Cellular network with continuum priority set

Transcription

1 Cellla netwok with ontinm pioity set Jean-Ma Kelif Fane Teleom eseah Development 9794 ssy Molinea, Fane Eitan Alman A P 9 69 Sophia Antipolis, Fane Eitan.Altman@sophia.inia.f Abstat e onside the following poblem of spatial downlink pioitization. Mobiles aive at a ell at loations that ae detemined aoding to some pobability distibtion. The fthe a mobile is fom the base station, the weake is its eeived powe ths the lowe is the tansmission ate to it. eside this nontollable phenomenon that diffeentiates between mobiles aoding to thei loation, one an design othe ontolled mehanisms that diffeentiate between them. e analyse vaios pioity poliies whee the assigned pioity is given in tems of the distane of the mobiles fom the base station. This gives ise to a whole ontinm of pioity levels. e stdy the inflene that the ombined loation density pioity poliy have on the qality of sevie of the mobiles on the netwok oveall pefomane. Applying o model to a HSDPA system, we allate a qality of sevie indiato, the sojon time, sing a pioity sheling stategy, a poesso shaing one a fist ome fist seved one. Consideing thee types of aival flow, a nifom one, a non nifom one a flow whih geneates a onstant load in the ell, we show the sojon time depends on the adopted stategy, bt also on the loation of the mobile on the aival flow type. n patila, a nmeial stdy based on o model shows that a maimm S pioity does not povide in any ase the minimm sojon time. Keywods: pioity, sheling, ontinm, HSDPA TODUCTO adio ommniations systems manage moe moe mobile data taffi. The available bwidth being limited, diffeent stategies ae adopted by opeatos to shae the limited esoes, to shele the se of adio hannels. e onside in this pape the sheling of downlink taffi we stdy the pefomane of the sblass of fied pioity poliies, whee pioity les ae defined as a fntion of the distane of a mobile fom the base station. This gives ise to a whole ontinm of pioity levels. e stdy the inflene that the ombined loation density pioity poliy have on the qality of sevie of the mobiles on the netwok oveall pefomane. This gives ise to a whole ontinm of pioity levels. The fist pat of the pape is devoted to the stdy of the eslting pioity qee model. e deive epessions fo the epeted sojon times of onnetions as a fntion of the loation of the mobile. e fthemoe obtain onsevation laws fo the wokload in the system fo a whole lass of wok onseving sheling poliies. e then se these tools to stdy the inflene that the ombined loation density pioity poliy have on the qality of sevie of the mobiles on the netwok oveall pefomane. e stdy the qality of sevie (QoS of a HSDPA system, onsideing thee types of aival flow, a nifom one, a non nifom one a flow whih geneates a onstant load density in the ell. e ompae the sojon time nde vaios sheling poliies: a pioity sheling stategy (P, a poesso shaing one ( a fist ome fist seved one (. e analyze the epeted sojon time sing a maimm S pioity (S ma a minimm S pioity (S min. e patilaly detemine that a S ma pioity does not povide in any ase the minimm epeted sojon time. elated wok on sheling poliies. e biefly mention some othe poliies that have been poposed fo downlink sheling fo HSDPA. The Fai algoithms ae bilt on the shae of the esoes in a faily way to the ses pesent in the ell. n the Effiient algoithms (maimm S[], the esoes ae alloated to the mobile with the best instantaneos link qality, so the thoghpt of the ell is maimized at eah time. The Effiient-fai algoithms [] do a ompomise between effiieny fainess, in ode to oveome the dawbaks of the pevios methods. The