Time-aware Utility-based Resource Allocation in Wireless Networks

Transcription

1 1 Tme-aware Utlty-based Resource Allocaton n Wreless Networks Caln Curescu, and Smn Nadjm-Tehran, Member, IEEE, Abstract Ths artcle presents a tme-aware admsson control and resource allocaton scheme n wreless networks, n the context of a future generaton cellular network. The qualty levels (and ther respectve utlty) of dfferent connectons are specfed usng dscrete resource-utlty (R-U) functons. The scheme uses these R-U functons for allocatng and reallocatng bandwdth to connectons, amng to maxmse the accumulated utlty of the system. However, dfferent applcatons react dfferently to resource reallocatons. Therefore at each allocaton tme pont the followng factors are taken nto account: the age of the connecton, a dsconnecton (drop) penalty and the senstveness to reallocaton frequency. The evaluaton of our approach shows a superor performance compared to a recent adaptve bandwdth allocaton scheme (RBBS). In addton we have studed the overhead that performng a reallocaton mposes on the nfrastructure. To mnmse ths overhead, we present an algorthm that effcently reduces the number of reallocatons, whle remanng wthn a gven utlty bound. Index Terms Bandwdth allocaton, QoS provsonng, C.2.1.k Wreless networks, Utlty-based optmsaton, C.2.3.a Network management I. INTRODUCTION A key feature of future generaton wreless networks s to provde moble users wth multmeda and data servces seamlessly. The bursty nature and varable bandwdth needs of most of the new servces call for novel treatments of the network resource management so that applcaton needs are satsfed, and at the same tme network provder resources are used n the best way. Many exstng works n resource allocaton focus on one part of ths equaton to the detrment of the other party. If end-to-end guarantees of user Qualty of Servce (QoS) requrements are n focus, then some decsons may become counterproductve seen from a system-level perspectve, and vce versa. In ths artcle we approach the problem by methods that brdge ths gap. The artcle presents a bandwdth allocaton and admsson control mechansm to be used n a rado network cell of a future generaton telecommuncaton network. As the man bottleneck we consder the bandwdth of the wreless lnk between the user equpment (UE) and the base transcever staton (BTS). The dfferent nature of the wreless channel (as compared to the wrelne) makes the QoS delvery more challengng. Frst, c 25 IEEE. Personal use of ths materal s permtted. However, permsson to reprnt/republsh ths materal for advertsng or promotonal purposes or for creatng new collectve works for resale or redstrbuton to servers or lsts, or to reuse any copyrghted component of ths work n other works must be obtaned from the IEEE. The authors are wth the Department of Computer Scence, Lnköpng Unversty, Lnköpng, Sweden. Emal: [calcu,smn]@da.lu.se the fxed capacty of the allocated wreless spectrum makes the system bandwdth-constraned, and hence allocaton problems cannot be solved by over-provsonng. Second, the resources avalable to a user mght vary greatly durng the lfetme of a connecton. Due to moblty, a user mght leave a cell where bandwdth s plentful and enter a congested area. Also, the effectve bandwdth of the wreless lnk may fluctuate due to fadng and nterferences. The above three factors descrbe a system where bandwdth avalablty s hghly varable n tme, and the system may often fnd tself n an overload stuaton. For the bandwdth manager to take the best allocaton decsons, we assume that a quanttatve measure of the utlty (beneft) generated by each connecton s avalable. One way to capture the applcatonspecfc perceved qualty dependng on resource avalablty s va resource-utlty (R-U) functons. Consequently, a straghtforward allocaton optmsaton crteron (that can be easly lnked to network operator revenues) s maxmsng the system utlty. Ths can be calculated as the sum of the utlty of each connecton 1. Moreover, for such an open dynamc system, resource reallocaton mght be needed n order to mprove total utlty (f bandwdth becomes avalable,.e. a connecton fnshes or leaves the cell) or to provde graceful degradaton (when bandwdth has to be reallocated to new connectons or ncomng handovers). In order to make more nformed decsons on resource reallocaton, n addton to utlty functons, we also consder the fact that dfferent applcatons react dfferently to resource reallocaton. For example, f a hard real-tme applcaton s degraded, we would expect no utlty from ths applcaton, and the resources nvested so far would be wasted. On the other hand, an FTP sesson wll have no restrcton to swtch between dfferent resource allocaton levels, no matter how often. Therefore, we propose a Tme-Aware Resource Allocaton scheme (TARA) that ams to provde bandwdth allocaton/reallocaton based on the utlty-effcency (utlty per bandwdth) of the competng connectons. The novelty s that our scheme dentfes how resource reallocaton decsons affect the utlty of the applcaton, and ntegrates ths nformaton nto the bandwdth management algorthm. Based on ther flexblty to reallocatons, we have categorsed applcatons n three classes: non-flexble, sem-flexble and fully flexble. The tme at whch a reallocaton decson s taken s also very mportant. Because of the nvested resources, dsconnectng a 1 Snce each connecton represents an applcaton the two terms wll be regarded as nterchangeable n the followng text.

