Time-domain Traffic Parameters
3.3 Simulation Results and Discussions
3.3.1 Simulation Environment
Assume that an ATM network is chosen to be the high-speed network supporting mul-timedia services. The input traffic is categorized into two types: real-time (type-1) and non-real-time (type-2) traffic. Video and voice services are examples of type-1 traffic, while data services are examples of type-2 traffic. The network system provides two separate finite
buffers with size Ki, in order to support different QoS requirements for type-i traffic, i=1 and 2. When the buffer is full, incoming cells are blocked and lost. The system reserves Cr portion of its capacity for type-1 traffic and the remaining (1 − Cr) portion for type-2 traffic.
When there is unused type-1 or type-2 capacity, it is used for the other type of traffic. In the simulations described here, K1 = K2 = 100 cells and Cr = 0.8. Also, the QoS requirement for type-1 traffic QoS1 = 10−5 and that for type-2 traffic QoS2 = 10−6.
The cell generation process for a video coder is assumed to have two motion states: one is the low motion state for the rate of interframe coding and the other is the high motion state for the rate of intraframe coding [30]. The rate of intraframe coding is further divided into two parts: the first part has the same rate as the interframe coding and the second part, called difference coding, is the difference between the rates of intraframe coding and interframe coding. The interframe coding and the difference coding are all modeled as discrete-state Markov-modulated Bernoulli processes (MMBP) with basic rates Ar and Aa. The state-transition diagram is shown in Figs. 3.3(a) and 3.3(b). Let λa(t), λr(t), and λ0a(t) denote the cell generation rates for intraframe coding, interframe coding, and difference coding at time t, respectively, from the video coder. Clearly, λa(t) = λr(t) + λ0a(t). The process of λr(t) is an (Mr+1)-state birth-death Markov process. The state-transition diagram for λr(t) uses the label mrAr to indicate the cell generation rate of interframe coding of a state and uses the labels (Mr− mr)γ and mrω to denote the transition probabilities from state mrAr to state (mr+ 1)Ar and from state mrAr to state (mr− 1)Ar, respectively. Similarly, the process for λ0a(t) is an (Ma+1)-state birth-death Markov process. The state-transition diagram for λ0a(t) uses the label maAato indicate the additional cell generation rate of a state due to intraframe coding and uses the labels (Ma− ma)φ and maψ to denote the transition probability from state maAa to state (ma+ 1)Aa and from state maAa to state (ma− 1)Aa, respectively. One should note that the long-term correlation behavior of a video source is resulted from the
Figure 3.3: Level transition diagram for (a) interframe coding λr(t) (b) difference state λ0a(t) (c)interframe and intraframe alternate model (d)voice source
process λa(t). The video source will alternate between interframe and intraframe, depending on the video source activity factor. As shown in Fig. 3.3(c), there is a transition rate c in the interframe state and a transition rate d in the intraframe state. The values of γ, ω, Mr, Ar, φ, ψ, Ma, Aa, c, and d can be obtained from the traffic variables Rp, Rm, and Tp.
The cell generation process for a voice call is modeled by an interrupted Bernoulli process (IBP) [28]. As shown in Fig. 3.3(d), during the ON (talkspurt) state, voice cells are generated with rate Av; during the OFF (silence) state, no cells are generated. A voice source has a transition rate α in the OFF state and a transition rate β in the ON state.
As for the data source, there are high-bit-rate and low-bit-rate data services. The gener-ation of high-bit-rate and low-bit-rate data cells is characterized by Bernoulli processes with rates θ1 and θ2, respectively. Also, the distributions of the holding times for video, voice,
high-bit-rate data, and low-bit-rate data are assumed to be exponentially distributed.