piniple of the Popotional-Fai algoithm [4] [5] is based on the tansmission to the se with the highest data ate elative to its ent aveage data ate. The Soe-ased algoithm [6] keeps tak of the last n vales of the feasible ate fo eah se then selets the se with the best soe, that is, with the best position. To deide whih stategy will be adopted to shae the tansmission between a geat nmbe of onsmes, a qeeing pioity analysis an be poposed. Diffeent kind of pioity analyses may be done: fo eample, the system an be onsideed as stati o dynami, the sevie disipline an be peemptive o non-peemptive. n data netwoks, a pioity disipline has to impove the mean delay o to satisfy the stingent delay eqiement of delay-sensitive taffis. elated wok on pioity les. elated woks on the sbjet mainly onside a disete limited set of pioities. The hannel alloation mehanism poposed in [7] is based on two pioity shemes, a high one fo hoff alls a low one fo new alls. To ee all bloking faile in a mobile ellla netwok, a dynamial pioity stategy is poposed in [8], fo aie alloation. n [9], the athos pesent an analytial famewok fo dynami pioity qeeing of hove alls in

2 wieless netwoks, with two lasses of pioity. n [], the athos popose a ombined peemptive o nonpeemptive pioity disipline. n [], the athos onside a pioity qeeing system with two diffeent types of taffi, modelled by ontinos flid flows, high low pioity. They onside a simple pioity qeeing system.. POTY MODEL Conside a maked point poess {T n,ν n,x n } whee T n is the time when the n th aival os, X n [,] indiates the lass to whih belong the n th aiving stome ν n denotes its sevie eqiement. A stome of lass has pioity level q(. Let S ] denote the epeted sevie time eqied by an aival of pioity. The aival lass of a stome is hosen aoding to some geneal distibtion F (P(X. e define the wokloads λ S ] F ( dξ, (.a [, ] λ S ] F ( dξ, (.b [, Define the pioity distibtion F q ( P(q(X. (.. MODEL: M/G/ O-PEEMPTVE HOL QUEUE Conside aivals of stomes aoding to a Poisson ate with paamete λ. The sevie eqiement boght by a stome of lass is geneally distibted (it may depend on with fist moment σ distibtion Σ. The aival pioity seqene is i.i.d. e wish to ompte the epeted waiting ( time of some tagged stome of pioity level. e poeed simila to [] [Vol., Chapte ]. t is the sm of (i the epeted esial sevie time es of the stome in sevie, (ii the epeted sevie time pesent, of all the stomes of pioity lage than o eqal to that wee in the system when the tagged stome aived, (iii the epeted sevie time fte, of all the aivals of stomes of pioities highe than the tagged stomes that aive ing the waiting time of the tagged stome. e have as in []: es λ/ [,]S ξ ] F (dξ (. ote that es does not depend on the pioities. ith M q denoting the nmbe of stomes with pioity q, we have by PASTA by Little s law { q( ξ q( } σξ d ξ ] { q( ξ q( } pesent ( ξ dξ finally, (. e onlde that ( fte, ξ ( { q( ξ q( } d (. es + { q( ξ q( } ( ξ dξ + ( { q( ξ q( } dξ e onlde that es + { q( ξ q( } ( ξ dξ ( (.4 { q( ξ q( } dξ whose soltion is es [,] ( ( { } q( ξ q( d ξ. (.5 APPLCATO: SCHEDULG HSDPA The HSDPA (High Speed Downlink Paket Aess has been intoed in UMTS (GPP speifiations fo elease 5 in ode to adapt moe dynamially the adio esoe to the nate of paket swithed taffi, to offe a thoghpt tansmission highe than in CDMA [][][4]. The HSDPA is, by nate, well adapted to on-eal Time (T sevies (no delay onstaint. The sheling stategies epesent one of the key fatos of the QoS of that system. e fist onside a single ell with a nit adis a single base station that tansmits at its maimm powe P. Mobiles aive aoding to a Poisson poess thei