AP06_3.vp 1 Introduction ATM technology arose as the basic communication code for B-ISDN worldwide broadband communication network. The ATM philosophy is based both on fast switching of very tiny cells of fixed length, and also on effective usage of band- width transmission. ATM enables us to realize transmissions with guaranteed quality of service for all services provided in broadband networking. If we want a setting with a large number of services to be effectively supported, we need an ATM control mechanism that will accept different quality requirements of particular services. This is called traffic management. 2 ATM traffic management The main task of traffic management is to protect the network and end systems from overloading in such a way that efficiency goals are achieved and the given quality of services is retained. If overloading of the network occurs, the next task of traffic management is to eliminate this overloading. An additional function is to increase the effective usage of net- work resources. Reaction management responds to network overloading when it happens, i.e. it reduces the consequences of overloading to an acceptable level. It regulates the opera- tive flow at the entry points on the basis of the current level of operation in the network with the help of management through feedback. Preventive management provides a fair allocation of the communication area in such way that during high load in the network it ensure that the operative flow stays within the specified range acceptable for the particular ser- vice. The chief idea of preventive management is to prevent overloading of the multiplex the entry point to the network in the process of connection building. 3 Call admission control Call admission control is the basic function of preventive management, which is defined as the series of acts done by the network during the phase of connection building in order to define whether the connection will be accepted or refused. The operation contact is made between the customer and the network at the time of connection building, which specifies the properties of the ATM connection on the UNI and NNI interfaces, that it goes through. The network will undertake to support the operation on a given level and the customer agrees not to overrun the given efficiency parameters. Main- tenance of the given QoS is important for ATM services with reference to fulfilling the operation contract. The given QoS is on to a great extent dependent on rationing the network devices, and this is what CaC determines. For CBR (Constant Bit Rate) services, for rt-VBR (real time-Variable Bit Rate) and also for nrt-VBR (non real time – Variable Bit Rate), CaC is compulsorily applied as the preventive function of traffic management. Judged on the basis of the operative parame- ters, PCR (Peak Cell Rate) is defined as the maximum rate of cell broadcasting for an individual ATM connection SCR (Sustainable Cell Rate) is measured over a long time period in respect of the T value, where PCR � 1/T and others. ABR (Available Bit Rate) and UBR (Unspecified Bit Rate) services characteristically use abundant network devices. To secure the QoS mechanism, ABR uses feedback control as a reactive function of traffic management. UBR does not have QoS or assigned network devices secured by the network. 4 The diffuse method The diffuse method [2] is based on two statistical formula- tions of the required bandwidth. In the first case, it is based on the cell loss ratio for a finite series PFB B C C � � � � � 1 2 2 2 2 2 � � � � �e e ( ) ( ) (1) derived from the model of an ATM multiplexor with finite ca- pacity. Relation (1) is based on the ratio of the line capacity overflow set by the Gaussian method P P r t Ci i N C overflow e� � � � � � � � � � � � � � � � � � � ( ) ( ) 1 1 2� � 2 22� (2) and on the exponential function e � �2B C( )� � (3) which represents the usage of the capacity of buffer store B according to the of diffuse method. The time of operation of buffer store cells of fixed size has a specified constant value. In dependence on the load of the line capacity, the time of operation of the buffer store can vary. The contrast � � C rep- resents the immediate average rate of cell access into the buffer store (drift), where � �� � � i i N 1 (4) is the central bit rate of cell access into the buffer store and C is the general line capacity (multiplexor). Parameter � deter- mines the immediate variance of cell access into the buffer store, and is defined as © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 57 Czech Technical University in Prague Acta Polytechnica Vol. 46 No. 3/2006 CaC in ATM – the Diffuse Method I. Baroňák, M. Vozňák Connection Admission Control is an element in the of preclusive mechanisms of ATM management. Its main task is to prevent overloading of the network