Uplink blocking probability calculation for cellular systems with WCDMA radio interface and finite source population

Transcription

1 Uplin blocing probability calculation for cellular systes with WCDMA radio interface and finite source population Mariusz Głąbowsi *, Macie Stasia *, Aradiusz Wiśniewsi and Piotr Zwierzyowsi * * Institute of Electronics and Telecounications, Poznań University of Technology, ul. Piotrowo 3a, Poznań, Poland, e-ail: stasia@et.put.poznan.pl PTK Centertel, ul Góreca 30, Poznań, Poland Abstract The paper presents and describes the uplin blocing probability calculation ethod in cellular systes with WCDMA radio interface and finite source population. The ethod is based on the odel of the full availability group with ulti-rate traffic streas. The proposed ethod can be easily applied to 3G networ capacity calculations during planning stages of its design.. Introduction Universal Mobile Telecounication Syste (UMTS) that uses WCDMA radio interface is one of the standards proposed for third generation cellular technologies (3G). The standard has been adopted in Europe and soe Asian countries. According to the ITU recoendations, the 3G syste should include services with circuit switching and pacet switching, transit data with the speed of up to 2 Mbit/s, and ensure access to ultiedia services [Weso 02]. In the GSM syste, the axial nuber of subscribers serviced by one cell was unequivocally defined and depended on the nuber of used frequency channels. Because the GSM syste was assued to perfor voice services only, all calculations of the networ capacity could be done on the basis of the nown dependencies wored out by Erlang. Capacity calculations of WCDMA radio interface, due to the possibility of resource allocation for different classes of traffic, is uch ore coplex. Moreover, all users serviced by a given cell ae use of the sae frequency channel and a differentiation of the transitted signals is possible only and exclusively by an application of orthogonal codes [Faru 96]. However, due to ultipath propagation occurring in a radio channel, not all transitted signals are orthogonal with respect to one another, and, consequently, are received by users of the syste as interference adversely and considerably affecting the capacity of the syste. Additionally, the increase in interference also arises fro the users serviced by other cells of the syste that ae use of the sae frequency channel as well as by the users aing use of the adacent radio channels. To ensure appropriate level of service of the UMTS networ it is thus necessary to liit interference by decreasing the nuber of active users or the allocated resources eployed to service the. It is estiated that the axial usage of resources of radio interface without decreasing the level of service will be at 50 80% [Hol 00]. This paper presents the uplin blocing probability calculation ethod for cellular systes with WCDMA radio interface and finite source population. To achieve this, the Kaufan-Roberts recursion used for the calculation of blocing probability for a full-availability group has been adopted and appropriately odified. It is expected that the presented ethod, due to taing into account decreasing nuber of sources, can yield ore accurate results than traditional Erlang approach. The paper has been divided into five sections. Section 2 discusses basic dependencies describing radio interface load for the uplin direction. Section 3 presents an analytical odel applied to blocing probability calculations for the uplin direction and finite source population. The following section includes a coparison of the results obtained in the calculation with the siulation data for a syste coprising seven cells. The final section sus up the discussion. P80/

2 2. Uplin load factor for WCDMA radio interface WCDMA radio interface offers enorous possibilities in obtaining large capacities, however, iposes any liits as regards the acceptable level of interference in the frequency channel. In every cellular syste with spreading spectru the radio interface capacity is drastically liited due to the occurrence of a few types of interference [Laih 02], naely: co-channel interference within a cell coing fro the concurrent users of a frequency channel within the area of a given cell, outer co-channel interference fro the concurrent users of the frequency channel woring within the area of adacent cells, adacent channels interference fro the adacent frequency channels of the sae operator or other cellular telecounication operators, all possible noise and interference coing fro other systes and sources, both broadband and narrowband. Accurate signal reception is possible only when the relation of energy per bit E b to noise spectral density N 0 is appropriate [Hol 00]. A too low value of E b / N 0 will cause the receiver to be unable to decode the received signal, while a too high value of the energy per bit in relation to noise will be perceived as interference for other users of the sae radio channel. The relation E b / N 0 for the -th user can be calculated as follows [Hol 00]: E b N 0 W = ν R I total P P, () in which the following notation has been adopted: P received signal power fro the user, W chip rate of spreading signal, v activity factor of the user, R bit rate of the user, I total total received wideband power including theral noise power. The ean power of the -user can be deterined with the help of the equation (2): I W + E b R N ν 0 total P = = L Itotal, (2) where L is the load factor for the user of class connection. L =. (3) W + R ν E b N 0 Table shows saple values E b /N 0 for different traffic classes and the atching values of the loadfactor L. Once the load factor of a single user has been established, it is possible to deterine the total load for the uplin connection: where, N is the nuber of users. N η UL = L, (4) = P80/2