distane to the base station is detemined aoding to the distibtion F. The powe gain between the base station a mobile at a distane is given by h min(, η whee η, the poweloss eponent, is typially between. e assme that mobiles ae seved aoding to the HOL non-peemptive pioity sheme.. Tansmission ate sevie time The tansmission ate to a mobile at a distane depends on the signal to noise atio. Speifially, we an onside the following models, aph / th, (. whee th is the themal noise. i.e. it is linea in the signal to noise atio. a is a onstant As a speial ase, we may assme that the sessions' sizes do not depend on the aival loation: Denoting S the sevie time (seond at the position, v the sevie eqiement (bits, we an wite: v v, then the sevie time eqied fo a file tansfe is given as ν S (.. Pioity qees e fos hee on non-eal time (T data tansfes. heeas all alls se CDMA, we assme that T alls ae

3 time-mltipleed (whih diminishes the amont of intefeene, ths ineasing the available aveage thoghpts. This ombination of time mltipleing ove CDMA is typially fo high speed downlink data hannels, sh as the High Speed Downlink Paket Aess (HSDPA [4] the High Data ate (HD in CDMA- systems []. e apply the model developed in setion. Consideing independent mobiles aivals in a ell, eah mobile aives at a given position fom its seving S. And eah mobile has to be seved with a given pioity depending on its distane fom the S. Let's onside that mobiles lose to the S have a highe pioity than the ones fa fom it: the pioity is a deeasing fntion of the distane. The sevie eqiement is distibted aoding to a distibtion g with a fist moment denoted E [ a seond moment denoted E v ]. e an wite the fist seond moment of the sevie time as: [ E [ S] Sg( v( g( (. ] S g( ( ( [ ] v g E v E [ S (.4 e onside a netwok denote P i the total tansmitting powe of a S i of the netwok. P CC epesents the powe dediated to the ommon hannels, α is the othogonal fato, th is the themal noise, i h the pathloss between the mobile loated at in a given ell of the netwok the S i. The tansmitting powe dediated to a mobile belonging to the ell is the total available powe P -P CC of the seving base station S. And the noise is e to the ommon hannels of the S, the powe tansmitted by the S othe base stations of the netwok the themal noise. The epession (. an be witten as: aph a αp ( P PCC h S i CCh + Ph i i + th (.5 ntoing the intefeene fato f(, fo a homogeneos netwok (all the base stations tansmit at the same powe, we an wite: S S i i f ( Pi h h (.6 P h h P P i ϕ we have ϕ a αϕ + f ( + Ph th i (.7 The tem with themal noise is vey low ompaed to the othe intefeenes so we an wite, denoting : ϕ a αϕ + f ( (.8. Load of the system e denote the loation aival distibtion of the mobiles (at the position. Fom (.b (., we an epess the load density as: d ( d (.9 Using (.8 it an be witten: d ( ( f ( + αϕ d (. a( ϕ V. POTY SCHEDULG STATEGY e popose heeafte a pioity sheling stategy based on the S eeived by the mobile. Denoting λ the mobiles aival ate in the ell, we onside a ila symmety in the ell: an be witten whee is the distane fom the S. V. Maimm S Pioity The pioity is given to mobiles with the highest eeived S. Fom (.8 sine f(. is an ineasing fntion of the distane (as established in [5] in setion V.4, the maimm S is eeived by the base station's losest mobiles. Conseqently, the epeted waiting time given by (.5 an be witten as ma ( is epessed as: ma ( λ ( [ ] E S S d ] d (4. e denote ω the vaiane of the sessions sizes aivals, ω [ E v ] - E [, the ell adis. Using the epessions (., (.4 (.8 we finally an wite ma ( ( f ( + αϕ ω (4. a + [ ] E v ϕ λ a ( f ( + αϕ The epeted waiting time is an ineasing qadati fntion of the sessions' size vaiability epessed by the stad deviation ω V. Minimm S pioity The highest pioity is given to mobiles with the lowest eeived S. Fom (.8 sine f(. is an ineasing fntion of the distane, the minimm S is eeived by the base station's fthest mobiles. Conseqently, we an wite the