and to ensure the required quality of service. This means that it has to predict the service of the network and according to its state it can manage both existing and new connections. This paper deals with the diffuse method, a CAC method that enables us to obtain the required results. Keywords: ATM, QoS, CaC – the diffuse method. � �� � � � i i i N c2 1 , (5) where c R b R b R p i 2 2 2 1 1 1 1 1 � � � � � � � � � � � � � � � � (6) is the variance coefficient of cell access (average time of active status b and average time of inactive status p). In the second case, we deal with the application of the cell loss ratio for an infinite series PIB B C C � � � � � � � � � � � � 2 2 2 2 2e e ( ) ( ) (7) derived from the ATM multiplexor model when the infinite capacity is considered. Relation (7) is determined from the ac- count of the top cell loss ratio P E r t Ci i N C loss e� � � � � � � � � � � � � � � � � � �� ( ) ( ) 1 2 2 � � � � � 2 2� , (8) where ri(t) is the immediate connection bit rate i and � � 2 2 1 � � � i i N (9) is the central quadratic diversion of the bit rate. Relation (3) is also derived from the exponential function. Let � represent the maximum accepted cell loss ratio. Consequently, two sta- tistical formulations of the required bandwidth marked as CFB and CIB can be derived. CFB denotes the statistical band- width derived from the diffuse model of a system with finite series for an ATM multiplexor. From relation (1) we obtain the quadratic equation ( ) ( )� � � � �� � � � �C C2 2 12 2 0, (10) where for the account we use artificial variables � � �� 2 2B (11) and � � �1 2� ln( ). (12) If C CFB� is valid than CFB � � � �� � � � � 2 2 12 . (13) CIB marks the statistical bandwidths gained from the dif- fuse model of a system with infinite series for an ATM multi- plexor. In the same manner as for CFB we can derive CIB, during which time we start from relation (8), and we get CIB � � � �� � � � � 2 2 22 , (14) where the artificial variable is determined � �� � �2 2� �ln( ) ln( ). (15) This formulation of two statistical bandwidths contains the usage of the cell loss ratio selected by the user, the general characteristics of the operation and also the available size of the buffer store. They also define the acceptable range for dif- ferent types of connection on the basis of their operation descriptors for different types of buffer stores. The statistical bandwidth for the diffuse method Cdf, which is needed for the particular connection, can be determined from the relation C C Cdf FB IB� max( , ). (16) 5 Simulation of the diffuse method By simulating the diffuse method we tried to ensure the required bandwidth for the connections. When simulating the CAC method we had to define the model of the ATM service for the CBR, VBR and ON/OFF service. We dealt with the case that there exist N � 100 independent connections in the network, and for each connection n = 100 values of service in time are generated in dependence on the PCR of the indi- vidual connections. The size of the line we had chosen was C � 155 Mbit/s. We chose a constant size of the PCR para- meter for all models of service CBR, VBR and ON/OFF, according to the formula PCR k C N � � , (17) where a supply constant occurs. When simulating the CAC method it is appropriate to generate the service in the net- work in such a way that the link capacity is accidentally overrun and the QoS of a few connections is corrupted. The constant k � 1.95 is defined for this purpose. The param- eter of the cell loss ratio is represented by CLR on the whole line, and we chose its value at CLR � 1.10�6. Buffer store B � 1 Mbit/s. 5.1 CBR service Fig. 1 shows the dependability of the cell loss ratio for fi- nite series PFB and for infinite series PIB for the diffuse method in CBR service. Both probabilities show zero values. Because the diffuse method is derived from the Gaussian method, this caused by the central quadratic derivation the of bit rate, which at the same immediate bit rate approaches zero. Thereby dividing by zero occurs in formulae (1) and (7). The statistical bandwidth obtained from the diffuse model with finite series CFB and with infinite series CIB for an ATM multiplexor in CBR service, and also the consequential band- width of the diffuse method Cdf, is shown in Fig. 2. The figure shows that for individual connections N both statistical band- widths extend with increasing connections and with equal estimated values, and therefore they are stated as the conse- quential bandwidth of the diffuse method Cdf . The 97 th con- nection overruns the line capacity C. In comparison with the case when for every new connection we reserved its maximal value PCR of required bandwidth Cpcr , the overrun of line capacity would already come by the admission of the 52nd connection. Here we have to take into account that the stan- dard deviation � is zero in CBR service. It follows that after substitution to formula 13 and 14, the bandwidths for CFB and CIB are determined only by the central bit rate, and therefore they are equal. In a real ATM this would cause a big derivation of delay, which cannot be accepted. For this reason the diffuse method is not appropriate for CBR service. 