted in C r, and it i totally deterined by the bandwidth allocated to the uplink and the downlink of C r. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Let i be ax 8j2½0;M1Š l i P i;lr þ ar i;j l i P i;lr ð1 Pi;lr Þ.We obtain r i > i: ð29þ In order to find a feaible threhold, contraint (29) hould be atified. Epecially, when l i P i;lr atifie qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l i P i;lr ar i;j l i P i;lr ð1 P i;lr Þ, i.e., l i ðar i;j Þ2 ð1p i;lr Þ P, a feaible threhold of cla i call to atify the firt adiion i;lr condition exit only if the axiu adiible nuber of cla i call in the current oberving cell i greater than the nuber of handoff cla i call fro all neighboring cell, i.e., r i >l i P i;lr. Fro the above analyi, we know that the reallocated bandwidth hould atify (29). Since the total bandwidth in a cell i fixed and B r d can be obtained fro B r B r u, we only how the relationhip between r i and B r u. Fro the definition of r i and (29), we depict B rb r u and Br b d u b a the u i i function of B r u, a hown in Fig. 7a. We can ee that the curve of r i conit of two egent repreented by the olid line in Fig. 7a. In order to atify (29), the bandwidth value of uplink ðb r u Þ hould be between Bi in and Bi ax, where B i in and Bi ax are the lower and upper bound of Br u, repectively. When we conider ultiple call clae in the

10 1320 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 Fig. 7. r i a a function of Br u. (a) One call cla. (b) Two call clae. Fig. 8. Th i;j ð r k Þ a a function of z when l i ¼ 0. cell, the feaible uplink bandwidth value hould be between ðb in ;B ax Þ, where B in ¼ B i in ð30þ ax 8i2½0;M1Š and B ax ¼ in B i ax : ð31þ 8i2½0;M1Š ðb in ;B ax Þ i the coon part of the range ðb i in ;Bi ax Þ ð8i 2½0;M 1ŠÞ. IfB ax i aller than B in, thi indicate that the feaible bandwidth allocation under current traffic condition cannot be found and we do not need to conider thi ituation a the proble becoe trivial. Fig. 7b how an exaple when there are two call clae. According to (30) and (31), the feaible uplink bandwidth value hould be between B 2 in and B1 ax. We regard the uplink bandwidth B r u between ðb in;b ax Þ a the feaible bandwidth. Accordingly, we can deterine the feaible downlink bandwidth B r d. When the yte ha feaible bandwidth on both uplink and downlink, we regard the bandwidth allocation ðb r u ;Br dþ a a feaible bandwidth allocation. Indeed, there could be ultiple feaible bandwidth allocation of the cell. We elect the one with inial ju r=r d Br u =Br dj to axiize the yte utilization a the olution, where u and d denote the tie-average traffic load during a period on uplink and downlink, repectively, a that defined in [3]. Then, we can try to find a threhold fro (15) and (17) for cla i baed on the adjuted bandwidth allocation. If we till cannot find a feaible threhold, we hould repeat the above proce to find the new bandwidth allocation until a feaible threhold of call cla i i found. The detail of the bandwidth reallocation algorith will be given in the ubequent ection. When B 2 4AC i equal to 0 (i.e., l i ¼ 0, z 1 ¼ z 2 ¼ a r i;j ð1 P Þ¼z 0), z in ut be greater than z 0. We can depict the curve of Th 1 i;j ðr kþ a the function of z in thi ituation, a hown in Fig. 8. Since l i i equal to 0, the nuber of handoff call fro C l during T i 0. In uch an extree cae, the threhold of cla i in C r cannot be aller than 0. Thu, there ut be a feaible threhold of the cla i call. 4.2 Cae 2 Next, let u conider the econd cae. The econd adiion condition require that the nuber of the new cla i call hould be liited in order to avoid the cla i call that handoff fro C r to C l in the near future fro violating the QoS requireent of oe higher priority call clae in C l. Fro (16) and (18), we can find that Th 2 i i highly dependent on the yte tate of C l. If we cannot find a feaible threhold of call cla i to atify the econd adiion condition, it ugget that the bandwidth allocation in C l be adjuted. By following the iilar procedure ued in cae 1, we could obtain the following condition: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l i >l i P i;l þ al i;j l i P i;l 1 Pi;l : ð32þ If the axiu adiible nuber of cla i call in C l doe not atify the above condition, we cannot find a feaible threhold of cla i call in C r to atify a pecific QoS requireent in C l no atter what yte tate C l i at. If condition (32) cannot be atified or the feaible threhold cannot be found through (16) and (18), it ean that the bandwidth allocation in C l need to be adjuted. If we conider cae 2 in cell C l, (32) i changed to rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r i >r i P þ ar i;j r i P Let i be equal to ax 8j2½0;M1Š r i P þ ar i;j and we have r i > i; 1 P : ð33þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r