3 Table. Exaples of E b /N 0 and v for different traffic classes and the atching load factor L Type of service () Speech Video call Data Data W [Mchip/s] 3.84 R [b/s] V 0.67 (E b /N 0 ) [db] L The above relation is true only when we deal with a syste that consists of a single cell. In fact, however, there are any cells available, in which the generated traffic influences the capacity of radio interface of other cells. Thus, the relation (4) should be copleented with an eleent that would tae into consideration interference coing fro other cells [Hol 00]. To achieve this, a variable i is introduced, which is defined as other cell interference over own cell interference. The total load for the uplin can thus be rewritten as: = ( + ) N UL i L = η. (5) The bigger the load of a radio lin, the higher level of the noise generated in the syste. The increase in the noise nr is defined as the relation of the total noise received in the syste to the theral noise and is described by the following equation: I total nr =, (6) PN ηul = where P N is the theral noise. When the load of the uplin approaches unity, the atching increase in noise tends towards infinity. Therefore, it is assued that the actual axial usage of the resources of a radio interface without lowering the level of the quality of service will aount to about 50 80% [Laih 02]. 3. Model of the syste Before aditting a new connection in the systes with WCDMA radio interface, adission control needs to chec whether the adittance will not sacrifice the quality of the existing connections. The adission control functionality is located in RNC (Radio Networ Controller) where the load inforation fro the surrounding cells can be obtained. The adission control algorith estiates the load increase that the establishent of a new call would cause in the radio networ [Hol 00]. This is done not only in the access cell, but also in the adacent cells to tae the inter-cell interference effect into account. The new call is reected if the predicted load exceeds particular thresholds set by the radio networ planning either in uplin or downlin [Laih 02]. 3.. Basic assuptions Our odel consists of seven cells with oni directional antennas, as it is shown in Figure. We apply load factor L for the user of class connection to estiate whether a new call can be aditted or bloced. We assue, for exaple, that the new call, which generates L load in the access cell, will generate part of that value in the surrounding cells (L L ). The proble of estiating L is not the subect of this paper. The easureents or theoretical calculations that ight be the subect of further research can estiate P80/3

4 these values. In our odel we assue that each call which generates load L in access cell will cause load L = L /2 in the neighbouring cells. new call L 7 6 L L L 2 L 5 L L 3 4 Figure. A seven-cell set odel of wireless cellular networ We assue that the odel of full availability group servicing a ixture of the ulti-rate traffic streas will approxiate a radio interface which services the load generated in that cell and the load fro the neighbouring cells (Figure 2) [Stas 04]. 7 6 access cell a,i a 33,i a 44,i a 55,i a 66,i a 77,i a,i a 4,i cell V cell 2 V cell 3 V cell 4 V cell 5 V cell 6 V cell 7 V Figure 2. A set of full availability groups as the odel of a wireless networ For Figure 2 the following notation is used: V - is the cell capacity, a zz, - is the ean traffic of class offered to the syste by the users in the cell z and a zr, - is the ean traffic of class offered in the cell r by the users of the cell z. To deterine the blocing probability of a new call appearing in the z-cell, it is necessary to tae into consideration the load generated by the call in the neighbouring cells. Therefore we propose a new analytical odel, which can be used for the calculation of uplin blocing probability in UMTS networ. In the odel, we have used the idea of the odel of the switching node servicing a ixture of ulti-rate unicast and ulticast traffic streas presented in [Stas 98] Analytical odel Full-availability group with infinite population of traffic sources Let us consider the full-availability group with different ulti-rate traffic streas. The fullavailability group is a discrete lin odel that uses coplete sharing policy [Cost 96]. This syste is an exaple of a state-independent syste in which the passage between two adacent states of the process associated with a given class strea does not depend on the nuber of busy bandwidth units in the syste. Let us assue that the syste services call deands having an integer nuber of the so-called BBU s (Basic P80/4