4 epeted waiting time as a fntion of the distane, sing its epession given by (.5, denoting ( as min ( in this ase: min ( λ ( [ ] E S S d ] d V. Consevation law The onsevation law is epessed as in []: P i (4. ii es (4.4 whee es is the esial sevie time, i is the epeted waiting time of the sevie i i is the load of the sevie i is the total load of the system. n o analysis we onside a ontinm of pioities in the ell so the epession (4.4 an be witten: ( ( d whee the load density (.9 an be epessed: es (4.5 d ( d (4.6 The epession (.5, onseqently (4. (4., was established fo a onsevative system: no wok (i.e. sevie eqiement is eated o destoyed within the system []. t appeas impotant to veify that the system is onsevative (see Anne. V.4 Stability ondition Consideing the epession of the epeted waiting time (.5 (4., the neessay stability ondition of the qee an be witten as λ a( ϕ ( f ( + αϕ > That ondition means that the epeted waiting time of any mobile has to be finite. t an be ewitten: ϕ > + λ a ( f ( αϕ This stability ondition epesses that when the amont of data aiving in the system is highe than the available tansmitting amont of data, the system an no moe answe the dem: the amont of data in the system ineases indefinitely, thee is no balane between the data aival thei depate. n the ase of a pioity sheling stategy based on a minimm S, sing the epession (4., we have the following ondition: λ ( f ( + αϕ > (4.7 a( ϕ V. OTHE SCHEDULG STATEGES t is inteesting to ompae the sheling stategy based on pioities between mobiles, to othe ones. e analyze the ases Fist Come Fist Seved (, Poesso Shaing (. V. ase Heeafte we develop the ase "withot pioity" [, hap.]. e an wite the mean epeted waiting time as: λ Using (. (.4 it beomes: a ( ϕ θ + [ ] E S λe S [ ] ( f ( + αϕ λ (5. a( ϕ ( f ( + αϕ V. Poesso Shaing ase n a Poesso Shaing ase, a mobile is seved as soon as it entes the ell: the epeted waiting time has no signifiane. The total apaity is eqally distibted (in time between the mobiles pesent in the ell: all the mobiles have the same aess hannel ation. n HSDPA, eah mobile is sheled alone. So we follow, fo the mobiles, a ond obin popotional sheling allowing to eah mobile the same hannel ation [6]. n this ase, we onside the mean sojon time T of a mobile in the system. That one only depends on the mean sevie time the load of the system, an be E( S witten T. Using the epessions (., (.9 (. we have finally T [ ] E S λe [ S ] ( f ( + αϕ a T ( ϕ ( λ f ( + αϕ a (5.

5 V. Epessions of the thee sheling stategies e denote D ( f ( + αϕ d (5. ( ( f ( + αϕ d (5.4 e an ewite the epessions of the epeted waiting times the sojon times as follows. V.. Pioity ase Epeted waiting time: ( + a ( ϕ [ ] E v D ( ( a ϕ Sojon time: λ ω (5.5a V.. ase Epeted waiting time: T ( ma ( + (5.5b λ ω + (5.6a a ( ϕ D( a( ϕ Sojon time T( + (5.6b V.. Poesso Shaing ase Sojon time: D( a( ϕ T (5.7 D ( a( ϕ Consideing the whole ell,, we obseve that the stability ondition (denominato > is the same fo the thee ases. n the pioity ase howeve, thee is a singlaity degee of ode fo the othe ases the singlaity is of ode. V.4 Analytial Model Using the model developed in [5] the epession (5.4 of the fato f( an be witten only depending on the distane : f ( f ( as: η η η [( k ( ] S.