i P ð1 P Þ ð34þ which can be ued to exaine the feaibility of a bandwidth allocation by given a threhold of cla i call during a control period. At any tie, the axiu adiible nuber of cla i call under a given bandwidth allocation hould atify (34). Otherwie, we ay not find feaible threhold of oe call clae in the neighboring cell C l to atify the QoS requireent of oe call clae in C r. 4.3 Bandwidth Reallocation Algorith for Multiervice Wirele Network Baed on the above analyi of cae 1 and cae 2, we can decribe the bandwidth reallocation algorith a follow: 1. At the beginning of a control period, if the adiion control chee cannot find the feaible threhold of oe call clae or the new call blocking probabilitie of oe call clae exceed the upper bound, the bandwidth reallocation function i triggered. 2. Then, the feaible bandwidth range ðb in ;B ax Þ i coputed and the feaible bandwidth allocation can be obtained accordingly by uing B r d ¼ B r B r u. Next, we ort all the feaible bandwidth allocation in acending order according to the value of ju r=r d Br u =Br dj. We elect the firt bandwidth

11 YANG AND FENG: BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY WIRELESS NETWORKS BASED ON DISTRIBUTED Fig. 10. Handoff RT call blocking probabilitie when r RT increae fro 0.05 to 0.12 while l NRT increae fro to iultaneouly (coparing DMS-AC with Jeon chee). call in C r ðc l Þ, repectively. The ean ervice tie of RT call and NRT call i aued to be 120 and 900 econd, repectively. The probability of a new RT call oving fro one cell to another i 0.4, and the handoff probability of a new NRT call i 0.2. We alo aue that the call will terinate in the target cell after it hand-off uccefully. Fig. 9. Peudocode of bandwidth reallocation algorith. allocation a the new bandwidth allocation for the yte. 3. The threhold are coputed for each call cla baed on the new bandwidth allocation. If the feaible threhold of oe call clae cannot be found or the new call blocking probabilitie of oe call clae exceed the upper bound, we elect the econd feaible bandwidth allocation a the new bandwidth allocation. Repeat thi tep until all feaible threhold are found for every call cla and the new call blocking probabilitie are below the upper bound. 4. Check whether the current bandwidth allocation and the threhold of cla i call atify (34) for all call clae. If (34) cannot be atified for oe call clae, we need to find a new bandwidth allocation and repeat tep 3 and 4 until (34) i atified for all call clae. The peudocode of the propoed bandwidth reallocation algorith i hown in Fig PERFORMANCE EVALUATION In thi ection, we deontrate the effectivene of DMS-AC and the bandwidth reallocation chee. The control interval i 15 inute. We conider a two-cell yte, which i copoed of C r and C l, and there i a total of 100 channel in each cell. Two call clae, real-tie (RT) call and nonreal-tie (NRT) call, are conidered. RT call require one channel on both uplink and downlink while NRT call require one uplink channel and three downlink channel. The highet tolerable handoff dropping probabilitie of RT call and NRT call are 1 percent and 5 percent, repectively. The upper bound of the new call blocking probabilitie for RT call and NRT call are 10 percent and 20 percent, repectively. We aue that the call arrival follow Poion ditribution and let r RT ðl RT Þ and r NRT ðl NRTÞ denote the ean call arrival rate of the new RT call and the new NRT 5.1 Coparing DMS-AC with Jeon Schee Firt, we copare the propoed DMS-AC chee with Jeon chee [7], which i propoed for obile network with traffic ayetry. We have conducted extenive experient to copare the perforance of the two chee in different cenario. Due to the liitation of paper length, we how the repreentative one here. We aue 50 channel are allocated to uplink in both C r and C l. Let r NRT and l RT be equal to 0.01 and 0.1, repectively. r RT increae fro 0.05to 0.12 while l NRT increae fro to iultaneouly. Fig. 10 and 11 how the handoff RT and NRT call blocking probabilitie of C r and C l, repectively. Since the new RT call blocking probabilitie of both DMS-AC and Jeon are very cloe and under the upper bound of RT call (10 percent), we do not how the curve of the new RT call blocking probability in the figure. Fro thee figure, we can find that with the increae of traffic load, DMS-AC i able to guarantee the handoff dropping probabilitie of RT and NRT call under the contraint no atter in C r or C l. Although Jeon chee obtain lower new NRT call blocking probability than DMS-AC, it cannot guarantee the handoff dropping probabilitie of both RT and NRT call under the contraint in both C r and C l when the Fig. 11. NRT call blocking probabilitie when r RT increae fro 0.05 to 0.12 while l NRT increae fro to iultaneouly (coparing DMS-AC with Jeon chee).

