Performance Modelling of W-CDMA Networks Supporting Elastic and Adaptive Traffic

Transcription

1 Performace Modeig of W-CDMA Networks Supportig Eastic ad Adaptive Traffic Georgios A. Kaos, Vassiios G. Vassiakis, Ioais D. Moschoios ad Michae D. Logothetis* WCL, Dept. of Eectrica & Computer Egieerig, Uiversity of Patras, Patras, Greece *Correspodig author: Abstract-We propose a ew mode, amed Widebad Threshod Mode (WTM) for the aaysis of W- CDMA etworks supportig eastic ad adaptive traffic. Mobie users geerate Poisso arrivig cas that compete for the acceptace to a W-CDMA ce uder the compete sharig poicy. A ewy arrivig ca ca be accepted with oe of severa possibe Quaity-of-Service (QoS) requiremets depedig o the resource avaiabiity i the ce. We propose a approximate method, which is a extesio of the Kaufma-Roberts agorithm, for the cacuatio of ca bockig probabiities i the upik directio. The accuracy of the proposed approximatio is verified by simuatio resuts. Keywords: Quaity-of-Service; Ca Bockig Probabiity; W-CDMA; Eastic Traffic; Adaptive Traffic.. Itroductio The ca-eve performace modeig of 3 rd geeratio (3G) wireess etworks is importat for the resource aocatio amog differet services, the avoidace of too costy over-dimesioig of the etwork ad the prevetio, through traffic egieerig mechaisms, of excessive throughput degradatio. Despite of its importace, the ca-eve performace modeig ad QoS assessmet remais a ope issue, due to the presece of eastic ad adaptive traffic. The Uiversa Mobie Teecommuicatio System (UMTS) is the proposa for 3G wireess etworks i Europe. The existig d geeratio (G) systems ike GSM are desiged primariy for voice services. UMTS etworks, however, aim at supportig wide rage of voice ad data services. The air iterface used i UMTS is the Widebad Code Divisio Mutipe Access (W-CDMA). It uses the Direct Sequece CDMA (DS- CDMA) techique ad supports very high bit rates, up to Mbps []. Herei we distiguish three types of traffic: stream, eastic ad adaptive. Stream traffic is geerated by cas that have fixed resource ad hodig time requiremets, which caot be reduced at ay time (e.g. reatime audio or video). Eastic ad adaptive traffic is geerated by cas that may have differet possibe resource requiremets depedig o the resource avaiabiity. The hodig time of a eastic ca is strogy reated to the resources aocated to this ca, whie the hodig time of a adaptive ca is aways costat ad idepedet of the resources aocated to this ca. The we-kow Erag Muti-rate Loss Mode (EMLM) is used for the aaysis of traditioa etworks supportig oy stream traffic. A recurret agorithm deveoped by Kaufma ad Roberts (K-R agorithm) faciitates the cacuatio of ca bockig probabiities i the EMLM [], [3]. Sice the, severa modificatios of this agorithm were proposed for wired ad mobie etworks [4]-[8]. I [4], a bocked ca ca retry may times, requestig for ess resources each time. I [5], cas arrive to the ik with severa possibe resource requiremets ad their request is made accordig to threshods, which idicate the tota umber of occupied resources. The Coectio-Depedet Threshod Mode (CDTM) [6] geeraizes the retry ad threshod modes (as we as the EMLM) by idividuaizig the threshods amog differet services. The abovemetioed modes are proposed for wired coectio-orieted etworks with eastic traffic ad they do ot cosider the resource aocatio scheme of W-CDMA wireess etworks. I [7], a stream traffic mode for W-CDMA is preseted where the cacuatio of ca bockig probabiities i the upik of a W-CDMA ce is based o a extesio of the K-R agorithm. I [8], a extesio of [7] is preseted i order to mode eastic traffic. I this mode, eastic cas may chage the occupied resources whie i-service, however it is ot possibe to have differet resource requiremets upo arriva. I this paper, we deveop a aaytica mode for W-CDMA etworks supportig both eastic ad adaptive traffic. Cas of differet services arrive to a W-CDMA ce with severa resource (QoS) requiremets, depedig o the tota umber of occupied resources at the time of arriva. Based o this mode, we preset a approximate recurret agorithm for the cacuatio of ca bockig probabiities i the upik directio. The remaider of the paper is as foows: I sectio we briefy review the EMLM ad the K-R agorithm. I sectio 3 we review the CDTM. I sectio 4 we propose the Widebad Threshod Mode; i sectio 4.

