Uplink Blocking Probability Calculation for Cellular ... - IEEE Xplore

2005 Asia-Pacific Conference on Communications, Perth, Western Australia, 3 - 5 October 2005.

Uplink Blocking Probability Calculation for Cellular Systems with WCDMA Radio Interface, Finite Source Population and Differently Loaded Neighbouring Cells1 Mariusz Głabowski, ˛ Maciej Stasiak, Arkadiusz Wi´sniewski, Piotr Zwierzykowski Institute of Electronics and Telecommunications, Pozna´n University of Technology ul. Piotrowo 3A, 60-965 Pozna´n, Poland Email: (mglabows, stasiak, pzwierz)@et.put.poznan.pl

Abstract— This paper presents the uplink blocking probability calculation method in cellular systems with WCDMA radio interface, finite source population and differently loaded neighbouring cells. The method is based on the model of the full availability group with multi-rate traffic streams. A fixed point methodology has been used in the proposed method. The proposed scheme could be utilized for cost-effective radio resource management in 3G mobile networks and can be easily applied to network capacity calculations.

I. I NTRODUCTION Universal Mobile Telecommunication System (UMTS) using WCDMA radio interface is one of the standards proposed for third generation cellular technologies (3G). According to the ITU recommendations, the 3G systems should include services with circuit switching and packet switching, transmit data with a speed of up to 2 Mbit/s, and ensure access to multimedia services [1]. Due to the possibility of resource allocation for different traffic classes, capacity calculation of WCDMA radio interface is much more complex than in the case of GSM systems. Moreover, all users serviced by a given cell make use of the same frequency channel and the differentiation of the transmitted signals is possible only and exclusively by an applying orthogonal codes [2]. However, due to multipath propagation occurring in a radio channel, not all transmitted signals are orthogonal with respect to one another, and, consequently, are received by users of the system as an interference adversely affecting the capacity of the system. Additionally, the increase in interference is caused by the users serviced by other cells of the system, who make use of the same frequency channel, as well as by the users making use of the adjacent radio channels. To ensure appropriate level of service in UMTS, it is thus necessary to limit interference by decreasing the number of active users or the allocated resources employed to service them. Several papers have been devoted to traffic modelling in cellular systems with WCDMA radio interface. In [3] the number of ongoing calls in a cell was modelled as a Poisson 1 This work was supported by the State Committee for Scientific Research Grant 3 T11D 01528

0-7803-9132-2/05/$20.00 ©2005 IEEE.

random variable and the total interference as a compound Poisson sum, assuming that no call will be blocked. However, such an assumption cannot be fullfiled in a real network. In [4] the total blocking probability in an access cell with infinite source population is calculated with the help of KaufmanRoberts recursion while other cell interference is characterized by a random variable with the lognormal distribution. This paper presents the uplink blocking probability calculation method for a cell with WCDMA radio interface, finite source population and differently loaded neighbouring cells. It is expected that the proposed method, due to taking into account a decreasing number of active sources, can yield more accurate results than the existing models assuming infinite source population. The paper has been divided into five sections. Section II discusses basic dependencies describing radio interface load for the uplink direction. Section III presents an analytical model applied to blocking probability calculations for the uplink direction and finite source population. The following section includes a comparison of the results obtained in the calculation with the simulation data for a system comprising seven cells. The final section sums up the discussion. II. U PLINK LOAD FOR WCDMA RADIO INTERFACE WCDMA radio interface offers enormous possibilities in obtaining large capacities; it imposes however a substantial number of limits as regards the acceptable level of interference in the frequency channel. In every cellular system with spreading spectrum the radio interface capacity is seriously limited due to the occurrence of a few types of interference [5], namely: (1) co-channel interference within a cell – from the concurrent users of a frequency channel within the area of a given cell; (2) outer co-channel interference – from the concurrent users of the frequency channel working within the area of adjacent cells; (3) adjacent channels interference – from the adjacent frequency channels of the same operator or other cellular telecommunication operators; (4) all possible noise and interference coming from other systems and sources, both broadband and narrowband.