π f ( (5.8 ( η hee S is the S density, is the ell adis k haateizes the size of the netwok. e onside an infinite netwok k >> η η 8 f ( η (5.9 Consideing η, / we have: V. f ( S π 8 (5. ( / SCHEDULG STATEGES COMPASO e will ompae the epeted waiting times the sojon times sing thee sheling stategies, maimm S (S ma pioity,, Poesso Shaing (. Fo eah stategy we will assme thee kinds of aival distibtions in the ell: a nifom one (UA, a non-nifom one (denoted A, an aival fo whih the ell's load is a onstant (denoted CL. Consideing the epessions (5.5a (5.6a (5.7, to analyze the diffeent ases, it is sffiient to allate the paametes ( f ( + αϕ d (6. ( ( f ( + αϕ d (6. D V. Unifom loation aival pobability e onside an aival pobability eqivalent at any loation of λ the ell, so we have, θ π n this ase we an wite (8 + αϕ (6. / D ( (8 + αϕ (6.4 V. on nifom aival pobability The taffi an be non nifom. n this ase we an onside a non nifom aival pobability λ ( λ, whee fo eample κ ep( b, whee κ b ae onstant π the nomalisation ondition is F ( dd θ. So b, θ ep( b epesents the π ep( b

6 pobability density to ente the ell at the point M (, θ b ep( b is the pobability density to ep( b ente the ell at the distane. p Aival pobability density.5.5 Fige : Aival pobability density in the ell e ths an wite (5. (5.4 as b ep( b (8 + αϕ ep( b d (6.5 b D( (8 + αϕ ep( b d (6.6 ep( b V. Constant load in the ell The povide may adopt a sheling stategy based on a onstant load density in the ell. Fom the load epession (. we wite: E v f + λ [ ]( ( αϕ d Kd a( ϕ whee K is a onstant. So we have the ondition K ( f ( + αϕ a ϕ ( And the nomalisation ondition is F ( d. So we an wite: αϕ ( f ( + whee αϕ + f ( e finally an wite ( f ( + αϕ (6.7 D ( (6.8 emak: The stability ondition (4.7 an be witten as D ( a( ϕ < (6.9 V. UMECAL APPLCATO e onside a nit ell adis, an othogonality fato α.8 ϕ.,. s. Fo the non nifom ase a we onside a vale b5. e notie that onsideing the thee stategies, we have, fom the epessions (6.4, (6.6 (6.8: Unifom ase ( 6. D on-nifom ase (. 9 D Constant load ase D (. 45 The less estitive stability ondition (6.9 is obtained with the non-nifom ase. e fist onside a vaiane eqal to zeo: E [ v ]. To genealize the eslts, it will be sffiient to allate the inflene of the vaiane, sing the epession (4.. V. Epeted aiting Times ompaison The figes a, b show the epeted waiting time vaiations with the distane. They allow to ompae two sheling appoahes, the maimm S pioity one the one, in the ase of nifom (fig. a, non nifom (fig. b mobiles aivals in the ell, also mobiles aival sh as the ell's load density is onstant (fig.. e fist obseve that the epeted waiting time ineases with the distane. Fo nifom aivals, this inease beomes vey high lose to the edge of the ell (fig. a. n the ase of non nifom "onstant load" aivals, this inease is elatively slow linea when the distane ineases (fig. b fig.. e obseve that the pioity sheling stategy is bette than the one, ntil a given distane d th depending on the mobiles aival distibtion: d th.9 fo nifom aivals, d th.6 fo non nifom ones, d th.5 fo "onstant load aival". Moeove, the non nifom onstant load ases (fig. b give epeted waiting times vey low ompaed to the nifom one (fig.a ( se distane Fige a: Epeted waiting time with Unifom aival distibtion λ Pioity