2 the descriptio of the mode is give, whie i sectios 4. to 4.4 we cacuate the oca bockig probabiities, the state probabiities ad the ca bockig probabiities, respectivey. I sectio 5 we preset a appicatio exampe ad compare the aaytica to simuatio resuts. We cocude i sectio 6.. Review of the Erag Muti-rate Loss Mode (EMLM).. Mode descriptio I the EMLM, a system with C uits of a resource accommodates Poisso arrivig cas of K differet categories (services). Cas compete for the avaiabe resource uits (r.u.) uder the compete sharig poicy []. Each service k (k=,,k) ca requests upo arriva r k r.u. If they are avaiabe, the ca is accepted i the system ad the r k r.u. are occupied by the ca for a time, expoetiay distributed with mea µ k -. Otherwise the ca is bocked ad ost. The EMLM is widey used for the aaysis of traditioa teecommuicatio etworks supportig stream traffic. The system ca be a trasmissio ik of certai capacity. The ik capacity correspods to the shared resource. For exampe if we defie a r.u. equa to the trasmissio rate of 64 Kbps, the a.8 Mbps ik cosists of C=0 r.u. A voice ca of R =64 Kbps wi request upo arriva r = r.u., whie a video ca of R =56 Kbps wi request r =4 r.u... Loca baace equatio ad resource share The system state j ( j=0,,c) is defied as the tota umber of r.u. occupied by the cas. The probabiity that the system is i state j is deoted by q( j). I the EMLM the foowig oca baace equatio exists betwee adjacet system states []: αkq( j-r k) =Yk( j) q( j ) where a k = λ k µ k - is the offered traffic oad of service k ad Y k ( j) is the average umber of service k cas i state j. We ca cacuate the resource share (proportio of the resource occupied by cas of a specific service) of service k cas i state j ( j>0), P k ( j) as foows: α ( ) ( ) ( ) () krq k j-rk Yk jrk α kbq k j-r = k =Pk ( j ) () jq( j) j jq( j) I Fig.. we show the state trasitio diagram for the EMLM. I this exampe, a ik of capacity C=4 is cosidered ad the resource requiremet of service k cas is r k =. ().3. State probabiities Figure. State trasitio diagram for the EMLM To cacuate the u-ormaized state probabiities, qˆ( j), the we-kow K-R agorithm is used [], [3]: ˆ( ) K q j = αkrq kˆ( j-rk), for j=,..., C j k= where qˆ(0) = ad qˆ( j) =0 for j<0. The state probabiities, q( j) are derived after ormaizatio, ( ) = ˆ( )/ C q j q j qˆ( j). j= 0 (3)

3 .4. Ca bockig probabiity A ew arrivig ca with requiremet r k r.u. is accepted i the system oy if j C- r k. Thus for the service k the states j=c- r k +,, C are bockig states. The ca bockig probabiity (CBP) of service k cas is determied by addig the state probabiities of a bockig states: B = k C j=c-r + k q( j ) (4) 3. Review of the Coectio-Depedet Threshod Mode (CDTM) 3.. Mode descriptio The Coectio-Depedet Threshod Mode (CDTM) is a extesio of the EMLM that ca be used for wired, coectio-orieted etworks supportig eastic traffic [6]. Assume a ik of capacity C r.u. commoy shared amog Poisso arrivig cas of K differet services. The arriva rate of service k cas is λ k (k =,,K) ad a arrivig service k ca has S k resource ad mea hodig time requiremets with vaues r k ad µ k -, (=,, S k ) respectivey, where r ksk < < r k < < r k < r k ad µ ksk - > > µ k - > > µ k - > µ k -. The hodig time of service k cas is assumed to be expoetiay distributed. The pair (r k, µ k - ) is used from service k cas whe the umber of occupied r.u. at the ca arriva is j J k, where J k is the owest threshod of the service k. The pair (r k, µ k - ), (for >), is used from service k cas whe J k < j J k+, where