model knapsack untuk umts

FUJITSU Sci. Tech. J., 38,2,p.183-191(December 2002) 183

Modified Stochastic Knapsack forUMTS Capacity Analysis

vMona Jaber vSyed Ammar Hussain vAdel Rouz (Manuscript received June 6, 2002)

This paper is a brief introduction to the complex task of UMTS (Universal Mobile Tele-communications System) network dimensioning, with emphasis on capacity analysisand the innovative solution developed by FLE for this purpose.Capacity analysis (an integral part of dimensioning) is a study that allows the estima-tion of required resources that can guarantee a defined level of satisfaction for theusers. Compared to fixed and 2G mobile networks, this task is much more challengingin 3G systems due to two main reasons. First is the fact that the cell edge in UMTS iscontinuously moving according to the traffic load, making dimensioning ambiguousand leaving room for under or over dimensioning. The second challenge is an out-come of the multiple data rates and switching modes supported by the 3rd generationnetworks. Traffic and capacity analysis for such mixed services is a new concept whichwas addressed by Fujitsu by the use of a modified Stochastic Knapsack traffic model.The Stochastic Knapsack is a multi service traffic model by definition and is generallyused in ATM multiplexer dimensioning. This paper introduces the steps involved inUMTS air interface dimensioning and describes in detail how the basic stochastic knap-sack was modified to provide a traffic model that captures the peculiarities of UMTStraffic.

1. IntroductionDimensioning of the radio access network for

W-CDMA (Wideband Code Division Multiple Ac-cess) is a very important but complex task. Thepurpose of dimensioning is to estimate the amountof hardware or resources required to provide asatisfactory grade of service (GoS) to users. It isimportant because it is the initial step consideredin network implementation; consequently, radiodimensioning will impact the network significant-ly. Its complexity arises from the fact that thecell edge in a CDMA environment is continuouslymoving. A CDMA cell radius varies with changesin the amount of interference in that area. Thesechanges occur due to traffic variations; for exam-ple, the cell radius for 10 users using a videoservice will not be the same as the cell radius for

10 voice users. Similarly, for a 2G CDMA system,the cell radius for 10 voice users will not be thesame as the cell radius for 30 voice users. Thischaracteristic is known as Cell Shrinking.

W-CDMA faces a new challenge compared toIS95note 1) due to its support for multiple data ratesand switching modes. This feature further com-plicates the estimation and prediction ofinterference levels and therefore the position ofthe cell edge.

Having said that, the similarity betweenW-CDMA and CDMA is still significant andFujitsu is very well positioned to utilize its exten-sive experience in CDMA-one system design andoptimization to improve the approach to W-CDMA

note 1) A 2G CDMA standard

184 FUJITSU Sci. Tech. J., 38,2,(December 2002)

M. Jaber et al.: Modified Stochastic Knapsack for UMTS Capacity Analysis

network design.This paper briefly discusses the entire dimen-

sioning process with an emphasis on capacityanalysis with the new traffic model.

2. Radio dimensioningThe objective behind the analytical dimen-

sioning process is to simplify the complex task ofdimensioning by making some assumptions andapproximations. The amount and accuracy ofthese hypotheses impact on the reliability one canexpect from this process. The major approxima-tion is obtained by considering a flat andhomogeneous landscape. That is to say, the tar-get area is divided into different morphologyclasses, or clutter types, which are considered sep-arately on the assumption that each clutter formsan exclusive homogeneous area. This assumptionresults in identical sites per clutter, which maybe considered prototype sites in the planningstage. The flow chart in Figure 1 describes theanalytical radio dimensioning procedure.

2.1 Traffic modelling with binomialapproachTraffic models like Erlang-B, Erlang-C, etc.,

are established models which can model single-service, circuit-switched traffic quite accurately.However, there are no established ways for mod-elling multi-service traffic in UMTS. In the earlystages of developing a dimensioning procedure forW-CDMA, it was considered that the traffic gen-eration probability conforms to a binomialdistribution for both packet-switched and circuit-switched services. This lead to the use of theBinomial model for air interface dimensioning.

However, the Binomial model could not dif-ferentiate between packet switched and circuitswitched services. Furthermore, it only consid-ered an aggregate GoS; that is, it did notguarantee a certain GoS per service type. Forinstance, securing a 2% aggregate GoS wouldprobably result in a higher GoS for data servicesand an equal or lower GoS for voice services. An-

other issue with the binomial approach is that theprobability of success or failure is always thesame, regardless of the current load of the sys-tem.

The binomial approach was considered pes-simistic and therefore a safe approximation fortraffic modelling. However, through a detailedcomparison of the Binomial and Knapsack mod-els, we found that this assumption was not alwaystrue.