12 1322 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 Fig. 12. Bandwidth utilization when r RT increae fro 0.05 to 0.12 while l NRT increae fro to iultaneouly (coparing DMS-AC with Jeon chee). TABLE 1 Call Arrival Rate in Experient Scenario Fig. 13. Change of the nuber of uplink channel when r RT increae fro 0.07 to 0.12 iultaneouly (experient 1). and l RT traffic load becoe heavier. Becaue of the higher priority of handoff call, it i reaonable for DMS-AC to ake uch a tradeoff between the new and handoff call. Since ore new NRT call are accepted, Jeon chee can achieve higher bandwidth utilization in two cell, a hown in Fig. 12. Fro thi experient, we know that bandwidth reallocation i deirable in order to iprove the bandwidth utilization and at the ae tie reduce the new call blocking probability in a heavy traffic load network. 5.2 Coparing DMS-AC with and without Bandwidth Reallocation Fro the above experient, we can find that the new NRT call blocking probability of DMS-AC exceed the predefined upper bound with the increae of traffic load. The propoed DMS-AC cannot achieve higher bandwidth utilization due to blocking ore NRT call. In uch a ituation, it i neceary to activate the bandwidth reallocation proce. Subequently, we copare the perforance of the yte with DMS-AC only (tered AC without BA ) to that with DMS-AC in conjunction with bandwidth reallocation chee (tered AC with BA ). In order to exaine the behavior and the perforance of the propoed approache coprehenively, we conduct iulation experient in three different cenario. The change of call arrival rate in the experient are hown in Table 1. In the firt two experient cenario, the call arrival rate of the ae call clae in two cell change iultaneouly. In the lat one, the call arrival rate of the different call clae in two cell change Experient 1 In thi experient, 30 channel are aigned to uplink in both cell initially. The average RT call arrival rate in both C r and C l increae fro 0.07 to 0.12 iultaneouly. With the increae of the RT call arrival rate in the yte, AC with BA allocate ore channel to uplink, a hown in Fig. 13. More RT call could be accepted. Without bandwidth reallocation, AC without BA block ore Fig. 14. New call blocking probabilitie of C r when r RT and l RT increae fro 0.07 to 0.12 iultaneouly (experient 1). Fig. 15. Total bandwidth utilization of C r when r RT and l RT increae fro 0.07 to 0.12 iultaneouly (experient 1). NRT call in order to guarantee the QoS of handoff RT call and thu caue the blocking probability of new NRT call to exceed the upper bound, a hown in Fig. 14. Obviouly, AC with BA achieve uch higher bandwidth utilization than AC without BA, a hown in Fig Experient 2 In thi experient, 50 channel are aigned to uplink in both cell initially. The average NRT call arrival rate in both C r and C l change fro to iultaneouly. With the increae of new NRT call arrival rate, the propoed bandwidth reallocation chee could aign ore channel to downlink, a hown in Fig. 16, and thu, AC with BA accept ore NRT call than AC without BA while the QoS requireent of other call clae are alo atified. Fig. 17 copare the NRT call blocking probabilitie of the two chee. AC with BA can guarantee the new NRT call blocking probability to be below the upper bound with

13 YANG AND FENG: BANDWIDTH REALLOCATION FOR BANDWIDTH ASYMMETRY WIRELESS NETWORKS BASED ON DISTRIBUTED Fig. 16. Change of the nuber of uplink channel when r NRT and l NRT increae fro to iultaneouly (experient 2). Fig. 19. Change of the nuber of uplink channel when r RT increae fro 0.06 to 0.11 while l NRT increae fro to iultaneouly (experient 3). Fig. 17. New NRT call blocking probability of C r when r NRT and l NRT increae fro to iultaneouly (experient 2). Fig. 20. New NRT call blocking probabilitie when r RT increae fro 0.06 to 0.11 while l NRT increae fro to iultaneouly (experient 3). (a) New NRT call blocking probability of C r. (b) New NRT call blocking probability of C l. Fig. 18. Total bandwidth utilization of C r when r NRT and l NRT increae fro to iultaneouly (experient 2). the increae of average NRT call arrival rate. AC with