7 ( se distane Pioity T( se distane Pioity Fige b: Epeted waiting time with on nifom aival distibtion λ Fige b Sojon time with on nifom aival distibtion λ ( se distane Fige : Epeted waiting time with Constant load aival distibtion λ Pioity T( se distane Fige Sojon time with Constant load aival distibtion λ Pioity V. Sojon Times Compaisons Fig a, b show that the sojon time is mainly bette (i.e. lowe eept at the edge of the ell in the pioity ase the ' one than in the poesso shaing ( ase, fo nifom, non nifom onstant load mobiles aivals. emak: the fige d shows the inflene of the vaiability of the session' sizes, fo diffeent distanes d fom the S. Fo almost the whole ell, when the distanes ae lowe than.9, we ω obseve that fo <, the pioity sheling stategy gives lowe sojon times than the one. This eslt is moeove obseved when the stad deviation eahes the vale fo distanes lowe than.5. T se. 4 6 d. d.5 d.9 d Fige d: Sojon time vs stad deviation of the session' size with nifom aival λ V. Aival ate inflene V.. Epeted waiting time Fig 4a Fig 4b show the epeted waiting time ineases with the aival ate. The pioity ase emains bette than ' one. T( se distane Fige a: Sojon time with Unifom aival distibtion λ Pioity ( se...5 distane Pioity.5.5 Pioity.. Pioity Fige 4a: Epeted waiting time with Unifom aival distibtion λ.5,.,

8 ( se....5 distane Pioity.5.5 Pioity.. Pioity Fige 4b Epeted waiting time with on nifom aival distibtion λ.5,., V.. Sojon time Fo non nifom aivals, Fig 5a 5b show the sojon time is bette in the pioity ase than in ones, even fo high aival ates, ntil a distane of.8. e an ompae these stategies by sing the epeted sojon time T of a mobile in the ell, whateve its position, as an indiato (Table. Consideing the fist ell's zone ntil a distane Z th.6, the seond one ntil the edge of the ell, we obseve (Table that the "hybid" stategy an be bette in tems of epeted sojon time than a S ma stategy. T (se λ λ4 S ma.8.75 S min.8.9 Hybid.6.9 Table : Epeted Sojon Time.6 T( se.6.4. Pioity ( se.4..5 Pioity Ma Pioity Min distane distane Fige 6a: Epeted waiting time with on nifom aival distibtion λ Fige 5a: Sojon time with on nifom aival distibtion λ T( se..5 distane Pioity ( se..5 distane Fige 6b: Epeted waiting time with on nifom aival distibtion λ4 Pioity Ma Pioity Min Fige 5b: Sojon time with on nifom aival distibtion λ4 V.4 Hybid sheling stategy n the ase of non nifom aivals, we obseve (Fig 6a 6b the epeted waiting time is lowe sing a sheling based on a maimm S pioity (S ma than a sheling based on minimm S pioity (S min fo distanes lowe than.6. This is a well-known eslt. e howeve also obseve that this last stategy is bette than the fist one in tem of epeted waiting time when the distane is highe than.6: the epeted waiting time beomes lowe. t old be inteesting to adopt a S min pioity sheling stategy, in some given ases. This onlsion old dive s to adopt a "hybid" stategy, dividing the ell into two zones: a fist one, lose to the S ntil a given distane Z th, a seond one fa fom the S, beginning at Z th ending at the edge of the ell. n the fist one, a S ma sheling stategy wold be adopted in the seond one a S min stategy wold be adopted. The fige 7a, 7b 7 show the sojon time pobability densities, fo diffeent aival ates, when the mobiles aivals ae nifom. Fo a low aival ate, λ., the pioity sheling based on S ma S min ae eqivalent. hen the aival ate ineases, the behavio of the ve desibing the pioity S min is modified. Fo a high vale of λ we obseve that the sojon times pobability density ompised between.8 is highe fo a sheling based on a S min pioity: it an be inteesting, in that last ase, to adopt a S min pioity sheling stategy than a S ma one. V. COCLUSO e onsideed a ontinm of pioity levels to analyse vaios pioity poliies whee the pioity is given in tems of the distane between mobiles thei seving base station. e established the inflene that the ombined loation density