2 2 connecton when t s nearly fnshed creates a bgger utlty loss than f t s dropped just after start and bandwdth has been nvested for a small perod of tme. Thus, the system has to be aware of the age of the connectons to take a good (re)allocaton decson. In addton to ths, two more factors have been consdered when reallocatng. Frst, the droppng penalty allows the user to specfy ts dssatsfacton of beng frst accepted and then rejected. Second, the senstvty of some of the connectons wth respect to the frequency of reallocatons s consdered. To evaluate our scheme we have bult a smulaton platform n whch we compare our approach wth a base-lne verson that s unaware of the prevously mentoned factors and a recent publshed algorthm, namely the Rate-based Bandwdth Borrowng Scheme (RBBS) [7]. Fnally we consder the overheads created by our bandwdth allocaton scheme as a result of the perodc reallocaton. Ths ncreases the resource demand from the nfrastructure (e.g. CPU tme for executng assocated control functons or addtonal bandwdth for sgnallng). Thus, by performng too many reallocatons n order to mprove utlty, the system mght get overloaded. Consequently, servce avalablty wll suffer, and the generated utlty wll decrease; contrary to what was ntended. We present and evaluate a new algorthm for controllng ths overhead. The artcle s organsed as follows. In Secton II we revew other approaches to QoS provsonng. Secton III presents background nformaton about resource-dependent utlty maxmsaton. In Secton IV we dentfy the factors affectng the utlty of a connecton f reallocatons are performed and n Secton V we show how we nclude them n our scheme. Secton VI descrbes the evaluaton setup and Secton VII presents the smulaton results of our allocaton scheme. In Secton VIII we present the above-mentoned overhead consderatons. The resultng conclusons are presented n Secton IX. II. RELATED WORK Research on QoS provsonng may pursue dfferent goals. Whle some research s geared towards end-to-end archtectures [2], others address ssues at end-system level or network layers. Mechansms lke Intserv [5] and RSVP [6] or Dffserv [4] provde the means of enforcng the necessary QoS parameters (lke bandwdth, delay, packet loss probablty). Many applcatons can be run at dfferent QoS levels, correspondng to a range of resource allocatons. These can be used for relatve dfferentaton between applcatons, but wthout a noton of mportance, the QoS management system wll not be able to prortse allocatons durng overloads. For meetng these needs, utlty functons provde an approprate way to specfy a quanttatve measure of the QoS perceved by the applcaton [11], [12]. A utlty functon s smlar to a QoS contract negotaton. The user specfes all ts optons and the provder chooses one of them. The advantage of utlty functons over run-tme negotatons s that the management system knows a-pror about the value correspondng to dfferent resource allocatons and mght be able to enforce an optmsed soluton. Chen Lee et al. [11] use resource-utlty functons n a QoS management framework wth the goal to maxmse the total utlty of the system. They propose two approxmaton algorthms, and compare the runtmes and soluton qualty wth an optmal soluton based on dynamc programmng. In our work we buld on top of such an utlty maxmsaton algorthm, but we also take nto account bandwdth reallocatons and ther effect on the connectons generated utlty. Another mportant factor for our scheme s the dynamc nature of the envronment. Some other approaches [15], [7], are geared towards moble networks and proposes adaptve bandwdth allocaton schemes wthout an explct use of utltes. These use a flexble allocaton approach, where connectons specfy a mandatory mnmal bandwdth and an deal maxmal bandwdth. Also, both schemes dfferentate between real-tme and best-effort connectons. In the work of Olvera et al. [15], the allocated amount of bandwdth durng the stay n a cell s fxed, t can be changed only at a handoff. El-Kad et al. [7] provde a more adaptve scheme, by allowng fxed portons of bandwdth to be borrowed from already accepted connectons. Although the scheme s adaptve, t does not nclude a quanttatve measure of the mportance of the dfferent connectons. Next we present several systems that allocate resources based on a certan maxmsaton technque of utlty functons, and also work n hghly dynamc envronments. Resource assurance (more or less), s a concern for all of these systems. Ru-Feng Lao et al. [12] use utlty functons n a bandwdth allocaton scheme for wreless packet networks. However as opposed to maxmsng the total utlty of the system, they provde utlty far allocaton to the connectons. Ther algorthm extends max-mn far allocaton, wth utlty replacng bandwdth as the farness crteron. Whle ths scheme provdes equalty to all connectons, t mght have counterproductve effects durng overload condtons, snce t degrades all the exstng connecton to a low common utlty. Abdelzaher et al. [1] propose a QoS-adaptve Resource Management System for Internet servers. A QoS contract s used to specfy acceptable QoS levels, along wth ther utlty. There s no restrcton n reallocatons (smlar to our fully-flexble class). However, there s a mnmum allocaton level that must be guaranteed. Otherwse a QoS volaton penalty (smlar to our drop penalty) s ncurred. They compare an optmal allocaton polcy based on dynamc programmng wth a frst-come frst-serve polcy where resources are not reallocated. A system that also addresses resource allocaton n moble networks s the TIMELY Archtecture proposed by Bharghavan et al. [3]. Whle we are concerned wth the allocaton at a polcy level ther system coordnates allocaton from the MAC-layer, through resource reservaton and resource adaptaton to the transport layer. Moreover, an end-to-end allocaton over both wrelne and wreless lnks s attempted. They employ a revenue model wth a 4-tuple: revenue functon, termnaton credt (smlar to our drop penalty), adaptaton credt (smlar n functon to what we wll call adaptaton tme) and an admsson fee. Maxmsng the revenue (based

3 3 on the max-mn crteron) s one of the crtera used durng allocaton and adaptaton. On the other hand, the same 4- tuple s used for all flows. Whle smplfyng allocaton, t prevents dfferentaton (as dfferent mportance or dfferent assurance needs) between flows. In our work we assume that the QoS specfcaton (as R-U functons, flexblty classes) s connecton specfc, and durng allocaton the system uses these parameters to dfferentate between connectons. An optmal samplng frequency assgnment for real-tme wreless sensor networks s proposed by Lu et al. [13]. In ther model, the underlyng network uses dedcated channels to communcate between neghbours such that nterferences are avoded. Nevertheless, a flow traverses several channels so the bandwdth allocaton of the dfferent wreless channels s not ndependent (as opposed to our work). Utlty loss ndex (that depends on the samplng frequency and s of convex form) characterses QoS and must be mnmsed across the network n order to optmse the system. Two algorthms are proposed, a centralsed that s better suted to small networks and a dstrbuted one that converges n several teratons, and s better wth large networks. In a more classcal real-tme approach, n ther QoS provsonng system [16] Rchardson et al. take a lower layer approach, by usng value based and real-tme schedulng technques and workng at the packet schedulng level. The prorty of each packet depends