138

TABLE I

New call

E XAMPLES OF Eb /N0 , νj AND Lj FOR DIFFERENT SERVICE CLASSES Class of service (j) W [Mchip/s] Rj [kb/s] νj (Eb /N0 )j [db] Lj

Speech

Video call Data 3.84 64 144 1 1 2 1.5 0.0257 0.0503

12.2 0.67 4 0.0053

2 7 L 3 1 6 4 5 L' j

Data

L' j

384 1 1 0.1118

j

'

Lj

`

'

Lj

'

Lj

Access cell

Accurate signal reception is possible only when the relation of energy per bit Eb to noise spectral density N0 is appropriate [6]. Too low value of Eb /N0 will cause the receiver to be unable to decode the received signal, while too high value of the energy per bit in relation to noise will be perceived as interference for other users of the same radio channel. The relation Eb /N0 for a user of the class j connection (service) can be calculated as follows [6]:
 Pj Eb W = Rj , (1) N0 j νj Itotal − Pj where: Pj – signal power received from a user of the class j connection, W – chip rate of spreading signal, vj – activity factor of a user of the class j service, Rj – bit rate of a user of the class j service, Itotal – total received wideband power, including thermal noise power. The mean power of a user of the class j service: Pj = Lj Itotal ,

(2)

where Lj is the load factor for a user of the class j connection:  −1 W . (3) Lj = 1 + Eb Rj νj ( N0 )j Table I shows sample values Eb /N0 for different traffic classes and the matching values of the load factor Lj . Once Lj of a single user has been established, it is possible to determine the total load for the uplink connection: M ηU L = Nj Lj , (4) j=1

where M is the number of traffic classes (services) and Nj is the number of users of the class j service. The above relation is true when we deal with a system that consists of a single cell. In fact, there are many cells available, in which the generated traffic influences the capacity of radio interface of other cells. Thus, (4) should be complemented with an element that would take into consideration the interference coming from other cells. To achieve this, a variable i is introduced, which is defined as other cell interference over proper cell interference. Thus: M Nj Lj . (5) ηU L = (1 + i) j=1

The bigger the load of a radio link, the higher level of the noise generated. The increase in the noise is defined as follows: ∆nr = Itotal /PN = (1 − ηU L )−1 , where PN is the thermal noise.

a11, j

a1, j

L' j

(6)

a)

a33, j

a44, j

a14, j

1

Cell 1

V

1

Cell 2

V

1

Cell 3

V

1

Cell 4

V

a55, j

1

Cell 5

V

a66, j

1

Cell 6

V

a77 , j

1

Cell 7

V

b)

Fig. 1. Cellular system; a) a seven-cell set system; b) a set of full-availability groups as the model of wireless cellular network

When the load of the uplink approaches unity, the matching increase in noise tends towards infinity. Therefore, it is assumed that the actual maximal usage of the resources of a radio interface without lowering the level of the quality of service will amount to about 50 – 80% [5]. III. M ODEL OF THE SYSTEM Before admitting a new connection in the systems with WCDMA radio interface, admission control needs to check whether the admittance will not sacrifice the quality of the existing connections. The admission control functionality is located in RNC (Radio Network Controller) where the load information from the surrounding cells can be obtained. The admission control algorithm estimates the load increase that would be caused in the radio network by the establishment of a new connection [6]. This is done not only in the access cell, but also in the adjacent cells, in order to take the inter-cell interference effect into account. The new call is rejected if the predicted load exceeds particular thresholds set by the radio network planning [5]. A. Basic assumptions Our model consists of seven cells with omni directional antennas (Fig. 1a). We use load factor Lj for a user of the class j connection to estimate whether a new call can be admitted or blocked. We assume that a new call, which generates Lj load in the access cell, will generate part of that value in the