58 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 46 No. 3/2006 Czech Technical University in Prague 5.2 VBR service Fig. 3 shows the dependability of the cell loss ratio for finite series PFB and for infinite series PIB for the diffuse method in VBR service. In comparison with CBR service there are changes of values in both probabilities. Up to the 72nd connection, their values are about zero. After the 72nd connection both probabilities increase, which reflects the close-up of several connections in the ATM network. An overflow of line capacity occurs in the network. After the admission of the 78th connection the overflow of line capac- ity for finite series PFB and after the admission of the 80 th connection, for infinite series PIB (Fig. 4) the line capacity overflows (Fig. 4). Fig. 3 shows that the line capacity overflow occurred at the set value of the cell loss ratio parameter on the lines CLR on 1�10�6. The Statistical bandwidth obtained from the diffuse mod- el of the system with finite series CFB and with infinite series CIB for the ATM multiplexor in VBR service, and also the resultant bandwidth of the diffuse method Cdf , are shown in Fig. 4. The figure shows that for individual connections N both statistical bandwidths with increasing connections expand, during which time the estimated values with finite series CFB are greater than the estimated values with infinite series CIB. For this reason the CFB values are stated as the resultant band- width of the diffuse method Cdf . During the development of the 78th connection for CFB, or let us say the 80 th connection for CIB, the line capacity C is overrun. In comparison with the case when, for each of the new connections, we reserved its maximum value PCR of required bandwidth Cpcr , the line ca- pacity overrun would occur already at the admission of the © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 59 Czech Technical University in Prague Acta Polytechnica Vol. 46 No. 3/2006 2 1 0 -1 -2 x 10 �6 P fb , P ib 0 10 20 30 40 50 60 70 80 90 100 N [Number of Connection] Pfb Pib Fig. 1: The cell loss ratio for finite and infinite series of the diffuse method in CBR service for constant PCR 200 150 100 50 0 C , C d f, C p c r /s [M b it ] 0 10 20 30 40 50 60 70 80 90 100 N [Number of Connection] Cpcr Cdf C Fig. 2: The bandwidth estimated by the diffuse method in CBR service for constant PCR 2 1.5 1 0.5 0 x 10 �6 P fb , P ib 0 10 20 30 40 50 60 70 80 90 100 N [Number of Connection] Pfb Pib Fig. 3: The cell loss ratio for finite and infinite series of the diffuse method in VBR service for constant PCR 52nd connection. In this way we can enter more connections by using of the diffuse method. For this reason, the diffuse method is appropriate for VBR service. We can enter more connections than are shown in Fig. 4 by using the diffuse method. We can achieve this with the use of greater buffer stores B in the network or, we can increase the cell loss ratio CLR parameter on the line. Figs. 5 and 6 shows the influence on possible accepted connections due to changes of the buffer store capacity B or the parameter of cell loss ratio CLR. When the CLR para- meter changes, Fig. 5 shows that, at low values of buffer store capacity B 0.1 till 1 Mbit/s, the number of possible ac- cepted connections is aliasingly greater and greater with increasing CLR. With a buffer store size of 10 Mbit/s we can see very similar aliasing growth and even 89 connections can enter. Fig. 6 shows changes, this time in dependence on the change of the buffer store capacity B. During the initial reflections it does not matter if we use a buffer store 0.01 or 0.6 Mbit/s in size, as the number of possible accepted connections is the same. Little improvement occurs at 1 Mbit/s. Sharp improve- ment occurs when the buffer store is over 10 Mbit/s in size. This means that if we change the buffer store size above B � 10 Mbit/s, the change in possible accepted connections increases linearly. For this reason we have to choose values like these when creating the layout of the ATM service. The change in the CLR parameter, and also the change in B cause sharp changes in the number of possible accepted connec- 60 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 46 No. 3/2006 Czech Technical University in Prague 200 150 100 50 0C , C if , C d f, C p c r M b it /s [ ] 0 10 20 30 40 50 60 70 80 90 100 N [Number of Connection] Cpcr Cib Cdf C Fig. 4: The bandwidth estimated using of the diffuse method