on the value of the connecton t belongs to and on ts deadlne. Total system utlty s used to measure system performance. III. BACKGROUND To explan how our bandwdth allocaton scheme works, we must frst present the noton of bandwdth dependent utlty functon, and a utlty maxmsaton algorthm. A. Applcaton utlty The utlty of an applcaton (and ts assocated connecton) represents the value assgned by the user to the qualty of the applcaton s results. In order to evaluate the utlty generated by dfferent resource allocatons, we assume that each connecton has a resource-utlty (R-U) functon, whch s specfed by the user of ths connecton, u : R R, dentfes the connecton and R s the set of non-negatve ratonal numbers, and u (r) descrbes the utlty that accrues gven a resource level r. In ths paper the resource s the wreless bandwdth n a cell. As a reflecton of varety of applcatons, utlty functons may exhbt dfferent patterns: concave, convex, lnear or step functons, the only restrcton beng that a R-U functon should be non-decreasng. For the ease of representaton, and to keep complexty low, t s necessary to quantse the utlty functon usng a small set of parameters. Thus, the utlty functons s represented by a lst of bandwdth-utlty pars, n ncreasng order of resource consumpton [11]: u = ( U,1 B,1 ),..., ( U,k B,k ) where k s the number of utlty levels of connecton and U,1 represents the resultng utlty f B,k s allocated to the connecton. B. System utlty maxmsaton Next we descrbe a general resource allocaton problem. We assume that the utlty of a system s the sum of the utltes of all applcatons n the system. Then the utlty maxmsaton problem can be formulated as follows: maxmse u(b 1,..., b n )= subject to n u (b ) =1 n b B max =1 where u : R n R s the system-wde utlty, b are the allocaton varables to be solved, and B max s the total avalable resource. The above allocaton optmsaton problem s an NP-hard problem closely related to the knapsack problem; Lee et al. present several approxmaton algorthms to solve t. As a basc ngredent n our scheme we use one of the algorthms proposed by Lee et al. that we further refer to as convex hull opt (referred as asrmd1 n [11]). Despte ts low complexty, the algorthm generates solutons close to the optmal soluton [1], [11]. As a frst step t frst approxmates all R-U functons by ther convex hull fronter, whch are pece-wse lnear, concave functons. Next, all convex hulls are splt n segments correspondng to ther lnear parts. Note that a segment bandwdth s ts projecton on the x-axs (the bandwdth ncrement between two levels). Then all the segments are ordered by a decreasng slope order (see Fgure 1), and bandwdth s allocated n ths order untl depleted. Thus, a connecton has allocated an amount equal to the sum of the bandwdths of ts allocated segments. The concave form of the convex hull ensures a consstent allocaton. Note that the slope of each segment, (U,j U,j 1 )/(B,j B,j 1 ), represents ts effcency n terms of contrbuton to the system utlty. Fg. 1. Optmal allocaton order

4 4 IV. REALLOCATION CONSEQUENCES The R-U functons present the bandwdth-utlty dependency n a statc manner. In a dynamc system, where resources need to be reallocated, the utlty gven by a R-U functon wll represent only a momentary value (u (t)). A better measure of the utlty generated by a connecton would be ts accumulated utlty n tme, whch s the utlty generated by the connecton over ts entre duraton. If, for some applcaton class, the accumulated utlty of a connecton (u a ) corresponds to the ntegral of all the momentary utltes, that s u a = T u (t)dt, then the followng equalty holds: n n u a = u a = T T n T u (t)dt = u (t)dt = u(t)dt = = where u a denotes the system-wde utlty accumulated over tme and u(t) s the momentary system-wde utlty. T represents a tme nterval. The above equatons show that n ths case, the maxmsaton of u a can be acheved by maxmsng u (t) at each tme pont t. However, for other applcaton classes u a T u (t)dt. For example, there are applcatons wth strong needs for resource assurance. That s, f the ntal agreed resource amount s degraded, then all the potental utlty generated untl that moment s lost. In the end u a =, and resources allocated to t snce ts arrval have been wasted. Therefore, our allocaton algorthm needs to take nto account the effect that reallocatons have on the accumulated utlty of the connectons. The man advantage of usng utlty functons s that the user (applcaton) has the possblty to quanttatvely specfy the value he s attachng to the results. Acceptng a connecton and allocatng a certan amount of bandwdth s smlar to negotatng and sgnng a a QoS contract between the user and provder. Snce the R-U functons provde a framework to specfy all the acceptable levels, the negotaton phase (and the assocated overheads) can be skpped. In the same lne of thought, each reallocaton would amount to a breach of contract and sgnng of a new contract. Because of dfferent applcaton types or user preferences, dfferent connectons have dfferent tolerance to bandwdth reallocaton. The challenge s to fnd a representatve (and small) set of parameters that satsfactorly descrbe the reallocaton effects for a large set of applcatons. The vson s to gve the user the possblty to specfy these parameters so that the system can take the rght (re)allocaton decson. Smlarly to the R-U functons they convey user expectaton and should not be regarded as a-pror fxed parameters tuned by the system operator. We have thus dentfed three factors that affect the perceved accumulated utlty of a connecton: the flexblty (adaptablty) to reallocatons, the senstvty to a complete dsconnecton (as opposed to only a bandwdth reducton), and the senstvty to the frequency of reallocatons. = A. Flexblty classes We frst dvde the applcatons nto three broad classes dependng on ther flexblty wth respect to reallocatons. Class I represents non-flexble connectons. They requre strct resource assurance to fulfll ther msson. That s, once accepted (wth ntal utlty u nt ), the resource amount cannot be re-negotated. If the management system cannot assure the ntal resource amount at any tme-pont durng the lfetme of the connecton, there wll be no utlty ganed for the whole duraton of the connecton, and already nvested resources are wasted. If accepted, any subsequent reducton of bandwdth s equvalent to droppng the connecton. Snce t uses the same amount of resources durng ts lfetme, ncreasng the bandwdth brngs no beneft. If the connecton s not dropped, the accumulated utlty of the connecton s calculated by ths formula: u a = unt duraton. Examples are hard realtme applcatons, crtcal control data, real-tme data streams. Class II represents sem-flexble connectons. These are applcatons that are judged by ther worst moment n ther lfetme. For ths type of connecton the lowest utlty (respectvely bandwdth) experenced durng ts lfetme s used for calculatng the utlty for the whole duraton: u a = umn duraton. Compared to class I, a resource degradaton, whle dmnshng utlty, s not dsastrous. However, once a certan level reached, the results cannot be mproved f the resource allocaton s ncreased at a later pont. For example, users often remember the worst porton of a multmeda stream, or a dstrbuted game. Another good example s sensor readngs where the resoluton bound s mportant. The resoluton of the whole stream s the lowest resoluton from all the readngs. Class III represents fully-flexble connectons. These are