J k ad J k+ are two successive threshods of the service k. The pair (r ksk, µ ksk - ) is used from service k cas whe J ksk - < j C- r k Sk. Fiay, a service k ca is bocked whe C- r ksk < j C. The offered traffic oad of service k cas with resource requiremet r k is defied as: a k = λ k µ k -. The tota offered traffic oad is equa for every pair (r k, µ k - ) ad is defied as: the product of the offered traffic oad by the required r.u. per ca, a k r k [9]. I Fig. we show the basic pricipe of the CDTM. A service k ca with oe threshod, J k =04 Kbps (or J k = 6 r.u.) ad two cotigecy trasmissio rate requiremets, Rk = 384 Kbps (r k = 6 r.u.) ad Rk = 8 Kbps (r k = r.u.) is accommodated to a trasmissio ik of capacity C= 048 Kbps (or C=3 r.u.). 3.. Assumptios Figure. Pricipes of the CDTM I order to derive a approximate recurret formua for the CBP determiatio i the CDTM, the foowig assumptios are ecessary [6]: Loca baace: we assume that the oca baace equatio exists betwee adjacet system states. Upward migratio approximatio: Cas accepted i the system with their maximum resource requiremet are egigibe withi a space, caed upward migratio space. More precisey, the mea umber of cas, Y k (j), with requiremet r k i state j is egigibe whe J + r k < j C ; the atter regio is reated to the variabe δ k (j), defied beow i (5). Migratio approximatio: Cas accepted i the system with other tha the maximum resource requiremet are egigibe withi a space, caed migratio space. More precisey, the mea umber of cas, Y k (j) (>) with requiremet r k i state j is egigibe whe 0<j<J k +r k ad J k+ +r k j C; the atter regio is reated to the variabe δ k (j) (for >), defied beow i (6). 3

4 Accordig to the above approximatios the two foowig expressios defie the parameters Deta:, whe j C ad r k = 0 ( > ) δk ( j ) =, whe ad 0 j J k +r k r k > (5) 0, otherwise, whe ( J k +r k < j J k +rk ) ad ( r k > 0) + δk ( j ) =, for > (6) 0, otherwise 3.3. Loca baace equatio ad resource share Due to the assumptios of Sectio 3. the foowig oca baace equatio exists betwee adjacet states: αk δk ( jq ) ( j-b k ) =Yk ( j) δ k ( jq ) ( j ) (7) where q( j) is the probabiity that the system is i state j. The resource share of service k cas with requiremet r k i state j (j>0), P k ( j) is determied by: αk r ( ) ( ) ( ) ( ) ( ) ( ) (7) k δ k j q j-r k Y k j r k δ k j α k b k δ k j q j-r k = = Pk ( j) jq( j) j jq( j) (8) 3.4. State probabiities The u-ormaized state probabiities are cacuated by the foowig recurret formua: K S qˆ( j ) = k ak r ( ) ˆ( ) for =,..., k δ k j q j r k j C (9) j k= = where qˆ(0) = ad qˆ( j) =0 for j<0. The state probabiities, q( j) are derived after ormaizatio, ( ) = ˆ( )/ C q j q j qˆ( j). j= Ca bockig probabiity The CBP of service k cas is determied by addig the state probabiities of a the bockig states: C B k = q( j ) (0) j=c-r k + Sk 4. The Widebad Threshod Mode (WTM) 4.. Mode descriptio Assume a W-CDMA system that supports K differet services. Our system cosists of a referece ce surrouded by eighbourig ces. We cosider oy the upik i.e. cas from the mobie users (MUs) to the base statio (BS). Each service k (k=,, K) is characterized by S k differet QoS eves. I the rest of the paper a service k ca of QoS eve (=, S k ) is referred to as simpy service k ca. There are two QoS parameters that characterize a service k ca: R k : Trasmissio bit rate (E b /N 0 ) k : Bit error rate (BER) parameter 4