surrounding cells Lj (Lj ≤ Lj ). The problem of estimating
Lj is not the subject of this paper. The measurements or theoretical calculations that might be the subject of further research can estimate these values. In our model, we assume that each call which generates load Lj in access cell will cause
load Lj = Lj /2 in the neighbouring cells (such assumption do not affect the accuracy of the proposed analytical model). In this paper we assume that the full availability group (Fig. 1b) servicing multi-rate traffic streams will approximate a radio interface which services the load generated in the access cell and the load from the neighbouring cells [7]. For Figure 1b the following notation is used: V – the cell capacity, az,j – the mean load offered to the system by users of the class j in the cell z, azh,j – the mean load offered in the cell h by user of class j in the cell z.

139

To determine the blocking probability of a new call appearing in the cell z, it is necessary to take into consideration the load generated by this call in the neighbouring cells. The call can be rejected when the increase in the load, both in the access cell and the neighbouring cells, will exceed acceptable thresholds. Consequently, service processes in the access cell and the adjacent cells are mutually dependent. To solve this problem we apply the Fixed Point Methodology [8]. B. Infinite population of traffic sources Let us consider the full-availability group (FAG) with different multi-rate traffic streams and infinite population of traffic sources. FAG is a discrete link model that uses the complete sharing policy [9]. Let us assume that the system services call demands having an integer number of the so-called BBU’s (Basic Bandwidth Units) [9]. The total capacity of the group is equal to V BBU’s. The assumed BBU in our model is 0.0001 of the load factor (the idea of expressing resources required by a call as the load factor was presented in [4]). The group is offered M independent classes of Poisson traffic streams having the intensities: λ1 , λ2 ,. . .,λM . The class j call requires Lj BBU’s to set up a connection. The holding time for calls of particular classes has an exponential distribution with the parameters: µ1 , µ2 , . . ., µM . Thus the mean traffic offered to the system by the class j traffic stream aj = λj /µj . A multi-dimensional service process occurring in a system with different multi-rate traffic streams can be approximated by the one-dimensional Markov chain. In the fullavailability group model, Markov chain can be described by the Fortet-Grandjean recursion [10] which is generally known as the Kaufman-Roberts recursion [11], [12]: M nP (n) = aj Lj P (n − Lj ), (7) j=1

where P (n) is the state probability in the multi-rate system. The blocking probability b(j) for the class j traffic stream can be written as follows: V P (n). (8) b(j) = n=V −Lj +1

Figure 2a shows a fragment of a diagram of the onedimensional Markov chain for FAG with two call streams (M = 2, L1 = 1, L2 = 2). The yj (n) symbol denotes reverse transition rates of the class j service stream outgoing from state n. These transition rates for the class j stream are equal to the average number of class j calls serviced in state n. From (7) it results that the knowledge of the parameter yj (n) is not required to determine the occupancy distribution in FAG with multi-rate traffic generated by infinite population of traffic sources. However, the value of this parameter in a given state of the group is the basis of the method of the occupancy distribution calculation in the group with finite population of traffic sources. As stated earlier, the yj (n) symbol denotes reverse transition rates of the class j service stream outgoing from state n. This parameter determines – for the class j traffic stream – the average number of class j calls

a)

...

a2L2

a2L2

a1L1 n-1

a1L1 n

L1 y1(n) L2 y2(n)

... n+1

L1y1(n+1 ) ...

... y2(n) = n2(n)

y 1(n) = n1(n)

[(N2 - y 2(n) )α2)]L2

b)

[(N1– y 1(n) )α1)]L1 n

...

n+1

Fig. 2. Fragment of a diagram of the one-dimensional Markov chain in a multi-rate system (M = 2, L1 = 1, L2 = 2); a) infinite source population; b) finite source population

serviced in state n and it can be determined on the basis of the following equation [13]:  aj P (n)/P (n + Lj ) for n + Lj ≤ V , yj (n + Lj ) = 0 for n + Lj > V . (9) C. Finite population of traffic sources Let us consider now a group servicing multi-rate traffic generated by finite population of sources [14]. Let us denote as Nj the number of sources of class j, the calls of which require Lj BBU’s for service. The input traffic stream of class j is built by the superposition of Nj two-state traffic sources which can alternate between the active state ON (the source requires Lj BBU’s) and the inactive state OFF (the source is idle). The class j traffic offered by an idle source is equal to: αj = Λj /µj ,