the connectons wth no real-tme requrements, and they can adapt to both ncreases and decreases of the bandwdth. The accumulated utlty s the sum of all the momentary utltes over the total duraton: u a = duraton u (t) dt. Examples are fetchng e-mal, fle transfer, or any type of connecton n the best effort category. A real-word applcaton could be a combnaton of dfferent connectons of dfferent class. For example t could consst of two parts, a mandatory one that s class I and a fully flexble, class III. For ths paper we consder applcatons to belong to only one of the above classes. Note that the shape of the R-U functon does not depend at all on the class of the connecton. The class does not affect the ntal allocaton possbltes, but only descrbes the effects at subsequent reallocatons. B. Drop penalty We assume that dsconnectng (droppng) a connecton before ts natural end wll brng ts accumulated utlty to zero. Ths shows that nvested resources wll be wasted by such a decson. In a smlar manner resources have been nvested on the user sde, and wll be lost. Therefore, the user should be able to specfy a certan drop penalty, whch represents the customer dssatsfacton when a connecton s dsconnected after beng admtted nto the system. Let P drop be the penalty for droppng a certan ongong connecton. If dsconnected, the fnal utlty of the connecton u a drop = P. If utlty s used n calculatng the revenue of the network operator, a negatve utlty wll mply some form of compensaton to the user.

5 5 C. Adaptaton tme Flexble (class III) applcatons can adapt to both ncreases and decreases n bandwdth. In a dynamc envronment, these connectons mght be subjected to very frequent reallocatons. But even these flexble applcatons mght need a certan amount of tme to adapt to the new mode after a reallocaton. For example, some algorthms for encodng, encrypton, compresson could be changed, some computatons need to be restarted. Performng frequent reallocatons mght be worse than keepng a connecton at a constant, lower resource level. A specfed adaptaton tme s a way to reflect the mnmum tme between reallocatons n order to keep the expected utlty. The effects of not respectng a mnmum adaptaton tme could greatly dffer for dfferent connectons. Nevertheless, we propose the followng performance degradaton model. If the tme between two bandwdth reallocatons (I )sless then a specfed adaptaton tme (A ) then we assume that the utlty generated durng ths nterval s only I /A of the utlty under normal crcumstances, thus charactersng a penalty for frequent reallocatons. Classes I and II should not be subject to frequent reallocatons (bandwdth ncreases are useless, decreases are few and bound by the allocaton levels of the utlty functon). Thus, ths penalty s meanngful only for class III connectons. V. DYNAMIC REALLOCATION Because of the hghly dynamc envronment, constant reallocaton s needed n order to obtan the best results. Bascally whenever a new connecton or handover request arrves or a connecton ends, a new reallocaton mght be needed to mprove system utlty. In a large system, ths event-based allocaton may lead to an unacceptable hgh call rate to the (re)allocaton algorthm. Ths overhead can be controlled by employng a perodc (re)allocaton method. New connectons and handovers are put n a queue and wll be processed at the begnnng of the next allocaton perod. For reasonably low values of reallocaton perod, the process wll be transparent to the user. Note that ongong connectons are treated at the same tme as requests for new connectons or handovers. For the latter two the (re)allocaton algorthm plays also the role of admsson control. Only requests that are allocated a bandwdth greater than zero are admtted. In Secton III-B we mentoned an near-optmal allocaton algorthm that uses the R-U functons as nput. The algorthm wll order and accept connectons based on ther effcency. We keep ths as a base allocaton algorthm. However, snce the orgnal R-U functons do not descrbe the hstory of a connecton, we have to take the addtonal factors that descrbe the effects of reallocatons (see Secton IV) nto account. Therefore we create artfcal R-U functons by modfyng the orgnal R-U functons at every (re)allocaton tme pont. For nstance, n an ongong class I connecton, resources have been nvested for some tme. The correspondng potental utlty however, wll only be ganed f the connecton s not dropped. When compared to a new connecton, the ongong connecton comes wth ths so far earned utlty, that effectvely ncreases the effcency of the connecton over the rest of ts lfetme. Thus by modfyng the R-U functons we make the connectons of all ages and classes comparable effcencywse. Whle at each allocaton pont we optmse based on the utlty-effcency of the dfferent connectons, only a clarvoyant algorthm that knows all the future arrvals could provde a truly optmal allocaton. For nstance a class I connecton accepted at some pont mght be dropped f an ncreased number of hgher effcency connectons arrve at a later pont. By not acceptng t n the frst place the system would have avoded payng the drop penalty. As clarvoyance s not a realstc assumpton the only other possblty would be do predctons based on proflng past arrvals. Even ths opton s consdered as unrealstc n our context. In the next subsectons we wll explan how the R-U functons are modfed at each reallocaton. Table I summarses the parameters utlsed n the process. TABLE I u u age u drop u adapt b (l) p drop t max t age I A u a u a NOTATION SUMMARY The orgnal R-U functon of conn. The age-modfed R-U functon of conn. The drop penalty modfed R-U functon of conn. The adaptaton-tme modfed R-U functon of conn. The bandwdth of conn. correspondng to QoS level l The drop penalty of conn. The duraton of conn. The current age of conn. The tme passed snce the last allocaton for conn. The adaptaton tme of conn. The value of the tme-accumulated utlty for conn. The value of the system-wde tme-accumulated utlty A. Age and class dependent modfcatons To get a feelng for why age modfcatons are needed, we start by gvng an example of a reallocaton decson where the orgnal, unmodfed R-U functon s used. Assume there s a class I or II connecton conn 1, whch has an R-U functon that evaluates to 3 for bandwdth 4 (u 1 (4) = 3). Assume the total duraton of the connecton t max 1 =1seconds of whch 5 seconds have elapsed, denoted by t age, and the allocated bandwdth durng ths tme was b 1 =4. Ths means that the accumulated utlty so far u curr 1 = u 1 (b 1 ) t age 1 =3 5= 15. At ths tme a new connecton conn 2 s competng wth the old one for the same bandwdth. Assume that for conn 2 the utlty correspondng to bandwdth 4 s 5 (u 2 (4) = 5). Because the convex hull opt allocaton algorthm s usng the slopes (utlty/bandwdth) of the R-U functons convex hulls to make decsons, and 3/4 < 5/4, t wll choose conn 2 n comparson wth conn 1 and u curr 1 wll be lost. Let s see what s the utlty ganed by the system after the next 5 seconds: u a = u 2 (4) 5=5 5=25. If the frst connecton had been kept, the utlty would have been u a = u 1 (b 1 ) t max 1 = 3 1 = 3, thus the swappng decson s wrong. Therefore, to replace an old connecton wth a new one, the utlty generated by the new connecton untl the completon tme of the old connecton should be greater than the utlty generated by the old connecton durng ts entre lfe tme (see shaded areas n Fgure 2). In our example, conn 1 should be swapped wth conn 2 only f u 2 (4) 5 >u 1 (4) 1.