The binomial distribution is a discrete dis-tribution (Figure 2). It gives the likelihood offinding x failures (or dropped or blocked calls) asopposed to success (or admitted calls). The find-ings are the results of n experiments (or callattempts). The binomial formula that representsthe probability of k successes (admitted calls) inN experiments (call attempts) is:

Pr (k, N) = N !(N - k)! k ! (1 - p)N - k

pk (1)

Subscriberdata

Designrequirements

Designfeatures

Propagationprofile

uplink

Channel capacity analysis Cell coverage analysisUplink link budgetAssume a

cell load aMax cell range

Max site area

Captured subscribersResulting

cell load b

b; aIf b> a increase a

decrease ano

yes

yes

yesDecrease UE Tx

no

no

If b< a

If DL> Max DL

TUNED uplink cell range

Downlink coverage andcapacity analysis

TUNED uplink and downlink cell range

downlink

1

2

3

4

5

Figure 1Analytical dimensioning.

185FUJITSU Sci. Tech. J., 38,2,(December 2002)


Consider an experiment in which a coin isflipped n times. Each trial has two possible out-comes, heads or tails, and these outcomes arecoded as 1 and 0, respectively. The trials are in-dependent. The probability of heads p is constantfrom one trial to another. For example, when acoin is flipped 12 times, n is 12 and p is 0.5.

The black vertical lines in Figure 2 representthe discrete binomial output. The y-axis representsthe probability of each outcome. As expected, get-ting 6 heads is the most likely outcome of 12 flips.The trend (bell-shaped) line represents the nor-mal distribution (continuous distribution), whichis often used to approximate the discrete binomial.

Example: Simplified UMTS traffic1) Two services are equally used: voice at

12.2 kb/s and circuit-switched data at 64 kb/s.2) The traffic load for voice is 30 mErl per user.3) The traffic load for data is 3 mErl per user.4) The pole capacitynote 2) is 40 voice users, which

represents the peak number of voice users.5) The required GoS-blocking rate is 2%.

In this application, the binomial distributionis approximated to a normal distribution. First,the inverse of the standard normal cumulative dis-tribution (mean = 0, standard deviation = 1) isderived for a probability of 98%. This gives a val-ue of 2.054, and the following formula applies:

Peak traffic = mean traffic + 2.054 (2)

Where:Peak traffic = pole capacity = 40Mean traffic = N 0.03 + N (64/12.2) 0.003 =0.0457 N

In the above equation, it is assumed that adata user consumes 64/12.2 resources, whereas avoice user consumes 1 resource. N is the numberof attempts, and s is the standard deviation forblocked/admitted calls on the assumption thatthere are equal numbers of voice and data at-tempts.2 = N 0.03 (1 - 0.03) + (64/12.2)2 N 0.003 (1 - 0.003) = 0.1114 NPeak traffic can be rewritten as:

Peak traffic = 0.0457N + 2.054 0.1114 N (3)

Solving for N gives the following results:N = 530 attemptsMean traffic = 24

This implies that one W-CDMA carrier witha pole capacity of 40 is dimensioned for 744 sub-scribers at an aggregate blocking probability of2%.

This method may be acceptable in some cas-es where all services are circuit switched and aglobal grade of service is sufficient to estimate theperformance of the system. Unfortunately, thisis not the case for UMTS air interface traffic, andconsequently an improvement to this approach isneeded.

2.2 Stochastic knapsackStochastic models are popular in ATM (Asyn-

chronous Transfer Mode) and other packet switchtraffic analysis. The model considers a fixed re-source and simulates the respective GoS of thevarious supported services. Due to its fixed ca-pacity feature, the knapsack is not valid forUTRAN capacity calculation in its original form.We therefore modified the basic stochastic knap-sack model so that it can capture the peculiaritiesof the UTRAN air interface by allowing flexibleresource availability and variable data rates.

Our study not only proved that the Knap-

note 2) The pole capacity is the maximum capacityof a UMTS cell (capacity is limited by theamount of interference).

Figure 2Binomial distribution curve.

0.2

0.1

10 2 43 76 8 109 11 125



or a fixed-capacity link). This is not the case withthe UMTS air interface, because there is no clearconcept of resource unit. If we try to apply theKnapsack concept to 2G systems, then it is easyto assume that the maximum allowed number ofusers is the peak capacity; hence, the resource unitis an active user. In this scenario, the stochasticknapsack capacity C would be equal to say 7(1 GSM carrier supports 8 timeslots: 1 time slotis reserved for control and the other 7 are usedfor user data) and the object size bk would be equalto 1. Alternatively, the knapsack size could beequal to the maximum throughput per carrier(spectrum efficiency) and bk could be equal to thedata rate.