5 Bandwidth Units) [Cost 96]. The total capacity of the group is equal to V BBU s. The assued BBU in our odel is, for exaple, of load factor (The idea of deanding resources by a call as the load factor was presented [Stae 03]). The group is offered independent classes of Poisson traffic streas having the intensities: λ, λ 2,..., λ. The class call requires L BBU to set up a connection (we assue that L corresponds to the load L generated by the user of -class connection). The holding tie for calls of particular classes has an exponential distribution with the paraeters: µ, µ 2,..., µ. Thus the ean traffic offered to the syste by the class traffic strea is equal to: λ a =. (7) µ A ulti-diensional service process occurring in a syste with different ulti-rate traffic streas can be approxiated by the one-diensional Marov chain characterised by a product for solution. In the fullavailability group odel, Marov chain can be described by the Fortet-Grandean recursion [Fort 64] which is generally nown as the Kaufan-Roberts recursion [Kauf 8], [Robe 8]: ( n P( n) = a L P n L ), (8) = where P(n) is the state probability in the ulti-rate syste. a 2 L 2 a 2 L 2 n- a L a L a L L y (n) n n+ L y (n+) n+2 L y (n+2) L 2 y 2 (n+) L 2 y 2 (n+2) Figure 3. Fragent of a diagra of the one-diensional Marov chain in a ulti-rate syste (=2, L =, L 2 =2) The blocing probability b for the class traffic strea can be written as follows: V b = P( n). (9) n= V L + The diagra presented in Figure 3 can be characterised by the Kaufan-Roberts recursion for the syste with two call streas (=2, L =, L 2 =2). The y (n) sybol denotes reverse transition rates of a class service strea outgoing fro state n. These transition rates for a class strea are equal to the average nuber of class calls serviced in state n. Fro the equation (8) it results that the nowledge of the paraeter y (n) is not required for the deterination of the occupancy distribution in the full-availability group with ulti-rate traffic generated by infinite population of traffic sources. However, the value of this paraeter in the given state of the group is the basis of the proposed ethod of the occupancy distribution calculation in the group with finite population of traffic sources. Accordingly, let us consider a part of the one-diensional Marov chain diagra constructed for a syste with ulti-rate traffic (Figure 3). As stated earlier, the y (n) sybol denotes reverse transition rates of a class service strea outgoing fro state n. This paraeter deterines for class traffic strea the average nuber of class calls serviced in state n and can be deterined on the basis of the following reasoning [Stas 00]. Each state of the one-diensional Marov chain in the ulti-rate syste (Figure 3) satisfies the following state equation: P80/5

6 P( n) a L + = = L y ( n) = a L P( n L ) + = = L y ( n + L ). (0) Fro the equation (8) it results that the su of service streas outgoing fro state n towards the lower states (states with lower nuber of busy BBUs) expressed in BBUs, is equal to n: n = L y ( n). () = According to the forulae (8) and (), the equation (0) can be expressed as follows: a L P( n) = L y ( n + L ) P( n + L ). (2) = = Expression (2) is the equation of statistical equilibriu between the total strea outgoing fro state n towards higher states and the total service strea entering state n fro higher states. This equation holds only when local balance equations for call streas of individual traffic classes are satisfied: a L P n) = L y ( n + L ) P( n + L ). (3) ( Based upon the equation (3), the reverse transition rate for class calls in (n+l ) state is equal to: a P( n) / P( n + L ) for n + L V y ( n + L ) =. (4) 0 for n + L > V Forula (4) deterines the average nuber of class calls serviced in the state n+l Full-availability group with finite population of traffic sources Let us consider now the group servicing ulti-rate traffic generated by finite population of sources [Glab 04]. Let us denote as N the nuber of sources of class whose calls require L for service. The input traffic strea of class is build by the superposition of N two-state traffic sources which can alternate between the active state ON (the source requires L ) and the inactive state OFF (the source is idle). The class traffic offered by idle source is equal to: α = Λ /, (5) µ where Λ is the ean arrival rate generated by an idle source of class and /µ is the ean holding (service) tie of class calls. In the considered odel we have assued that the holding tie for the calls of particular classes has an exponential distribution. Thus, the ean traffic offered to the syste by the idle class traffic sources is equal to: a = ( N n ) α, (6) where n is the nuber of active (in-service) sources of class. Interrelation between the offered traffic load and the nuber of in-service sources of a given class (eq. 6) aes the direct application of the Kaufan-Roberts recursion (8) for deterination of occupancy distribution in the considered syste ipossible. The paper [Glab 04] proposes a new approxiate ethod which enables us to ae the ean value of traffic offered by class dependent on the occupancy state (the nuber of occupied BBUs) of the group, and thereby deterination of the syste with finite population of sources by the Kaufan-Roberts recursion. Let us notice that reverse transition rate y (n) of class deterines the average nuber of class calls serviced in the state of n busy BBUs. In the proposed ethod, it is assued that the nuber of inservice n sources of class in the state of n BBUs being busy is approxiated by the paraeter y (n), i.e. P80/6