6 Fg. 2. Utlty old connecton, Tme Replacement opportunty now new connecton In the above example we assumed that we have the choce only to swap conn 1 wth conn 2, at the same bandwdth level. In general, we need to consder a connecton that has multple acceptable bandwdth levels (n ts R-U functon), of whch one s the current allocaton. To reflect the age, and thus the accumulated utlty at the reallocaton tme pont, we need to modfy the R-U functon of the exstng connecton as follows. Each allocaton corresponds to a level l n the R-U functon, where 1 l k, andk s the maxmum number of levels. We denote the bandwdth at level l by b (l), and the correspondng utlty by u (b (l)). For nstance, n Fgure 3 (a): b (1) =, u (b (1)) =, b (2) = 2, u (b (2)) = 1, etc. Let the already exstng allocaton level at a reallocaton tme pont be j. In Fgure 3, j =3and b (j) =4. Utlty (a) ntal R U functon Bandwdth Utlty (b) class II after age modfcatons Bandwdth Fg. 3. Age modfcaton for class I and II, wth t age and actual bandwdth b =4 Utlty 3 3 (c) class I after age modfcatons Bandwdth =5, t max =1, Here we explan how a modfed R-U functon for a class II connecton s constructed and refer to Fgure 3 (a) and (b) as an example. When constructng the modfed R-U functon, we can dvde the allocaton levels n two sets (correspondng to two stuatons). If the bandwdth allocaton stays the same or s ncreased, u a remans the same. Thus, for all these levels, the modfed R-U functon, denoted by u age, wll be equal to the utlty for the exstng allocaton: u age (b (l)) = u (b (j)) j l k Decreasng the bandwdth results n losng a porton (or all) of the connecton s accumulated utlty so far. So we frst compute the lost utlty: ( ) u lost (l) = u (b (j)) u (b (l)) t age 1 l<j Then we reduce the utlty that can be accrued at the respectve levels by modfyng u to u age : u age (b (l)) = u (b (l)) ulost (l) t max t age 1 l<j Note that for l < j there s a larger dfference between two adjacent utlty levels n u age compared to u ;thats, the slopes of the segments of the convex hull of u age (for l<j) are steeper. That s, a reducton of the allocaton can only be compensated by a hgher utlty ganed from other connectons. More precsely, the slope ncrease n the modfed R-U functon s exactly large enough so that, f bandwdth s reallocated to other connectons, the newly accepted (mproved) connectons wll generate not only a hgher utlty for the reallocated bandwdth, but n addton also recover the utlty lost by degradng ths connecton. The lost utlty wll be recovered durng the nterval t max t age (that s, before the tme pont at whch the degraded connecton would have released the bandwdth naturally). For class I connectons, any decrease n bandwdth means the connecton s dropped (leads automatcally to bandwdth). The modfed R-U functon for a class I connecton s presented n Fgure 3 (c), f the orgnal R-U functon was the same as that depcted n Fgure 3 (a). For ths class, the zerobandwdth level s calculated smlarly to the class II case. Class III connectons do not lose utlty (waste resource) n case of a reallocaton, thus ther orgnal R-U functon needs no age modfcaton. Now the queston becomes, do we assume that the real duraton of every connecton s known? Obvously ths s too unrealstc to assume. In practce we have to resort to an estmate of a connecton s duraton. The better the estmaton of the connecton duraton, the more accurate the modfcaton wll be. Ths s because overestmatng/underestmatng the duraton of a connecton wll underestmate/overestmate the mportance of a bandwdth decrease for ths connecton. In Secton VII-A we further dscuss how the system behaves n the absence of an exact knowledge of the duraton. B. Drop penalty nfluence Class I and II connectons are dropped (dsconnected) whenever ther momentary bandwdth becomes zero, snce that connecton yelds no utlty n the end. Class III connectons should not be dropped because of bandwdth shortage, snce they can recover at a later tme, wthout penalty. Recall that each connecton comes wth ts own drop penalty, P drop.to reflect ths senstvty to dsconnectons, the R-U functon s further modfed (the effect s addtonal to the age-dependent modfcaton) as follows: u drop u age (b (l)) = (b (l)) P drop t max t age for l =1 u age (b (l)) l 1 Smlar to u lost n the prevous subsecton, n order to mprove the accumulated utlty, ths penalty should be recovered before the natural end of the connecton. 6

7 7 Note that the modfcaton s only appled to the frst level (where b (1) = ), because f bandwdth s not reduced to zero, the connecton s not dropped. Fgure 4 presents the further modfcaton of the class II R-U functon from Fgure 3 (b) gven a drop penalty P drop =8. before drop modfcatons after drop modfcatons Utlty ntal R U functon Utlty after adapt modfcatons 3 3 Utlty Bandwdth Utlty Bandwdth Fg. 4. Class II drop modfcaton wth P drop =8, t age =5, t max =1, and actual bandwdth b =4 C. Adaptaton tme nfluence Ths modfcaton, that reflects senstvty to bandwdth fluctuatons, s only appled to class III connectons. Classes I and II wll not be subject to frequent reallocatons (bandwdth ncreases are useless, decreases are bounded by the number of the R-U functon levels). As presented n Secton IV-C, for a flexble class III connecton, f reallocaton s performed before the adaptaton tme requred by the applcaton (I <A ), the ganed utlty n ths nterval (normally u I ) s dmnshed to an I /A of the normal ganed utlty. Ths could be seen as a new form of penalty computed as P adapt = u I (A I )/A,to be subtracted from u a. Each tme there s a reallocaton, the R-U functon s modfed to represent the senstvty to the current reallocaton frequency. If I <A and there s a change