Both applications are possible to implementbecause only one type of traffic is considered. How-ever, for UMTS it is not a straightforwardapplication for two reasons. Firstly, the maximumcapacity of one carrier (pole capacity) is not a fixed

sack model allows for a more realistic represen-tation of the actual traffic behaviour, but it alsoshowed some hidden flaws in the previous bino-mial approach. For instance, the binomialapproach has an uncontrollable Max GoS and, de-spite its reputation as a safe approach, it canresult in under-dimensioning.

The original Knapsack model is similar to Er-lang-B,note 3) except that the objects handled by thenetwork can be grouped into K different classes.In class k, each object has a size of bk, an arrivalrate of k, and a mean call duration of k. Thesize of each object is the amount of network re-source it occupies, (i.e., the data rate of theconnection: 12.2 kb/s, 384 kb/s, etc.).1)

The stochastic knapsack has a fixed capaci-ty C. A call is blocked if the knapsack does nothave enough free capacity to take the call, asshown in Figure 3.

The model gives us the following equation.2)

PB, k = 1 -

K

j=1set Sk / nj !nj

j

K

j=1set S / nj !nj

j

(4)

Where: PB,k is the probability of blocking an object in

class k. Sk is the set of states that can accommodate

an object from class k. S is the set of all the knapsack states. j (j/j) is the network load from class j. nj is the number of objects in the knapsack

from class j.

2.3 Fujitsu knapsack model and uplink(UL)note 4) capacity analysisThe basic stochastic knapsack cannot be ap-

plied directly for UMTS air traffic modelling. Asexplained in the previous section, the Knapsackmodel is based on a fixed resource (e.g., a buffer

note 3) This is a famous traffic model for circuitswitched traffic.

note 4) Radio link when the mobile is transmittingand the base station is receiving.

K classes ofobject size =bk for class k

Callarrivalrate = k

Blockedcalls

Call completion

Stochastic KnapsackCapacity C

Mean call duration=1/k

Figure 3Stochastic knapsack.



value; it depends on the traffic mix, the quality ofservice requirements within the cell, and the traf-fic activity in neighbouring cells. Secondly, it isnot obvious how to define the resource unit in thiscase. If the resource unit is equal to one user, isthe user a voice, CS data, or PS data user? If theresource unit is kb/s, then the object size could bethe data rate, in which case, the knapsack sizewould be the maximum throughput per carrier(spectrum efficiency). However, this applicationoverlooks one important factorthe QoS (Quali-ty of Service).

Let us consider a scenario with two servicesat 64 kb/s. Service 1 is for e-mail (QoS is low Eb/Nonote 5) is low [Eb/No is energy per user bit overspectral noise density]).3) Service 2 is for videoconferencing (QoS high Eb/No high). A higherQoS means a lower block error rate, which wouldrequire a higher level of energy per user bit tosecure a lower rate of errors at the receptor. Ahigher Eb/No requirement would necessitate ahigher transmit power from the terminal, whichwould generate a higher level of interference. Thisaspect of multi-services cannot be represented byassuming a resource unit related to the through-put (kb/s).

The only unit that is independent of the ser-vice type and captures the different QoSrequirements is the power level. The modified sto-chastic knapsack represents the power or noiselevel of a given UMTS carrier. The model is tightlyrelated to the pole capacity concept of spread spec-trum systems, which represents the infinite noiselevel at which the system diverges.

2.3.1 UL pole capacityDetermining the pole capacity of a UMTS

carrier (cell) is an important step in capacity anal-ysis. Since the frequency reuse of the W-CDMAsystem is 1, the system is typically interference-limited by the air interface and the amounts ofinterference and delivered cell capacity need to

be estimated. The theoretical spectrum efficien-cy of a W-CDMA cell can be calculated from thepole capacity equation, which refers to the 100%cell load or the soft capacity limit.3) The pole ca-pacity is derived from the definition of Eb/No. Thefinal expression of pole capacity in terms of thenumber of active users is as follows:

Npole =

S

s=1

UL

W

(1 + fUL) UL UL ULps vs Rs

EbNo

EbNo

ULRsW

s

1 +

(5)

Where: Npole is the maximum number of active users

allowed. S is the number of offered services. W is the chip rate. fUL is the average other-cell interference on

the uplink. Vs is the activity factor of service s. Ps is the percentage of active users using ser-

vice s. (Eb/No)s is the required Eb/No for service s

(assuming ideal power control, the Eb/No canbe regarded as constant for all mobiles usingservice k).