in VBR service for constant PCR 100 90 80 70 10 �2 10 �1 10 0 10 1 10 2 B [Mbit/s] Cdf (CLR=1.0e 05)� Cdf (CLR=1.0e 06)� Cdf (CLR=1.0e 07)� N u m b e r o f p o s s ib le c o n n e c ti o n D M Fig. 6: The number of possible accepted connections of the diffuse method with the change of B in VBR service for constant PCR 90 85 80 75 70 N u m b e r o f p o s s ib le c o n n e c ti o n D M 10 �8 10 �7 10 �6 10 �5 10 �4 CLR Cdf (B=0.1[ Mbit/s]) Cdf (B=1[ Mbit/s]) Cdf (B=10[ Mbit/s]) Fig. 5: The number of possible accepted connections of the diffuse method with the change of CLR in VBR service for constant PCR tions. The best combination is to use the greater possible cell loss ratio CLR as possible and as great buffer store size B. However in reality these parameters are influenced by many other factors. 5.3 ON/OFF service Fig. 7 shows the dependability of the cell loss ratio for finite series PFB and for infinite series PIB for the diffuse method in ON/OFF service. Up to the 70th connection their values are about zero. After the 70th connection both proba- bilities increase, which reflects the entry of several connec- tions in the ATM network. Line capacity overflow occurs in the network. After the admission of the 74th connection the line capacity overflows for the finite series PFB and after the admission of the 76th connection it overflows for infinite se- ries PIB (Fig. 8) as well. Fig. 7 shows that line capacity overflow also occurred at a set value of the cell loss ratio parameter on the whole line CLR at 1�10�6. The statistical bandwidth obtained from the diffuse model of the system with finite series CFB and with infinite series CIB for the ATM multiplexor in ON/OFF service as well as the resultant bandwidth of the diffuse method Cdf is shown in Fig. 8. The figure shows that for individual connections N both statistical bandwidths with increasing connections expand, during which time the estimated values with finite series CFB are greater than the estimated values with infinite series CIB. For this reasons values CFB are stated as the resultant band- width of the diffuse method Cdf . During the development of the 74th connection for CFB, or let us say the 76 th connection for CIB, the line capacity C is overrun. In the case when for each of the new connections we reserved its maximum value PCR of required bandwidth Cpcr , the line capacity overrun would occur already at the ad- mission of 52nd connection. In this way we can enter more connections with the use of the diffuse method. However we have to take into account the fact that with a few entered con- nections bandwidth CFB as well as CIB is slightly greater than if we had reserved its maximum capacity Cpcr for the connec- tion. This factor can be eliminated with the use of greater buffer stores B to allow a greater cell loss ratio CLR on the line. The diffuse method is also appropriate for ON/OFF ser- vice, but with the use of few connections it can be ineffective. For this reason we have to focus on the proper arrangement of the service. Also in this case we can enter more connections than are shown in Fig. 8 when we use greater buffer stores B, or we can increase the cell loss ratio parameter CLR on the line. Fig. 9 and 10 show the influence on possible accepted connections due to changes in buffer store capacity B or the cell loss ratio parameter CLR. When the CLR parameter changes, Fig. 9 shows that at low values of buffer store capacity B 0.1 till 1 Mbit/s the num- ber of possible accepted connections grows with increasing CLR. With a buffer store size of 10 Mbit/s we can see very simi- lar growth and as many as 95 connections can enter. Fig. 10 shows changes, this time in dependence on the change in buffer store capacity B. During initial reflections it does not matter if we use a buffer store 0.01 or 0.1 Mbit/s in size, as the number of possible accepted connections is the same. A sharp improvement occurs when the size of the buffer store rises above 10 Mbit/s. This means that if we change B about © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 61 Czech Technical University in Prague Acta Polytechnica Vol. 46 No. 3/2006 200 150 100 50 0 0 10 20 30 40 50 60 70 80 90 100 N [Number of Connection] Cpcr Cib Cdf C C , C ib , C d f, C p c r M b it /s [ ] Fig. 8: The statistical bandwidth estimated using of the diffuse method in ON/OFF service for constant PCR 2 1.5 1 0.5 0 x 10 �6 0 10 20 30 40 50 60 70 80 90 100 N [Number of Connection] Pfb Pib P fb , P ib Fig. 7: The ratio of line capacity overrun for finite and infinite series of the diffuse method in ON/OFF service for constant PCR 10 Mbit/s, the change of possible accepted connections in- creases linearly. An absolute decay occurs at about 60 Mbit/s. This is why we have to choose of the buffer store values of about 10 Mbit/s when creating the layout