from the current allocaton level (j) then an adaptaton penalty s ncurred: u adapt (b (l)) = u (b (l)) P adapt l j and I <A I u (b (l)) for l = j or I A An example of modfcatons dependng on adaptaton tme s shownnfgure5. D. Algorthm overvew To summarse, Fgure 6 presents a hgh-level verson of our allocaton algorthm, that s nvoked perodcally and ndependently for each cell of the network. The methods contanng modfy n ther name construct the modfed R-U functons as descrbed n the prevous sectons. Some of the parameters used n the algorthm are presented n Table I, and the followng are added: class s the connecton class, b s the current allocated bandwdth, new b the new allocaton decson, and b mn the lowest bandwdth granted n the connectons lfetme, and perod represents the runnng Bandwdth Bandwdth Fg. 5. Class III adaptaton modfcaton wth A =5, I =4, P adapt =2, and actual bandwdth b =4 perodcty of the algorthm. As nput the algorthm has all n connectons that want bandwdth n ths cell (new, old and handed over). Besdes the proper (re)allocaton algorthm we present also the utlty accountng algorthm, that once an allocaton decded, calculates the up-to-date system-wde utlty, that s our man performance metrc. Bandwdth (Re)allocaton & Utlty accountng Algorthm: nput: 1 n: b,u,class,t max,t age,p drop,a,i,b mn output: 1 n: new b //result of ths allocaton 1 n: u a, u a //result of utlty accountng Bandwdth (Re)allocaton: for := 1 to n do //modfy the R-U functons f class = I or class = II then u := age modfy(u, class, b, t max, t age ); u := drop modfy(u, class, P drop, t max, t age ); f class = III then u := adapt modfy(u, class, b, A, I ); (new b 1,..., new b n):=convex hull opt(u 1,..., u n) //new allocaton computed Utlty Accountng: for := 1 to n do f class = I or class = II then f (class = I and new b b ) or (class = II and new b =)then u a := P drop ; //rejected, apply drop penalty else //not rejected u a := u (b mn ) t age ; //set accum. utlty so far f class = III then //update accum. utlty so far u a := u a + u (new b ) perod; f I <A then //apply adaptaton penalty u a := u a u (b ) I (A I )/A ; f new b b then //mark new reallocaton I := ; else P I = I + perod ; u a n := :=1 ua ; Fg. 6. Algorthm overvew VI. EVALUATION SETUP To evaluate the advantage of usng utlty-based characterstcs of a connecton we have compared our scheme, the Tmeaware resource allocaton scheme (TARA), wth a recent flexble allocaton scheme that addresses smlar network problems. We begn wth a short descrpton of the Rate Based

8 8 Borrowng Scheme (RBBS) proposed by El-Kad et al. [7]. We then explan how we have reconstructed that algorthm n our smulaton envronment to make vald comparsons (by ensurng that the choces of parameters were compatble and reproducng ther earler results). The RBBS paper proposes an admsson control and bandwdth allocaton scheme for cellular networks. In order to not deny servce to requestng connectons (both new or handovers), bandwdth wll be borrowed from already accepted connectons. The algorthm uses the followng strategy. Each connecton that arrves n the system comes wth a mnmum (mn ) and a maxmum (max ) bandwdth requrement. The actual borrowable bandwdth (abb ) s calculated as a fracton (f) of the dfference between maxmum and mnmum bandwdth, abb = f (max mn ),wheref s a cellwde parameter. Another cell-wde parameter s λ whch s the number of equal shares the abb s dvded nto. When there s not enough bandwdth avalable at a certan admsson pont, bandwdth s freed by decreasng the allocaton to all connectons wth one level (a share from the abb ). Moreover, n order to provde a smooth change n bandwdth allocaton, only one share from the borrowable part can be lent at any tme. RBBS dvdes connectons n two classes. Class I are consdered real-tme connectons and a certan amount (e.g. 5%) of the cell bandwdth s reserved to be exclusvely used for handovers for ths class. Ths s because class I connectons should have always (and can be handed over wth) at least mn bandwdth allocated, otherwse they should be dropped. Class II applcatons are consdered best-effort and can be handed over wth any allocated bandwdth (greater than zero) n the new cell. Requests for new connectons (both class I and II) are treated more strctly, they are only accepted f enough bandwdth s avalable to accommodate them at the same level as the cell. When connectons termnate or are handed over the avalable bandwdth ncreases. If there are connectons degraded below the cell level (due to handovers), they wll be upgraded frst. Otherwse, when enough bandwdth becomes avalable, the whole cell moves to a better QoS level. The above work s very nterestng because the authors take nto consderaton many of the characterstcs of a Thrd Generaton (3G) network. They consder dfferent traffc types (descrbed next), wth dfferent bandwdth requrements, multple allocaton levels, resource assurance classes, etc. On the other hand they do not use a quanttatve performance metrc (such as utlty), that could glue such a complex system together and steer allocaton, but use the usual performance metrcs such as blockng/droppng probabltes, that are more suted for fxed allocaton / sngle servce systems (e.g. 2G). We wll return to ths ssue later n the paper. To get a good comparson of our scheme and the RBBS we have used the same traffc characterstcs as those used for evaluaton of RBBS [7]. The same traffc mx has been used frst by Olvera et al. [15] as representatve for future moble communcaton networks. The frst 9 columns of Table II are dentcal wth the ones n the RBBS paper. As n ther experments, the requested bandwdth and connecton duraton are not fxed, but follow a geometrc dstrbuton wth