5 We distiguish three types of services: Stream type: services that have oy oe QoS eve (S k =). Eastic type: services that have more tha oe QoS eves (S k >) ad the cas mea hodig time strogy depeds o the QoS eve. Adaptive type: services that have more tha oe QoS eves (S k >) ad the cas mea hodig time is the same for every QoS eve. The arriva rate of service k cas is Poisso with mea λ k. The service k cas hodig time is expoetiay distributed with mea µ k -. For eastic services it hods: µ ksk - > > µ k - > > µ k - > µ k -, whie for adaptive services: µ ksk - = = µ k - = = µ k - = µ k -. The offered traffic oad of a service k is defied as: a k = λ k µ k -. For the purposes of our aaysis, we express ater i the paper the differet service s QoS requiremets as differet resource requiremets. 4.. Iterferece ad ca admissio cotro We assume perfect power cotro i.e. at the BS, the received power from each service k ca is the same ad equa to P k []. Sice i W-CDMA systems a users trasmit withi the same frequecy bad, a sige user sees the sigas geerated by a other users as iterferece. We distiguish the itra-ce iterferece, I itra, caused by users of the referece ce ad the iter-ce iterferece, I iter, caused by users of the eighbourig ces. We aso cosider the existece of the therma oise, P N, which correspods to the iterferece of a empty system. The ca admissio cotro (CAC) i W-CDMA systems is performed by measurig the oise rise, NR which is defied as the ratio of the tota received power at the BS, I tota to the therma oise power, P N : NR I I + I + P P P tota itra iter N = = () N N Whe a ew ca arrives, the admissio cotro estimates the oise rise ad if it exceeds a maximum vaue, NR max, the ew ca is bocked ad ost. 4.. User activity A user, durig his ca s duratio, aterates betwee trasmittig ad siet periods. This behavior is characterized by the activity factor v k, which represets the fractio of the ca s hodig time durig which the user is occupyig system resources. Obviousy we have 0 <v k. Users that at a time istat occupy system resources are referred to as active users. The rest of the users (passive users) are i siet period ad do ot occupy ay system resources. The service k user activity at a ew ca arriva ca be modeed by a Beroui radom variabe with probabiity of success equa to the activity factor v k [0] Load factor ad ce oad The ce oad, is defied as the ratio of the received power from a active users (at the referece or eighbourig ces) to the tota received power: Iitra + Iiter = I + I + P itra iter N Hece from () ad () we ca derive the reatio betwee the oise rise ad the ce oad: NR = ad (3) () NR = NR We defie the maximum vaue of the ce oad, max as the ce oad that correspods to the maximum oise rise, NR max. Typica vaue is max = 0.8 ad it ca be cosidered as the shared system resource. The oad factor, L k of (4) ca be cosidered as the resource requiremet of a service k ca [7]: Lk ( Eb / N0) k * R k = W + ( Eb/ N0) k * Rk By W we deote the chip rate of the W-CDMA carrier which is 3.84 Mcps. (4) 5

6 The ce oad ca be writte (see (7) beow) as the sum of the itra-ce oad, itra (ce oad that derives from the users of the referece ce) ad the iter-ce oad, iter (ce oad that derives from the users of the eighbourig ces). They are defied i (5) ad (6), respectivey: K S itra k k k= = k = m L where m k is the umber of active users of service k. (5) iter I = ( ) iter max (6) P = itra + iter N I Fig. 3 we show a simpe exampe of the mode. Two users of the referece ce (cotroed by BS-) durig their active periods occupy L ad L resources which cotribute to the itra-ce oad itra as it is measured at the BS-. The users from the two eighbourig ces (cotroed