Rs is the data rate of service s.A cell load concept is defined which is relat-

ed to the pole capacity as follows:

UL = NumberofActiveUsersPoleCapacity (6)

The cell load represents the amount of traf-fic intensity within a carrier, which directly resultsin what is called the shrinking phenomena inUMTS. In essence, what is happening is that be-cause all users are using the same frequency atthe same time, the other users activity is seen byNode B as interference. This means that a termi-nal needs to transmit at a higher level to overcomethe interference level from other users and allowthe signal to reach Node B with the required QoS.note 5) Energy per bit/noise power density



If we consider a user who is at the cell edge andalready transmitting at maximum power, the us-ers signal will not be stronger than theinterference from other users and will not reachNode B with the required QoS. In this case, theuser is considered to be out of coverage due to cellshrinkage. This tight cause-and-effect relation-ship between the capacity and coverage can berepresented, respectively, by the relationship be-tween the cell load and noise risenote 6) (Figure 4).

2.3.2 Modified stochastic knapsackAs explained in the previous section, it is

necessary to find a cell edge that incorporatesboth the capacity limitation (cell load) and cov-erage limitation (noise rise) at the required GoS.The GoS for circuit-switch services is very wellrepresented by the blocking probability. Forpacket-switch services, blocking is not a perfor-mance measure: indicators such as throughputand delay are more representative of the userssatisfaction. For the capacity analysis, which isthe step that estimates the required cell load toguarantee the required GoS, we have adopted themodified knapsack as explained below: The knapsack capacity C represents the cell

load. C = 0 to 100%.

The object size bk is the interference contri-bution by a user of class k:

bk =W

(1 + fUL) UL ULvs RsEb

No

ULRkW

k1 +

EbNo

k

100 (7)

Where, W is the chip rate. fUL is the other-cell interference on the up-

link. Vk is the activity factor of service k (circuit

switch services would have a very differentvalue than packet switched services).

(Eb/No)k is the required Eb/No for service k(assuming ideal power control, the Eb/No canbe regarded as constant for all mobiles usingservice k).

Rk is the data rate of service k.The GoS for circuit switch services will be

measured as a blocking probability using the fol-lowing formula:

PBk = 1 -

K

j=1nSk nj!

njj

K

j=1nS nj!

njj

(8)

And the GoS for packet switch services willbe expressed in terms of throughput, which rep-resents the long-run throughput per service. Thethroughput is derived by considering the long-runrate at which users of this service enter the airinterface (or Knapsack) and the data rate per userby employing the following formula1):

THk = RK k (1 - PBk) (9)

Where, k is the arrival rate of service k assuming a

Poisson process. PBk is the probability of blocking for service k. Rk is the data rate of service Blocking proba-

bility of service. nj is the number of objects in the knapsack

from class j.note 6) Noise rise over thermal noise due to inter-

ference = -10 log10 (1 - UL).

Figure 4Noise rise versus cell load.

0

5

10

15

20

25

0 20 40Capacity

Interference curve

Noi

se ri

se (d

B)

60 80 100



The UL analysis is an iterative process thatcontinues as we tune between the capacity andcoverage analyses.3) UL coverage analysis refersto calculating the UMTS link budget for the up-link. Like all radio link budgets, the purpose ofthe UMTS link budget is to find the maximumallowed path loss. However, it has one main dif-ference from other radio link budgets in that italso includes the noise rise due to captured sub-scribers. The value of noise rise is not alwaysequal to the noise rise calculated from our load-ing equation, which is why we need to tune thesetwo analyses. Figure 5 shows the tuning proce-dure for the UL.

2.4 Downlink analysisOnce the uplink is tuned (i.e., step 4 in

Figure 1 is reached), the downlink analysis is per-formed. The downlink analysis differs slightlyfrom the uplink analysis in that the coverage andcapacity are considered simultaneously, not iter-atively. The downlink analysis checks whetherthe Node B power allocation is enough to coverthe captured subscribers (from the uplink analy-sis). If the power is not enough, the uplink cellrange needs to be reduced (by reducing the TXpower of UEs) and the whole process is repeatedfrom step 1).