(10)

where Λj is the mean arrival rate generated by an idle source of class j and 1/µj is the mean holding (service) time of class j calls. In the considered model we have assumed that the holding time for the calls of particular classes has an exponential distribution. Thus, the mean traffic offered to the system by idle sources of class j aj = (Nj − nj )αj ,

(11)

where nj is the number of in-service sources of class j. Interrelation between the offered traffic load and the number of in-service sources of a given class (11) makes the direct application of Kaufman-Roberts (7) to the determination of occupancy distribution in the considered system impossible. In this paper we applied the method proposed in [14], which allows us to make the mean value of traffic offered by class j dependent on the occupancy state (the number of occupied BBU’s) of the group, and, thereby, on the determination of the system with finite population of sources by (7). Let us notice that the reverse transition rate yj (n) of class j determines the average number of class j calls serviced in the state of n busy BBU’s. In the proposed method, it is assumed

140

that the number of in-service nj sources of class j in the state of n BBU’s being busy is approximated by yj (n): nj (n) ≈ yj (n).

(12)

In such approach it is assumed that the average number of given class calls being serviced in a given state of the group with infinite population of traffic sources is approximate to the average number of calls being serviced in the same state in the case of finite source population. Thereby, yj (n) can be determined by (9), where probabilities P (n) are calculated by (7), under the initial assumption that the offered traffic load is not dependent on the number of in-service sources: aj = Nj αj .

(13)

The determined values yj (n) enable to make the mean value of the offered traffic dependent on the occupancy state of the group:
(14) aj (n) = (Nj − yj (n)) αj . Eventually, the occupancy distribution in FAG with multirate traffic and finite population of sources can be calculated as follows: M


aj (n − Lj )Lj P (n − Lj ). (15) nP (n) = j=1

D. Blocking probability in WCDMA radio interface In the proposed model, it is assumed that a new call is rejected when the increase in the load, both in the access cell and the neighbouring cells, will exceed acceptable thresholds. This means that service processes for a new call, occurring in the access cell and the adjacent cells, are mutually dependent. Therefore, the blocking probability Bzz,j of the class j call occurring in the access cell z also depends on the blocking probability Bzh,j of those calls in the adjacent cells (h). The blocking probability of a class j call coming from the cell z in the cell h (h = z) can be expressed by the following function:   (ahh,1 , Lhh,1 ), . . . , (ahh,M , Lhh,M )

Bzh,j = f . (16) (azh,1 , Lzh,1 ), . . . , (azh,M , Lzh,M ) Thus, the blocking probability of the class j traffic streams coming from the cell z, in the cell h depends on "internal" traffic streams – generated in the cell h (i.e. the traffic streams ahh,j ) and on the contributing traffic streams from the cell z. For better clarity, it is assumed that the radio interface load of each cell h (h = z) is constant. This assumption makes it possible to express the probability Bzh,j as only dependent on the traffic streams which influence the call h from the access cell z. Therefore, we obtain:



(17) Bzh,j = f (azh,1 , Lzh,1 ), . . . , (azh,M , Lzh,M ) . The probabilities Bzh,j can be determined on the basis of FAG servicing a mixture of multi-rate traffic streams, both for finite and infinite traffic sources. To determine the value azh,j , we used the Fixed Point Methodology [8], [15] (cf. [16]). According to the method, a given cell can be offered such a traffic which is not blocked in the neighbouring cells. This