the gven mnmum, maxmum and mean values (columns 2 to 6) TABLE II TRAFFIC MIX USED IN THE EXPERIMENTS Applc. Group Bandwdth Requrement (Kbps) Connecton Duraton (sec) Examples mn max avg mn max avg Voce Servce & Audo Phone Vdeo -phone & Vdeo -conference Interact. Multmeda & Vdeo on Demand E-Mal, Pagng, & Fax Remote Logn & Data on Demand Fle Transfer & Retreval Servce RBBS class TARA class Relatve utlty per bt I I 1 I II 1/3 I II 1/1 II III 3 II III 1/5 II III 1/7 The mnmum acceptable bandwdth s fxed and presented n Column 2. The second column from rght represents how we mapped the dfferent applcaton groups nto to our connecton classes (non-adaptve, sem-adaptve, fully-adaptve). Snce the RBBS s not based on utltes, we had to assocate each of the 6 applcaton groups wth an R-U functon shape. For example, the shape of the R-U functon for applcaton group 3 (the one representng nteractve multmeda) s presented n Fgure 7. All R-U functons that we used, follow the mnmum and maxmum bandwdth requrements as specfed n Table II. Utlty mn Bandwdth Fg. 7. R-U functon shape for group 3 The rghtmost column n Table II reflects a relatve mportance between applcaton groups. For example, snce one mght be ready to pay roughly three tmes more for a vdeophone conversaton, whch has a bandwdth demand of 256 Kbps, the utlty per bt should be almost three tmes hgher for an audo-phone that requests only 3 Kbps. It represents the utlty per bt assocated wth the requested bandwdth, e.g. f the requested bandwdth of a connecton n applcaton group 3 s 6, Kbps then the utlty for ths bandwdth s 6,, 1/1 = 6,. Havng fxed the relatve dfference at the maxmum level, all the other utlty values of the R- U functon are calculated followng the shape of the functon. Whle assgnng utlty values s always a subjectve problem, we tred to use early practce values n our experments. Ruben et al. [17] performed a study at Ercsson Cyberlab n Sngapore and had access to current concevable busness models. In our smulaton envronment, connectons arrve at the user equpments (UE) followng an exponentally dstrbuted nterarrval tme wth a mean of 15 mnutes. All the 6 applcaton groups arrve wth equal probablty. Moblty s modelled n the followng way: the tme at whch a UE changes cell (and requests a handover f a connecton s ongong) follows a geometrc dstrbuton startng from 6 sec and mean 3 sec, max

9 9 wth equal probablty to move n any of the neghbourng cells. Fluctuatons of the wreless lnk, mentoned as a source of bandwdth varablty n the ntroducton, have not been mplemented n the smulator. Nevertheless, the random handover and new connecton arrval together wth the dfferent szes and R-U functons of the connectons ensure a very dynamc resource varablty. We beleve that snce our system deals wth ths varablty properly, the rado lnk varablty can be dealt wth analogously. Our smulatons were performed n a smulaton envronment descrbed by Jonasson [9] and bult on top of JavaSm, a component-based, smulaton envronment developed at Oho State Unversty [18], [8]. We have smulated a hexagon cellgrd of 16 cells, 4 4, and a go-around world model to preserve unformty n our grd. Each cell has a capacty of 3 Mbps. For all the schemes the bandwdth allocaton/reallocaton has been performed wth a perod of 2 seconds. The drop penalty was set usng the followng formula P drop = 2% u (b req ) t avg,whereb req s the requested bandwdth, and t avg s the average connecton duraton (accordng to Table II). Adaptaton tme was set to 5 seconds. As our man performance metrc we use the accumulated system utlty (u a ) generated by the dfferent connectons n the system. The accumulated system utlty s ndependent of the allocaton algorthm and s calculated n the same way for all the smulated schemes and accordng to Secton IV. VII. EVALUATION RESULTS Fgure 8 presents the accumulated utlty generated by 5 allocaton schemes (descrbed shortly) durng one smulated hour. On the x-axs we have the arrval rate (number of new connectons per second). The values n parenthess represent the correspondng offered load as compared to the capacty of the cell. Thus.2(2.56) means that the offered load wth an arrval rate of.2 was 2.56 tmes the maxmum capacty of the cell. The offered load s calculated usng the bandwdth requests of the connectons. For each of the arrval rates and for each bandwdth allocaton scheme we conducted fve dfferent experments (by changng the seed of the varous dstrbutons) and plotted the average value. The coeffcent of varance (CV )wasless than.6 n almost all of the cases (CV = σ/µ, that s the standard devaton dvded by the average). A smlar statstcal confdence apples also to the results presented n the forthcomng fgures. A. Comparson to basc maxmsaton algorthm To see the mpact of our class and age aware modfcatons, we have compared three flavours of TARA. TARA-normal and TARA-perf-est both use modfed R-U functons as presented n Secton V. The dfference s that for TARA-normal we have used the average connecton duraton (see Table II) to estmate the duraton of each connecton when calculatng the modfcatons (see Secton V), whle for TARA-perf-est we used the real duraton from the traffc generator. Thus, the latter provdes the best possble case to hope for. Although Total Utlty per Cell x 11 TARA normal TARA perf est TARA no update RBBS normal RBBS frendly.2(.25).5(.65).1(1.3).2(2.56).5(6.5) 1.