BA alo iprove the yte reource utilization ignificantly, a hown in Fig Experient 3 In thi experient, there are 50 channel on uplink in both cell initially. Let r RT increae fro 0.06 to 0.11 and l NRT increae fro to iultaneouly. It ean that the traffic load ayetry degree decreae in C r but increae in C l. Fig. 19 how the nuber of uplink channel aigned to uplink in both C r and C l when AC with BA i applied. Fro the figure, we find that the change of the uplink channel in C r i ore evident than that of C l. Since RT call have ore tringent blocking probability requireent, the yte i ore enitive to the change of the RT call arrival rate. In order to atify the QoS requireent of the high priority call clae, AC without BA block ore new NRT call in both C r and C l, Fig. 21. Total bandwidth utilization when r RT increae fro 0.06 to 0.11 while l NRT increae fro to iultaneouly (experient 3). (a) Total bandwidth utilization of C r. (b) Total bandwidth utilization of C l. a hown in Fig. 20a and 20b. Undoubtedly, AC with BA can achieve uch higher bandwidth utilization in both cell, a hown in Fig. 21a and 21b. 6 CONCLUSION In ultiervice obile wirele network, bandwidth allocation to uplink and downlink hould be ayetric to atch the traffic pattern/load. Under dynaic traffic load condition, bandwidth ayetry degree i changing accordingly. Thu, bandwidth adjutent or reallocation becoe an effective approach to axiize the reource utilization while guaranteeing the QoS requireent of uer. In thi paper, we have tudied the proble when and how to adjut bandwidth allocation between uplink and downlink under dynaic traffic load condition in ultiervice obile wirele network. The deign objective

14 1324 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 7, NO. 11, NOVEMBER 2008 i to iprove the yte reource utilization while atifying different QoS requireent of variou call clae. We addre the proble baed on a ditributed adiion control chee. When the traffic load brought by oe call clae exceed the control range of the eployed adiion control chee and thu the QoS requireent of oe call clae ay not be guaranteed, the bandwidth reallocation chee i perfored. Baed on the propoed adiion control chee, we have identified certain contraint that can be ued to verify the feaibility of the bandwidth allocation of a cell. Nuerical reult how that the propoed adiion control chee in conjunction with the bandwidth reallocation chee can guarantee the QoS of handoff call, and at the ae tie, the new call blocking probabilitie are aintained below oe reaonable level in a dynaic traffic load environent. Copared with that in tatic bandwidth allocation, the bandwidth utilization uing our bandwidth reallocation chee under dynaic traffic load ha been ignificantly iproved. ACKNOWLEDGMENTS The author would like to thank the anonyou referee for their helpful uggetion, which iproved thi paper. Thi work wa partially upported by China NSFC Grant ( ). REFERENCES [1] P. Chaudhury, W. Mohr, and S. Onoe, The 3GPP Propoal for IMT-2000, IEEE Co. Magazine, vol. 37, pp , Dec [2] M. Zeng, A. Annaalai, and V.K. Bhargava, Recent Advance in Cellular Wirele Counication, IEEE Co. Magazine, vol. 37, pp , Sept [3] D.G. Jeong and W.S. Jeon, CDMA/TDD Syte for Wirele Multiedia Service with Traffic Unbalance between Uplink and Downlink, IEEE J. Selected Area Co., vol. 17, pp , May [4] D.G. Jeong and W.S. Jeon, Tie Slot Allocation in CDMA/TDD Syte for Mobile Multiedia Service, IEEE Co. Letter, vol. 4, pp , Feb [5] X. Yang and G. Feng, Optiizing Adiion Control for Multi- Service Wirele Network with Bandwidth Ayetry between Uplink and Downlink, IEEE Tran. Vehicular Technology, vol. 56, pp , Mar [6] X. Yang, G. Feng, and C.K. Siew, Call Adiion Control for Multi-Service Wirele Network with Bandwidth Ayetry between Uplink and Downlink, IEEE Tran. Vehicular Technology, vol. 55, pp , Jan [7] W.S. Jeon and D.G. Jeong, Call Adiion Control for Mobile Multiedia Counication with Traffic Ayetry between Uplink and Downlink, IEEE Tran. Vehicular Technology, vol. 50, pp , Jan [8] W.S. Jeon and D.G. Jeong, Coparion of Tie Slot Allocation Strategie for CDMA/TDD Syte, IEEE