phenomenon leads to a decrease in the value of real traffic offered to a given cell and is called thinning effect [8]. The class j traffic stream (decreased by the thinning effect), which is offered to the cell h by the calls occurring in the access cell z, has been named effective traffic and can be calculated as follows: u (18) azh,j = az,j h=1 (1 − Bzh,j ), h
=r

where az,j is the real traffic of class j, offered to the system by the users from the cell z. Let us notice that to determine the value of the effective traffic azh,j , it is indispensable to know the blocking probability Bzh,j of the traffic of the same class in the neighbouring cells. Therefore, the iterative method should be used. The known values of blocking probability Bzh,j of class j calls in the cell h, coming from cell z make it possible to determine the total blocking probability Bz,j in the access cell z: u (1 − Bzh,j ). (19) Bz,j = 1 − h=1

In case of differently loaded surrounding cells, to calculate blocking probability, we can take into account only the neighbouring cell with the highest blocking probability. Such assumption is justified by the way in which the admission control works. A new call is rejected if the load in at least one cell would increase over particular threshold. In our model each call causes the same load in the neighbouring cells. With this assumption in mind, we can conclude the blocking of a connection from the access cell z can only occur in the most overloaded adjacent cell h. Then, to calculate the blocking probability we have to consider only two cells: the most loaded cell and the access cell. Thus, the uplink blocking probability can be expressed in the following form (based on (19)): Bz,j = 1 − (1 − Bzz,j )(1 − Bzh,j )

(20)

where h (h = z) is the most loaded neighbouring cell. IV. N UMERICAL RESULTS AND SIMULATIONS In order to confirm the proposed method of blocking probability calculation in a cell with WCDMA radio interface, finite source population and differently loaded neighbouring cells, the results of analytical calculations have been compared with the results of simulation experiments. The study has been carried out for users demanding a set of services (Table I). It was assumed that the services are demanded in equal proportions. The maximum uplink load ηU L was set to 80%. The capacity V of each cell was equal to 8000 BBU’s. The load in the neighbouring cells was equal to 28%, 35%, 42%, 45%, 48% and 50% of maximum uplink load, respectively. Figure 3 shows the mean blocking probability of a new call as a function of the mean load for infinite number of sources. Figures 4 and 5 present blocking probabilities for a system with finite number of sources. All the presented results show the robustness of the proposed method of blocking probability calculation. In each case, regardless of the offered traffic load and the number of traffic sources, the results are characterised by fair accuracy.

141

V. C ONCLUSIONS

blocking probability

1,E+00

1,E-01

1,E-02

1,E-03

1,E-04 35%

50%

65%

80% 95% 110% 125% 140% 155% traffic load

Fig. 3. Blocking probability in the access cell for infinite number of sources. The load of neighbouring cells equals 28%, 35%, 42%, 45%, 48% and 50%. Calculations: —— speech; – – – video. Simulations:
speech;
video. 1,E+00

R EFERENCES

blocking probability

1,E-01

1,E-02

1,E-03

1,E-04

1,E-05 35%

50%

65%

80% 95% 110% 125% 140% 155% traffic load

Fig. 4. Blocking probability in the access cell for finite number of sources. The number of sources for both classes equals 400 (200/200). The load of neighbouring cells equals 28%, 35%, 42%, 45%, 48% and 50%. Calculations: —— speech; – – – video. Simulations:
speech;
video.

blocking probability

1,E+00

1,E-01

1,E-02

1,E-03 35%

The admission control in wireless networks with WCDMA radio interface admits or blocks new calls, depending on the current load situation both in an access cell and in neighboring cells. A new call is rejected if the predicted load exceeds particular thresholds set by the radio network planning. In this paper, we present an uplink blocking probability calculation method for cellular systems with WCDMA radio interface, finite number of traffic sources, and differently loaded neighbouring cells. In our model, we use load factor Lj to estimate whether a new call of class j service can be admitted or blocked. The obtained results show that taking into account the decreasing number of active sources in the system yields lower blocking probability. This can be essential for services which demand higher capacity. The calculations are validated by a simulation. The proposed method can be easily applied to 3G network capacity calculations.