by BS- ad BS-3) cotribute to the iter-ce oad iter. Accordig to the CAC poicy as it was described i sectio 4.., the foowig coditio is used at the BS i order to decide whether to accept a ew ca or ot: +L k max (8) (7) Figure 3. Itra-ce ad iter-ce oad i W-CDMA 4.. Loca bockig probabiity Due to the coditio of (8), the probabiity that a ew service k ca is bocked whe arrivig at a istat with itra-ce oad itra is caed oca bockig probabiity (LBP) ad ca be cacuated by: β k ( itra ) = P( itra + iter + Lk > max ) (9) I order to cacuate the LBP of (9) we ca use (5)-(8). We otice that the oy ukow parameter is the iter-ce iterferece, I iter. Simiary to [], we mode I iter as a ogorma radom variabe (with parameters µ I ad σ I ), that is idepedet of the itra-ce iterferece. (A aterative approach is to mode the iter-ce iterferece as a ratio of the itra-ce iterferece [], [3]). Hece, the mea, E[I iter ] ad the variace, Var[I iter ] of I iter are cacuated by (0) ad (): σ µ I + EI [ iter ] = e I (0) I I+ σ µ σ Var[ I ] = ( e ) e I iter Cosequety, because of (6), the iter-ce oad, iter wi aso be a ogorma radom variabe. Its mea, E[ iter ] ad the variace, Var[ iter ] are cacuated by: () 6

7 σ µ + E [ ] = = max iter e EI [ N 0 iter ] () σ [ ] ( µ ) + σ Var ( max iter = e e = ) Var[ Iiter ] (3) N0 where µ ad σ are the parameters of iter, which ca be foud by sovig () ad (3): ( + CV[ Iiter ] ) µ = ( E[ Iiter]) + ( max) ( P N) (4) CV Ii ter (5) σ = ( + [ ] ) The coefficiet of variatio, CV [I iter ] is defied as: CV[ I ] = iter Var[ I ] iter EI [ ] iter Note that (9) ca be rewritte as: β ( ) = P( L ) k itra iter max itra k The Right Had Side (RHS) of (7), is the cumuative distributio fuctio (CDF) of iter. It is deoted by P( iter x)=f (x) ad ca be cacuated from: x µ F( x) = [ + erf( )] σ where erf( ) is the we-kow error fuctio. Hece, if we substitute x= max - itra - L k ito (8), from (7) we have: -F ( x), x 0 β k ( ) = itra (9), x < State probabiities As we stated before, i W-CDMA etworks the ce oad, ca be cosidered as shared resource ad the oad factor, L k as the resource requiremet of a service k ca. Thus, we ca use a modificatio of the K-R agorithm (described i sectio.3) for the cacuatio of state probabiities i such etworks. Beow we preset five steps eeded i order to obtai a modificatio of the K-R agorithm suitabe for the WTM: 4.3. Resource discretizatio. The K-R agorithm cosiders discrete state space. The discretizatio of the ce oad, ad the oad factor, L k is performed with the use of the basic ce oad uit, g [7]: (6) (7) (8) max C = (30) g r k Lk = roud( ) (3) g The resutig discrete vaues of (30) ad (3) ca be cosidered as the system capacity ad the service k resource requiremet, respectivey Icorporatio of the user activity. The K-R agorithm cosiders users that are active durig the etire duratio of their cas hodig time. However, i W-CDMA etworks we ca expoit the fact that passive users do ot cosume ay resources. 7

8 Hece, i the WTM a state j does ot represet the tota umber of occupied resources as it happes i the EMLM. Istead, it represets the tota umber of occupied resources whe a users are active. We deote by c the tota umber of occupied resources at a istat. Note that i the EMLM, c is aways equa to j, whie i the WTM, we have 0 c j. The case c=0 correspods to a situatio whe a users are passive, whie whe c=j, a users are active. We deote by q(j) the probabiity of the state j. The resource occupacy Λ(c j) is defied as the coditioa probabiity that c resources are occupied i state j ad ca be cacuated from (3) recursivey: K S Λ( c j) = k Pk ( j)[ v ( ) + ( ) ( )], for =,..., max ad kλ c rk j r k v k Λ c j rk j j c j (3) k= = where Λ(0 0)= ad Λ(c j)=0 for c>j Icorporatio of oca bockigs. I W-CDMA systems, due to the iter-ce iterferece, bockig of a service k ca may occur at ay state j with a probabiity LB k ( j). This is caed oca bockig factor (LBF) ad ca be cacuated from (33): j LBk ( j) = ( ) ( ) k c c j c= 0 β Λ (33) Note that for j=0 we have LB k (0)=β k (0). I Fig. 4 we show the state trasitio diagram for the WTM. We see that, due to the oca bockigs, the trasitio rates from ower states to higher, are reduced by the factor - LB k ( j) i compariso to the EMLM (see Fig. ). The highest reachabe state i the diagram is deoted by j max Determiatio of the resource share. Figure 4. State trasitio diagram for the WTM The service k resource share i state j, P k ( j), is derived from () by icorporatig the LBFs ad the parameters deta of (5) ad (6): Pk ( j) αk( -LBk ( j-rk )) rk δk ( j) q( j-rk ) jq( j) = Cacuatio of state probabiities. The u-ormaized state probabiities are give by extedig (3) due to the presece of oca bockigs: (34) K S qˆ( j ) = k αk (-L ( )) ( ) ˆ( ), for =,..., k j-r k r k δ k jq j-r k j j max j k= = where qˆ(0) = ad qˆ( j) =0 for j<0. (35) j Fiay, the ormaized state probabiities, q( j) are cacuated from q( j) = qˆ( j)/ qˆ( j). j= Ca bockig probabiities The CBP of service k are give by addig a the state probabiities mutipied by the correspodig LBFs: max 8

9 j max S B q( j) γ ( j) LB ( j) (36) k = k k j= 0 = k, whe j Jk, whe J k < j J k+ where γ k ( j ) = ad γ k ( j ) = 0, otherwise 0, otherwise, for > (37) 5. Evauatio I this, sectio a appicatio exampe is preseted. We compare the aaytica versus simuatio CBP resuts for the WTM i order to show its accuracy. The simuatio resuts have bee obtaied as mea vaues from 6 rus with cofidece iterva of 95%. However, the resutat reiabiity rages of our measuremets are sma eough ad therefore we preset oy the mea CBP resuts. 5. Appicatio exampe We cosider a W-CDMA system with three services: voice, data ad video. The traffic parameters used for each service are as foows (see aso Tabe ): Voice service requires a trasmissio rate of R =. Kbps which ca be reduced to R =8.4 Kbps depedig o the threshod J = 0.7. The activity factor is chose to be v =0.5 ad the required BER parameter is (E b /N 0 ) =5dB. This service is adaptive sice the reductio of the trasmissio rate does ot affect the hodig time. Data service requires a trasmissio rate of R =64 Kbps which ca be reduced to R =3 Kbps depedig o the threshod J = 0.6. The activity factor is chose to be v =.0 ad the required BER parameter is (E b /N 0 ) =4dB. This service is eastic sice the reductio of the trasmissio rate correspods to the same icrease of the hodig time. Video service requires a trasmissio rate of R 3 =44 Kbps which ca be reduced to R 3 =8 Kbps ad to R 33 = Kbps depedig o the threshods J 3 = 0.4 ad J 3 = 0.6. The activity factor is chose to be v =0.3 ad the required BER parameter is (E b /N 0 ) =3dB. This service is adaptive sice the reductio of the trasmissio rate does ot affect the hodig time. We take measuremets for eight differet traffic oad poits (x-axis of Fig.5). Each traffic oad poit correspods to some vaues of the offered traffic oad of three cosidered services as it show i Tabe. I this exampe the mea vaue for the iter-ce iterferece is: E[I iter ] = 3*E-8 mw ad CV [I iter ]=. Figure 5. CBP versus offered traffic oad for the appicatio exampe 9