7 n ( n) y ( n). (7) Such an approach assues that the average nuber of the given class calls being serviced in a given state of the group with infinite population of traffic sources is approxiate to the average nuber of calls being serviced in the sae state in the case of finite source population. Thereby, the paraeter y (n) can be deterined by the equation (4), where probabilities P(n) are calculated by the Kaufan-Roberts recursion, under initial assuption that the offered traffic load is not dependent on the nuber of in-service sources and is equal to: a = N α. (8) The deterined values y (n) enables us to depend the ean value of the offered traffic on the occupancy state of the group in the following anner: ( N y ( n) ) α a ( n) =, (9) Eventually, the approxiated recurrent equation which deterines the occupancy distribution in the full-availability group with ulti-rate traffic and a finite population of sources can be calculated by the forula: np ( n) = a ( n L ) L P ( n L ). (20) = I the proposed odel, it is assued that a new call is reected when the increase in the load, both in the access cell and the neighbouring cells, will exceed acceptable thresholds. This eans that servicing process for a new call occurring in the access cell and the adacent cells, are utually dependent. Therefore, the blocing probability B zz, of the class call occurring in the access cell z also depends on the blocing probability B zh, of those calls in the adacent cells (h). The blocing probability of class call coing fro the cell z in the cell h ( h z ) can be expressed in the following function: B = f ( a, L ),...,( a, L ), K,( a, L ),...,( a, L )). (2) zh, hh, hh, hh, hh, zh, zh, zh, zh, Thus, the blocing probability of the class traffic streas coing fro the z cell, in the h cell depends on internal traffic streas generated in the cell h, i.e. the traffic streas a hh, and on the contributing traffic streas fro the cell z. For better clarity, it is assued the radio interface load of each cell h ( h z ) is constant (i.e. 25 percent). This assuption aes it possible to express the probability B zh, as only dependable on the traffic streas which influence the call h fro the access cell z. Therefore we obtain: { B = f ( a, L ),...,( a, L ), (22) zh, zh, zh, zh, zh, The probabilities B zh, can be deterined on the basis of the full-availability group servicing a ixture of ulti-rate traffic streas (eq. 8 and 9). To deterine the value a zh, influencing the load of cell h by the load generated in access cell z (for class calls), we used the Fixed Point Methodology [Kell 89], [Stas 98]. According to the ethod, a given cell can be offered such a traffic which is not bloced in the neighbouring cells. This phenoenon leads to a decrease in the value of real traffic offered to a given cell and is called the thinning effect [Kell 89]. The class traffic strea decreased by thinning effect which is offered to the cell h by the calls occurring in the access cell z has been naed effective traffic. The traffic can be deterined on the basis of the following equation: u ( zh, = az, r = h r ) } a B, (23) where a z, is the real traffic class offered to the syste by the users for the cell z and u is the nuber of cells in the considered syste. zr, P80/7

8 Let us noticed that to deterine the value of the effective traffic a zh, of class it is indispensable to now the blocing probability B zh, of the traffic of the sae class in the neighbouring cells. Therefore, the iterative ethod is used to deterine the values a zh,. The nown values of the blocing probability B zh, of class in the cell h coing fro cell z ae it possible to deterine the total blocing probability B z, of calls in the access cell z: ( B = u ). (24) z, B zh, h= 4. Nuerical results and siulations In order to confir the proposed calculation ethod of uplin blocing probability in cellular syste with WCDMA radio interface and with finite nuber of traffic sources, the results of analytical calculations have been copared with the results of siulation experients. The study has been carried out for subscribers deanding a set of services. Figure 4 shows the ean blocing probability of a new call as a function of the ean load for speech and video calls (values in Table ) for infinite nuber of sources with load of neighbouring cells of 25 percent. The assued axiu usage of radio interface resources is equal to 80%. Figures 6-9 present blocing probabilities for a syste with finite nuber of sources. The ratio of the nuber of traffic sources of all classes and the cell capacity expressed in BBU s: N V = {, 2, 5, 0, 00}. / = All the presented results (Figures 4-9) show the robustness of the proposed ethod of blocing probability calculation. In each case, regardless of the offered traffic load and the ratio of the nuber of traffic sources, the results of the calculation are characterised by fair accuracy. 5. Conclusions The adission control in wireless networ with WCDMA radio interface adits or blocs new calls depending on the current load situation both in access cell and in neighbouring cells. A new call is reected if the predicted load exceeds particular thresholds set by the radio networ planning. In this paper, we present uplin blocing probability calculation ethod with finite nuber of sources, which eploys analytical odel of the node in ulti-service networ. In our odel, we use load factor L to estiate whether a new call can be allowed or bloced. The proposed ethod allows us to odel cellular syste ore accurately due to considering liited nuber of custoers (traffic sources). The obtained results show that taing into account decreasing nuber of active sources in the syste yields lower blocing probability than in odels assuing infinite nuber of sources. This can be essential for services, which deand higher capacity. The calculations are validated by a siulation. The proposed ethod can be easily applied to 3G networ capacity calculations during planning stages of its design. References [Cost 96] Broadband Networ Teletraffic, Final Report of Action COST 242, (edited by J.W. Roberts, V. Mocci, I. Virtao), Published by the Coission of the European Counities, Springer Verlag, Berlin, 996. [Faru 96] S. Faruque: Cellular Mobile Systes Engineering, Artech House, Inc, 996 [Fort 64] R. Fortet and C. Grandean, Congestion in a loss syste when soe calls want several devices siultaneously, Electrical Counications, vol. 39, no. 4, pp , 964, ITC-4. [Glab 04] M. Glabowsi, M. Stasia, An Approxiate Model of the Full-availability Group with Multi-rate Traffic and Finite Source Population, accepted for publishing on 3 rd Polish-Geran Teletraffic Syposiu. [Hol 00] H. Hola, A. Tosala, WCDMA for UMTS. Radio Access For Third Generation Mobile Counications, John Wiley & Sons, Ltd., [Kauf 8] J.S. Kaufan: Blocing in a shared resource environent, IEEE Transactions on Counications, vol. COM-29, No. 0, 98, s P80/8