50%

65%

80% 95% 110% 125% 140% 155% traffic load

Fig. 5. Blocking probability in the access cell for finite number of sources. The number of sources for particular classes equals 400 (100/100/100/100). The load of neighbouring cells equals 28%, 35%, 42%, 45%, 48% and 50%. Calculations: —— speech; – – – video; - - - data 144kb/s; – - - data 384kb/s. Simulations:
speech;
video; ◦ data 144kb/s; + data 384kb/s.

[1] K. Wesołowski, Mobile Communication Systems, John Wiley and Sons, 1st edition, 2002. [2] S. Faruque, Cellular Mobile Systems Engineering, Artech House, 1996. [3] A.M. Viterbi and A.J. Viterbi, “Erlang capacity of a power controlled CDMA system.,” IEEE Journal on Selected Areas in Communications, vol. 11, no. 6, pp. 892–900, 1993. [4] D. Staehle and A. Mäder, “An analytic approximation of the uplink capacity in a UMTS network with heterogeneous traffic,” in 18th International Teletraffic Congress (ITC18), Berlin, 2003, pp. 81–91. [5] J. Laiho, A. Wacker, and T. Novosad, Radio Network Planning and Optimization for UMTS, John Wiley & Sons, Ltd., 2002. [6] H. Holma and A. Toskala, WCDMA for UMTS. Radio Access For Third Generation Mobile Communications, John Wiley & Sons, Ltd., 2000. [7] M. Stasiak, A. Wi´sniewski, and P. Zwierzykowski, “Blocking probability calculation in the uplink direction for cellular systems with WCDMA radio interface,” in Proceedings of 3rd Polish-German Teletraffic Symposium, P. Buchholtz, R. Lehnert, and M. Pioro, Eds., Dresden, Germany, Sept. 2004, pp. 65–74, VDE Verlag GMBH, Berlin, Offenbach. [8] F. Kelly. Loss networks. The Annals of Applied Probability, 1(3):319– 378, 1991. [9] J.W. Roberts, V. Mocci, and I. Virtamo, Eds., Broadband Network Teletraffic, Final Report of Action COST 242, Commission of the European Communities, Springer Verlag, Berlin, Germany, 1996. [10] R. Fortet and C. Grandjean, “Congestion in a loss system when some calls want several devices simultaneously,” Electrical Communications, vol. 39, no. 4, pp. 513–526, 1964. [11] J.S. Kaufman, “Blocking in a shared resource environment,” IEEE Transactions on Communications, vol. 29, no. 10, pp. 1474–1481, 1981. [12] J.W. Roberts, “A service system with heterogeneous user requirements — application to multi-service telecommunications systems,” in Proceedings of Performance of Data Communications Systems and their Applications, G. Pujolle, Ed., Amsterdam, Holland, 1981, pp. 423–431, North Holland. [13] M. Stasiak and M. Głabowski, ˛ “A simple approximation of the link model with reservation by a one-dimensional Markov chain,” Journal of Performance Evaluation, vol. 41, no. 2–3, pp. 195–208, July 2000. [14] M. Głabowski ˛ and M. Stasiak, “An approximate model of the fullavailability group with multi-rate traffic and a finite source population,” in Proceedings of 3rd Polish-German Teletraffic Symposium, P. Buchholtz, R. Lehnert, and M. Pioro, Eds., Dresden, Germany, Sept. 2004, pp. 195–204, VDE Verlag GMBH, Berlin, Offenbach. [15] M. Pióro, J. Lubacz, and U. Korner, “Traffic engineering problems in multiservice circuit switched networks,” Computer Networks and ISDN Systems, vol. 20, pp. 127–136, 1990. [16] M. Stasiak and P. Zwierzykowski, “Analytical model of ATM node with multicast switching,” in Proceedings of 9th Mediterranean Electrotechnical Conference, Tel-Aviv, Israel, May 1998, vol. 2, pp. 683–687.

142