(13) Connecton Arrval Rate Fg. 8. Accumulated utlty the age-dependent modfcatons play an mportant role n our scheme, the dfference between TARA-normal and TARAperf-est n Fgure 8 s margnal. It seems that n most of the cases, the dfference between the real duraton and the average value, s too small to result n the wrong decson (to decsvely change the slopes of the modfed R-U functons). We have also smulated a verson of TARA where the modfcatons of the orgnal R-U functons are not performed, denoted as TARA-no-update. Bascally, TARA-no-update s the convex hull opt allocaton algorthm (see Secton III-B) nvoked perodcally. By not takng nto consderaton the connecton classes, the droppng penalty and the adaptaton tme, TARA-no-update exhbts a 35% decreased system utlty when workng n areas where the offered load s between 1.3 and 2.6. At hgh overloads (correspondng to.5 and 1 arrval rate) the applcatons wth the lowest utlty per bt, whch belong to applcaton group 3, class II, are all rejected at the begnnng, and snce the lowest utlty per bt connectons stll accepted are now applcatons n group 6 class III, whch can be put ndefntely on hold, TARA-no-update comes closer to the other two. Ths s an expected behavour wth a traffc n whch the allocaton borderlne (the last bandwdth allocated) les frmly wthn connecton class III. B. Comparson wth RBBS The results for RBBS have been plotted as RBBS-normal. There s a large dfference between TARA and RBBS whch amounts to 45% when the system gets overloaded wth traffc. The man factor that contrbutes to ths result s the absence of utlty consderaton by RBBS. Whle TARA s rejectng only low utlty per bt connectons, RBBS s rejectng a comparable amount from all applcaton groups.

10 1 Besdes the orgnal RBBS we also used a slghtly modfed verson of RBBS to make the comparson more favourable towards that scheme (shown as RBBS-frendly). The orgnal RBBS may both lower and rase bandwdth for all connectons. Hence, we modfed RBBS not to replensh connectons of TARA class II (because no utlty s ganed), and set the borrowable part of TARA class I connectons to zero. For both RBBS schemes, reserved bandwdth was r =5%, number of levels λ =1, and borrowng factor f =.5 [7]. C. QoS per applcaton group So far we have presented the results only from the perspectve of the total system utlty. A more specalsed vew s presented n Table III, the applcaton groups on the x- axs refer to those n Table II. We can observe that only connectons that have the lowest utlty effcency are blocked (new connectons) or dropped (ongong connectons). Snce applcaton group 6 s a class III connecton, t can accept zero allocaton stuatons, so there are no ongong connectons dropped n that case. Also, even at 13 tmes overload, most of the small, mportant applcaton groups reman unscathed. Nevertheless t s mportant to note that the man goal of the system s to generate the hghest utlty and not to mnmse the number of rejected/dropped connectons. TABLE III STATISTICS PER APPLICATION GROUP AT LOAD 2.42 AND 13 load = 2.56 load = 13 applcaton groups accepted new rejected new rejected ongong allocaton level (%) D. Choce of performance metrc As the man performance metrc, we use the accumulated system utlty. Hence, we depart from the tradtonal call blockng probablty (CBP) and call droppng probablty (CDP) as performance metrcs. We argue that they are obsolete n a system where the requested bandwdth of one connecton mght be only a small fracton of another connecton s demands, but both contrbute equally n calculatng CBP or CDP. The argument s confrmed by Fgure 9, whch shows the CBP of the smulatons. The applcaton group most blocked by TARA has a bg bandwdth demand, and by blockng few of them a lot of bandwdth s saved for other connectons. Snce RBBS treats all connectonsequallyt has to reject muchmore connectons to equal the number of bts. Although the am of our algorthm s to maxmse the utlty and not to ensure a low droppng (or blockng) probablty, droppng an accepted connecton reveals a certan degree of mscalculaton. Thus we present the CDP n Fgure 1. Snce TARA can also drop ongong connectons whch are not handed over, we use a dfferent formula for CDP. CDP = rejectedongong + rejectedhandovers acceptednew + acceptedhandovers Even wthout reservng a certan amount of bandwdth to be used exclusvely for handovers (RBBS reserves 5% for ths Connecton Blockng Probablty TARA normal TARA perf est TARA no update RBBS normal RBBS frendly.2(.25).5(.65).1(1.3).2(2.56).5(6.5) 1.(13) Connecton Arrval Rate Fg. 9. Connecton blockng probablty Connecton Droppng Probablty TARA normal TARA perf est TARA no update RBBS normal RBBS frendly.2(.25).5(.65).1(1.3).2(2.56).5(6.5) 1.(13) Connecton Arrval Rate Fg. 1. Connecton droppng probablty purpose), TARA-normal and TARA-perf-est are able to keep the number of droppngs qute low. Handovers are not regarded as new connectons n the cell where they are handed over. We want to emphasse here that the ncreased mportance due to the agng mechansm provdes a natural dfferentaton between handovers and new connectons, and the algorthm does not have to use some knd of forced dfferentaton mechansm to dfferentate between them. The experments show that the agng mechansm, the droppng penalty, and the flexblty of class III connectons are able to protect handovers as well as other ongong connectons from beng dropped. The consequence of not takng n to consderaton these factors s shown n the plot of TARA-noupdate. Whle blockng less connectons, t s droppng more than TARA-normal. The effects on the accumulated utlty were already presented n Fgure 8. E. Complexty consderatons From a computatonal complexty pont of vew, the convex hull maxmsaton algorthm that we use, has a complexty of O(nL log n), wheren s the number of ongong and new connectons, and L s the maxmum number of utlty levels of an R-U functon. The utlty functon modfcatons that we ntroduce have the complexty of at most O(nL), snce they have to manpulate each level n the R-U functon. The RBBS