9 ,000000, , , , , , , , , , , , ,40 0,55 0,70 0,85,00,5,30,45 0, ,45 0,65 0,85,05,25,45 speech (calulations.) video call (siulations) speech (siulations) speech (calculations) video call (siulations) speech (siulations) Figure 4. Blocing probability in the access cell for infinite nuber of sources. Load of neighbouring cells equals 25%. Figure 5. Blocing probability in the access cell for finite nuber of sources. Nuber of sources for both classes equals 800 (400/400). Load of neighbouring cells equals 25%.,000000, , , , , , , , , , , , ,40 0,60 0,80,00,20,40 0, ,40 0,60 0,80,00,20,40 speech (calculations) video call (siulations) speech (siulations) speech (calculations) video call (siulations) speech (siulations) Figure 6. Blocing probability in the access cell for finite nuber of sources. Nuber of sources for both classes equals 600 (800/800). Load of neighbouring cells equals 25%. Figure 7. Blocing probability in the access cell for finite nuber of sources. Nuber of sources for both classes equals 4000 (2000/2000). Load of neighbouring cells equals 25%. P80/9

10 ,000000, , , , , , , , , , , , ,40 0,60 0,80,00,20,40 0, ,40 0,60 0,80,00,20,40 speech (calculations) video call (siulations) speech (siulations) speech (calculations) video call (siulations) speech (siulations) Figure 8. Blocing probability in the access cell for finite nuber of sources. Nuber of sources for both classes equals 8000 (4000/4000). Load of neighbouring cells equals 25%. Figure 9. Blocing probability in the access cell for finite nuber of sources. Nuber of sources for both classes equals (20000/20000). Load of neighbouring cells equals 25%. [Kell 89] F.P. Kelly: Fixed Point Models of loss networs, Journal of Australian Matheatics Society, vol. B3, 989, s [Laih 02] J. Laiho, A. Wacer, T. Novosad: Radio Networ Planning and Optiization for UMTS, John Wiley & Sons, Ltd., [Robe 8] J.W. Roberts: A service syste with heterogeneous user requireents, [in] Perforance of Data Counications Systes and their Applications, (edited by G. Puolle), North Holland Pub. Co., Asterda, 98. [Stae 03] D. Staehle, A. Mader: An Analytic Approxiation of the Uplin Capacity in UMTS Networ with Heterogeneous Traffic, University of Wurzburg, Report No. 30 May [Stas 00] M. Stasia, M. Głąbowsi, A siple approxiation of the lin odel with reservation by a one-diesional Marov chain, Journal of Perforance Evaluation, vol. 4, no. 2-3, pp , July [Stas 98] M. Stasia, P. Zwierzyowsi: Analytical odel of ATM node with ulticast switching, Proceedings of 9 th IEEE Mediterranean Electrotechnical Conference, Tel- Aviv, Israel, May 8-20, 998, vol. 2, s [Stas 04] M. Stasia, A. Wisniewsi, P. Zwierzyowsi: Blocing probability calculation in the uplin direction for cellular systes with WCDMA radio interface, accepted for publishing on 3 rd Polish-Geran Teletraffic Syposiu. [Weso 02] K. Wesołowsi: Mobile Counication Systes, John Wiley and Sons, P80/0