The downlink load factor can be definedbased on a similar principle as the one for the

uplink; however, there are some additional param-eters involved. The DL pole capacity is alsoderived from the definition of Eb/No energy peruser bit over spectral noise density, which can beexpressed as follows for a user j:

(Eb / No) j =

RjvjW Pj

Ctotal

c=2 Iown + Iexternal, c + Nthermal

(10)

Where,P j = Received signal power by user j intended forthat user (watts)Iown = Total received wide-band power from own-cell base station = Orthogonality factor (signals from the cellsthemselves are partially received as interferencedue to imperfect orthogonality)

We can say that the received power is pro-portional to the own-cell transmitted power: Pj =Iown j, where j, which is the ratio of powerallocated to user j, and the total received powercan be calculated as follows:

j = + +(Eb / No)j vj

(W / Rj) IownIother

Iown

Nthermal

(11)

This ratio between other-cell and own-cell in-terference can be written as follows:

fDLj =+

Iown

Nthermal

Iexternal

j(12)

Here, j becomes:j max (13)

The maximum value of j would mean the maxi-mum power that is allowed to be allocated to userj for normal operation.4) There will be an outagewhen j exceeds max. The probability of an out-age for user j can be stated as follows:

Poutagej = Pr (j > max) (14)

The downlink loading is the ratio betweenthe total power that the BS transmits to the max-imum power that it is capable of transmitting:

Figure 5UL tuning.

Tuned uplink

n-cap = n-cov?

-cap

UL load

n-cov

Coveredsubscribers

Coverageanalysis

Capacityanalysis Cell load



Pmax

PtotalDL = (15)

Since j represents the allocation ratio for oneuser, then:

jN

j=1(16)

Where is the percentage of traffic channels and1 - would be the ratio of the common channels.The equation can be rewritten as follows:

/ 1 jN

j=1 (17)

Where N represents the total number of connec-tions, including the connections due to softhandovernote 7):

N = N (1 + SHO) (18)

Where N is the number of active users and SHOis the overhead due to soft handover. The loadingformula can now be written as follows:

(Eb / No)j vjN (1 + SHO)

j=1 (W / Rj)+ fDL j)( / DL = (19)

3. Conclusions and future workIn this paper, we described a UMTS air in-

terface dimensioning procedure. This newlydeveloped model solves many problems which

could not be answered by the previous approach.However, there are still improvements which canbe made to our dimensioning procedure.

Currently, our model is a loss model; that is,we do not incorporate queuing for packets. There-fore, the reader should keep in mind that thisqueuing is different from the one which may bepresent in the core network or the Radio NetworkController. We are referring here to queuing solelyin the air interface. This is an important issue,but the problem is not as big as it may seem. Onthe UL, Node B has no means to make queues forpackets, but it is possible to have a queuing mech-anism for the DL packet traffic.

We are currently studying this possibility andhope to improve our model based on the results.

References1) Keith W. Ross: Multiservice Loss Models for

Broadband Telecommunication Networks.Springer, 1995.

2) J. M. Pitts and J. A. Schormans: Introductionto IP and ATM Design and Performance, JohnWiley & Sons Ltd., 2000.

3) H. Holma and A. Toskala: WCDMA for UMTSRadio Access for Third Generation MobileCommunications. John Wiley & Sons, 2000.

4) Andrew J. Viterbi: CDMA: Principles ofSpread Spectrum Communication (Addison-Wesley Wireless Communications). 1st ed,Prentice Hall PTR, June 1995.

note 7) A state where one mobile terminal is connect-ed to multiple base stations.



Mona Jaber received the B.E. in Com-puter and Communication Engineeringfrom the American University of Beirut,Beirut, Lebanon in 1996. She joinedMSI (Metapath Software International)as a radio consultant in London in 1998and later joined the Fujitsu Europe R&DCenter, UK in 2000 as a Senior Engi-neer. In October 2001, she joined theMobile System division of Fujitsu Lab-oratories of Europe Ltd., UK as a Prin-

cipal Research Engineer. She is in charge of 3G network planningresearch and business support at that division.

E-mail: [email protected]

Syed Ammar Hussain received theB.E. in Telecomunication Engineeringfrom the National University of Scienc-es and Technology, Pakistan in 1999.He started his carrier as a researcherwith the Army Signals Research & De-velopment Establishment (Pakistan).Later he joined Motorola Pakistan. In2001, he joined Logica Mobile NetworksUK as an RF Consultant Engineer.Since 2002, he has been working with

FLE as a Research Engineer for Mobile Systems Development.


Adel Rouz received the Msc & Ph.D. inComputer Science from the Universityof Electro-Communications, Tokyo,Japan in 1991 and 1992, respectively.He joined Fujitsu Ltd., in 1991 and thenjoined the Fujitsu Europe R&D Center,UK in 1996 as a Principal Engineer.Since October 2001, he has been theDirector of the Mobile CommunicationResearch Division in Fujitsu Laborato-ries of Europe Ltd., UK, where he is in

charge of the 3G & Beyond research activities in Europe; OpenMobile Architecture; IP based mobile networks; Radio NetworkPlanning and Terminal Development.


model knapsack untuk umts

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