J. Selected Area Co., vol. 18, pp , July [9] J. Zhang, J. Huai, R.Y. Xiao, and B. Li, Reource Manageent in the Next-Generation DS-CDMA Cellular Network, IEEE Wirele Co. Magazine, vol. 11, pp , Aug [10] M. Haardt, A. Klein, R. Koehn, S. Oetreich, M. Purat, V. Soer, and T. Ulrich, The TD-CDMA Baed UTRA TDD Mode, IEEE J. Selected Area Co., vol. 18, pp , Aug [11] W. Jeong and M. Kavehrad, Dynaic-TDD and Optiu Slot- Allocation in Fixed Cellular Syte, Proc. 54th IEEE Vehicular Technology Conf. (VTC 01), vol. 1, pp , [12] F. Nazzarri and R. Orondroyd, An Effective Dynaic Slot Allocation Strategy Baed on Zone Diviion in WCDMA/TDD Syte, Proc. 56th IEEE Vehicular Technology Conf. (VTC 02), vol. 2, pp , Sept [13] J. Nareddine and X. Lagrange, Tie Slot Allocation Baed on a Path Gain Diviion Schee for TD-CDMA TDD Syte, Proc. 57th IEEE Vehicular Technology Conf. (VTC 03), vol. 2, pp , Apr [14] D. Hong and S.S. Rappaport, Traffic Model and Perforance Analyi for Cellular Mobile Radiotelephone Syte with Prioritized and Nonprioritized Handoff Procedure, IEEE Tran. Vehicular Technology, vol. 35, pp , Aug [15] R. Rajee, R. Nagarajan, and D. Towley, On Optial Call Adiion Control in Cellular Network, Proc. IEEE INFOCOM 96, vol. 1, Mar [16] M. Naghhineh and M. Schwartz, Ditributed Call Adiion Control in Mobile/Wirele Network, IEEE J. Selected Area Co., vol. 14, pp , May [17] J. Kaufan, Blocking in a Shared Reource Environent, IEEE Tran. Co., vol. 29, pp , Oct [18] K.W. Ro and D.H.K. Tang, The Stochatic Knapack Proble, IEEE Tran. Co., vol. 37, pp , July [19] B.M. Eptein and M. Schwartz, Predictive QoS-Baed Adiion Control for Multicla Traffic in Cellular Wirele Network, IEEE J. Selected Area Co., vol. 18, pp , Mar [20] T.-C. Chau, K.Y.M. Wong, and B. Li, Optial Call Adiion Control with QoS Guarantee in a Voice/Data Integrated Cellular Network, IEEE Tran. Wirele Co., vol. 5, pp , May [21] J. Ni, D.H.K. Tang, S. Tatikonda, and B. Benaou, Optial and Structured Call Adiion Control Policie for Reource-Sharing Syte, IEEE Tran. Co., vol. 55, pp , Jan [22] I.F.A. David, A. Levine, and M. Naghhineh, A Reource Etiation and Call Adiion Algorith for Wirele Multiedia Network Uing the Shadow Cluter Concept, IEEE/ACM Tran. Networking, vol. 5, pp. 1-12, Feb [23] W.-S. Soh and H.S. Ki, A Predictive Bandwidth Reervation Schee Uing Mobile Poitioning and Road Topology Inforation, IEEE/ACM Tran. Networking, vol. 14, pp , Oct [24] A. Papouli, Probability, Rando Variable, and Stochatic Procee. McGraw-Hill, Xun Yang received the BEng degree in inforation and electronic engineering fro ZheJiang Univerity, Hangzhou, China, in 1999 and the PhD degree in electrical and electronic engineering fro Nanyang Technological Univerity, Singapore, in She i currently a potdoctoral reearch fellow at the Coonwealth Scientific and Indutrial Reearch Organiation, Sydney, Autralia. Her reearch interet include dynaic reource anageent in obile/ wirele network, adiion control in ultiervice obile/wirele network, and QoS proviioning in wirele eh network. She i a eber of the IEEE Coputer Society. Gang Feng received the BEng and MEng degree in electronic engineering fro the Univerity of Electronic Science and Technology, Chengdu, China, in 1986 and 1989, repectively, and the PhD degree in inforation engineering fro the Chinee Univerity of Hong Kong in He joined the School of Electric and Electronic Engineering, Nanyang Technological Univerity in Deceber 2000 a an aitant profeor and wa prooted a an aociate profeor in October Before that, he worked for one year in the Departent of Electronic Engineering, City Univerity of Hong Kong, a a enior reearch aitant. He i currently a profeor in the National Key Laboratory of Counication, Univerity of Electronic Science and Technology of China. He ha extenive reearch experience and ha publihed widely in coputer networking reearch with contribution to routing, buffer anageent, flow and congetion control in the Internet, ulticat protocol, and o forth. Recently, he branche out to work on packet cheduling, adiion control, and reource allocation in ultiervice wirele network. He i a enior eber of the IEEE.