9 pioity poliy have on the epeted waiting time on the sojon time. Applying o analysis to a HSDPA system, we ompaed a pioity sheling stategy to a poesso shaing one a one. Consideing thee types of aival flow, a nifom one, a non nifom one a flow whih geneates a onstant load density in the ell, we showed the sojon time depends on the adopted stategy, on the loation of the mobile on the aival flow type. e moeove showed that a S ma pioity sheling stategy does not povide in any ase the lowest epeted sojon time: dividing the ell into two zones onsideing a non-nifom aival of mobiles, we showed a "hybid" stategy ombining a S ma sheling stategy a S min one allows to obtain a lowe epeted sojon time. Pobability Density Sojon Time Pioity Ma Pioity Min Fige 7a: Sojon time Pobability density with Unifom aival distibtion λ. Pobability Density Sojon Time Pioity Ma Pioity Min Fige 7b: Sojon time Pobability density with Unifom aival distibtion λ.5 Pobability Density Sojon Time Pioity Ma Pioity Min Fige 7: Sojon time Pobability density with Unifom aival distibtion λ AEX: COSEVATO LA Maimm S Pioity Using (. (. (.4, the epeted waiting time (4. an be witten: es ma ( (A- ( d So we have ( ma ( d esd (A- ( d emak: e an denote the following key hange of vaiables (A- (A-4 : D( λ (A- ( F ( F ( d Conseqently we an wite So we have ( ma ( d D ( ( D( D ( ( D( es d es d D ( (A-4 ( ma ( d ( (A-6 es ( D( ( D( e notie that D( λ (A-7 D( λ (A-8 Finally we an wite the onsevation law ( ( (A-5 ma ( d ( es es (A-9

10 Minimm S pioity n a simila appoah, when the highest pioity is given to the base station's fthest mobiles (with the minimm S, we an wite: es min ( (A- ( d e an wite λ E v λ [ ] ( So we have λ The epession (A- an be witten es min ( ( + d So we an wite So we have ( min ( ( d min ( + ( d d D ( ( + D( d es (A- n an analoge way as the one sed fo the maimm S pioity, we wite: ( min ( ( d ( es es ( + D( ( + D( es ( ( + es Finally we an wite the onsevation law ( ( d min es (A- EFEECES [] P. ende, P. lak, M. Gob,. Padovani,. Sindhshayana A. Vitebi, CDMA/HD: A bwidth-e_ient high-speed wieless data sevie fo nomadi ses", EEE Commn. Magazine, 7{77, Jly. [] GPP TS 5.8, UTA High Speed Downlink Paket Aess (HSDPA; Oveall desiption, elease 5,. [] GPP TS 5.4, Physial Laye Poees(FDD, elease 5,. [4] S. Pakvall, E. Dahlman, P. Fenge, P. eming,m. Pesson, The high speed paket data evoltionof CDMA, in: Po. of the th EEE PMC,. [5] J-M Kelif., E. Altman., Downlink flid model of CDMA netwoks, VTC 5 Sping. [6] A popotionally fai sheling algoithm with QoS pioity in XEV-DO, Kenyong Kim, Hoon Kim, Yongnam Han, Poeedings PMC [7] Tsang-Ling She Hsin-Yan Lin, A Pioity-based Channel Alloation Sheme fo Cellla etwoks, Poeedings of CC [8] Xefeng Dong Ten H. Lai, An Effiient Pioity-ased Dynami Channel Alloation Stategy fo Mobile Cellla etwoks, nfoom 997 [9] Aiton E. Xhafa Ozan K. Tongz, Dynami Pioity Qeeing of Hove Calls in ieless etwoks: An Analytial Famewok, EEE Jonal of Seleted Aeas in Commniations, Vol., n 5, Jne 4 [] Yo Ze Cho Chong Kwan Un, Analysis of the M/G/l Qee nde a Combined Peemptive/onpeemptive Pioity Disipline, EEE Tansations on ommniations, Vol. 4,, Janay 99 [] Chales Knessl Chales Tie, A Simple Flid Model fo Seviing Pioity Taffi, EEE Tansations on atomati ontol, Vol. 46, 6, Jne [] L. Kleinok, Qeeing Systems, Vol, iley, 976. [] Yoshiaki Ofji, Akihito Moimoto, Sadayki Abeta, Mamo Sawahashi,, Compaison of Paket Sheling Algoithms fosing on se thoghpt in HSDPA, Poeedings PMC [4] J.M. Holtzman, CDMA fowad link wate filling powe ontol. Po. of EEE VTC Sping,. [5] J.M. Holtzman, Asymptoti analysis of Popotional Fai algoithm. Po. of th EEE PMC,. [6] T. onald, A soe-based oppotnisti shele fo fading adio hannels, Po. of Eopean ieless 4.