10 Tabe. Traffic parameters for the appicatio exampe Voice Data Video Type Adaptive Eastic Adaptive Trasmissio rates (Kbps) R =. ad R =8.4 R =64 ad R =3 R 3 =44, R 3 =8 ad R 33 = Threshods J = 0.7 J = 0.6 J 3 = 0.4 ad J 3 = 0.6 Activity factor v =0.5 v =.0 v 3 =0.3 BER parameter (E b /N 0 ) =5dB (E b /N 0 ) =4dB (E b /N 0 ) 3 =3dB Tabe. Offered traffic oad for the appicatio exampe Traffic oad poit Traffic oad (er) Voice (α ) Data (α ) Video (α 3 ) I Fig. 5 we show the aaytica ad simuatio resuts for three services versus the offered traffic oad. The resuts show that the mode s accuracy is absoutey satisfactory, especiay for ow offered traffic oad. 6. Cocusios We propose a ew mode for the aaysis of a W-CDMA system supportig eastic ad adaptive traffic. We provide a recurret formua for the cacuatio of the ca bockig probabiities. Simuatios are used to verify the accuracy of the proposed cacuatios. We show by umerica exampes that the accuracy of the ew mode is absoutey satisfactory. I this mode, we assumed for each service ifiite umber of users that geerate cas. This assumptio restricts the mode s appicabiity to ces of very high desity. I our future work we are goig to ivestigate the modeig of fiite umber of users i the WTM i.e. the umber of users of each service wi be imited. Ackowedgmet Work supported by the research program PENED-003 of the Geera Secretariat of Research ad Techoogy of the Greek Miistry of Deveopmet. Refereces [] H. Homa ad A. Toskaa, eds., WCDMA for UMTS. Joh Wiey & Sos Ltd., 00. [] J. Kaufma, Bockig i a Shared Resource Eviromet, IEEE Tras. Commu. COM-9 (0) (98) [3] J. W. Roberts, A Service System with Heterogeeous User Requiremets, i: G. Pujoe (Ed.), Performace of Data Commuicatios systems ad their appicatios, North Hoad, Amsterdam, pp.43-43, 98. [4] J.S. Kaufma, Bockig i a Competey Shared Resource Eviromet with State Depedet Resource ad Residecy Requiremets, Proc. IEEE INFOCOM 9, pp. 4-3, 99. [5] J.S. Kaufma, Bockig with Retrias i a Competey Shared Resource Eviromet, Performace Evauatio, 5, pp. 99-3, 99. [6] I. Moschoios, M. Logothetis ad G. Kokkiakis Coectio Depedet Threshod Mode: A Geeraizatio of the Erag Mutipe Rate Loss Mode, Performace Evauatio, Vo. 48, issue -4, pp , May 00. [7] D. Staehe ad A. Mäder, A Aaytic Approximatio of the Upik Capacity i a UMTS Network with Heterogeeous traffic, i 8th Iteratioa Teetraffic Cogress (ITC8), (Beri), Sep 003. [8] G. Fodor ad M. Teek, A Recursive Formua to Cacuate the Steady State of CDMA Networks, Proc. of Iteratioa Teetraffic Cogress 005, Beijig, Chia, September 005. [9] H. Akimaru, K. Kawashima, Teetraffic Theory ad Appicatios, Spriger-Verag, 993. K.W. Ross, Mutiservice Loss Modes for Broadbad Teecommuicatio Networks, Spriger, Beri, 995. [0] A. Viterbi ad A. Viterbi, Erag Capacity of a Power Cotroed CDMA System, IEEE Joura o Seected Areas i Commuicatio, vo., August 993. [] D. Staehe, K. Leibitz, K. Heck, B. Schröder, A. Weer, ad P. Tra-Gia, Approximatig the Otherce Iterferece Distributio i Ihomogeeous UMTS Networks, i Proc. IEEE VTC Sprig, (Birmigham, AL), May 00. [] Gabowski M, Stasiak M, Wisiewski A, Zwierzykowski P. Upik Bockig Probabiity Cacuatio for Ceuar Systems with WCDMA Radio Iterferece ad Fiite Source Popuatio, Proc. of d Iteratioa Workig Coferece o Performace Modeig ad Evauatio of Heterogeeous Networks (HET-NETs 04), Ikey, West Yorkshire, U.K., 6 8 Juy 004; 80/ 80/0. [3] Iverse VB, Beetis V, Ha NT, Stepaov S. Evauatio of Muti-service CDMA Networks with Soft Bockig, Proc. of ITC Speciaist Semiar, Atwerp, Begium, August/September 004;