of the ATM service. The change in the CLR parameter as well as the change in B cause sharp changes in the number of possible accepted con- nections. The best combination is to use the greatest possible cell loss ratio CLR and buffer store size B about 10 Mbit/s. 6 Conclusion The diffuse method cannot be used in CBR service be- cause the central quadratic derivation of bit rate � � 2 ap- proaches zero in equal immediate bit rate, i.e. dividing by zero occurs in formulae (1) and (7). Afterwards the bandwidths for CFB and CIB are deter- mined only by the central bit rate. In the real ATM service this could cause big derivation delays, which cannot be accepted. For this reason the diffuse method is not appropriate for CBR service. In VBR and cluster ON/OFF service the method can be used effectively. In both models of the service the results were much better than if we were to reserve for each of new connections its maximal value of PCR. In the diffuse method, an even greater number of connections can enter than was shown in the figures with the use of greater buffer stores B in the network or we can expand the cell loss ratio CLR parameter on the line. In comparison with other methods, the diffuse method maintains the values of the cell loss ratio during which it is more effective during allocation of the required bandwidth. It is appropriate for homogeneous and also for heterogeneous type of service. In comparison with classic models, the account of this method is effective. It is easily employable as a CAC algorithm. Acknowledgment This work is a part of AV 1002/2004, VEGA 1/0156/03 and VEGA 1/3118/06 projects. References [1] Baroňák, I., Kajan, R.: Quality of ATM Services and CAC Methods. FEI STU Department of Telecommunications, Bratislava, 1999. [2] Shiomoto, K., Yamanaka, N., Takahashi, T.: Overview of Measurement-based Connection Admission Control Methods in ATM Networks. IEEE Communications Surveys, First Quarter 1999. [3] Marzo, I., Lazaro, J. L.: Enhanced Convolution Approach for CAC in ATM Networks, an Analytical Study and Implementa- tion. Girona, 1996, ISBN 84-8458-106-53. [4] Baroňák, I., Kvačkaj, P.: Submission to CAC. Communica- tions, Scientific Letters of the University of Žilina, Vol. 6 (2004), No. 4, p. 80–83. [5] Kvačkaj, P.: CAC Method of Effective Bandwidth. Inter- national Competition STUDENT EEICT 2004, section 62 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ Acta Polytechnica Vol. 46 No. 3/2006 Czech Technical University in Prague 90 85 80 75 70 10 �8 10 �7 10 �6 10 �5 10 �4 CLR Cdf (B=0.1[ Mbit/s]) Cdf (B=1[ Mbit/s]) Cdf (B=10[ Mbit/s]) N u m b e r o f p o s s ib le c o n n e c ti o n D M Fig. 9: The number of possible connections of the diffuse method with the change of CLR in ON/OFF service for constant PCR 100 90 80 70 10 �2 10 �1 10 0 10 1 10 2 B [Mbit/s] Cdf (CLR=1.0e-05) Cdf (CLR=1.0e-06) Cdf (CLR=1.0e-07) N u m b e r o f p o s s ib le c o n n e c ti o n D M Fig. 10: The number of possible connections of the diffuse method with the change of CLR in ON/OFF service for constant PCR Telecommunications, Bratislava, May 27, 2004, p. 232–237. [6] The ATM Forum: Traffic Management Specification Version 4.0. af-95-0013R13, Letter Ballot, April 1996. [7] Engel, R.: Design and Implementation of a New Connection Admission Control Algorithm Using a Multistate Traffic Source Model. Department of Computer Science, Washington University St. Louis, 1996. [8] Jakab, F., Giertl, J., Bača, J., Andoga, R., Mirilovič, M.: Contribution to Adaptive Sampling of QoS Parameters in Computer Networks. Acta Electrotechnica et Informatica, Vol. 1 (2006 ), p. 52–59, ISSN 1335-8243. [9] Marchevský, S., Čižmár, A.: Converging the PSTN/ISDN and the Internet. In: ITTW 98 – International Workshop. TEMPUS Telecomnet Project. Barcelona, 1998, p. 77–81. [10] Marchevský, S., Kocúr, D., Longauer, L., Čížová, J.: Sim- ulation of AdaptiveBlind Multi-User Detection of CDMA Signals by System Design Tool-System View. In: Recent Trends in Multimedia Information Processing. IWSSIP 2003 – Proceedings of the 10th International Workshop on System, Signal and Image Processing. Prague, Czech Re- public, 10 – 11 September 2003, p. 203–206. Doc. Ing. Ivan Baroňák, Ph.D. Department of Telecommunications Slovak Technical University, Bratislava Faculty of Electrical Engineering and Information Technology Ilkovičova 3 Bratislava 1, SK - 812 19, Slovak Republic Ing. Miroslav Vozňák, Ph.D. phone: +420 596 991 699, +420 234 680 468 e-mail: miroslav.voznak@vsb.cz Department of Electronics and Telecommunications VSB - Technical University of Ostrava Faculty of Electrical Engineering and Computer Science 17. listopadu 15 708 33 Ostrava-Poruba, Czech Republic © Czech Technical University Publishing House http://ctn.cvut.cz/ap/ 63 Czech Technical University in Prague Acta Polytechnica Vol. 46 No. 3/2006