In the simulations, for the arrival process of a video source, it is assumed that Rp=3.31 × 10−2, Rm=1.10 × 10−2, and Tp=0.5 seconds, which would give Mr=Ma=20, Ar=1.34 × 10−3, Aa=3.15 × 10−4, γ= 3.77 × 10−6, ω=5.65 × 10−6, φ=ψ=2.83 × 10−5, c=5.65 × 10−6, and d=5.09 × 10−5; for the arrival process of a voice source, it is assumed that Rp=4.71 × 10−4, Rm=2.12×10−4, and Tp=1.35 seconds, which would give Av=4.71×10−4, α=1.71×10−6, and β=2.09 × 10−6; for high-bit-rate data sources, it is assumed that Rp=7.36 × 10−2, Rm=7.36 × 10−3, and Tp=3.14×10−2seconds, which would give θ1=0.1, and for low-bit-rate data sources, it is assumed that Rp=3.68 × 10−2, Rm=7.36 × 10−4, and Tp= 2.88 × 10−2 second, which give θ2=0.02. The mean holding time is 60 minutes for a video service, 3 minutes for a voice service, and 18 seconds for both high- and low-bit-rate data services. Notice that the values of Rp and Rm have been normalized by the network capacity.
Two kinds of cell loss ratios for type-i traffic are considered: the source loss ratio due to selective discarding at the customer side ps,i and the node loss ratio due to blocking at the network side pn,i. The overall cell loss ratio for type-i traffic pl,i is defined as
pl,i= κps,i+ pn,i, i = 1, 2, (3.7)
where κ is used to indicate the significance of the node loss ratio over the source loss ratio.
κ = 0.8 is assumed here because selectively discarding cells at the source should have less effect on information retrieval than blocking cells at the node. In the simulations, the cell loss ratio is estimated as the total loss cells divided by the arriving cells during the whole simulation interval.
3.3.2 Simulation Results and Discussions
On the basis of prior knowledge concerning CAC, the rule structure and parameters of the NFCAC controller can be initially set and then properly adjusted via the learning
algorithm. The membership functions of the linguistic variables for type-1 and type-2 traffic were initially specified in the left-hand side of Fig. 3.4(a) and Fig. 3.4(b), respectively. As we know, the available capacity Ca, deduced from the equivalent capacity Ce of the existing calls, may possess estimation errors. In order to utilize the network as much as possible, we may employ an idea of “budget deficit” to over-assign the capacity. Thus, the mean value m(I)11 of the membership function of N E was set to be a negative value and the mean value m(I)12 of the membership function of E was set to be a value close to zero.
The behavior of the congestion indicator y could be monitored from the congestion and congestion-free states during a long-term simulation of the network operation. Thus, the membership functions of y could be initially optimized based on the obtained information.
The mean value m(I)22 of the membership function of P would be set to be the mean value of the queue-length change rate during congestion-free periods, the mean value m(I)21 of the membership function of N would be set to be the mean value of the queue-length change rate during congestion periods, and let σ21(I) = σ(I)22 = m(I)22 − m(I)21. These parameters could be further off-line optimized via GA by simulation.
The initial membership functions of the cell loss ratio pl were set according to the QoS requirement. The mean value m(I)32 of the membership function of N S would be set to be the QoS requirement, the mean value m(I)31 of the membership function of S would be set to be a fraction of the QoS requirement, and the standard deviations would be set to be σ31(I)=σ(I)32= m(I)32 − m(I)31. As a result, there exists a safety margin between the membership functions of terms S and N S provided to tolerate the dynamic behavior of the network operation and insure the QoS requirement.
Here, little information about the setting of initial values for the mean m(O)j of the term set T(ˆz) could be employed; therefore, the values of m(O)j are set to be equally spaced in the range of [0,1]. Based on the initial membership functions, an optimal rule structure shown
Figure 3.4: Membership functions of Ca, y, pl and ˆz for (a) type-1 traffic, (b) type-2 traffic
Rule Ca y pl zˆ Rule Ca y pl zˆ
1 NE N NS R 5 E N NS WR
2 NE N S WR 6 E N S WA
3 NE P NS R 7 E P NS WA
4 NE P S WR 8 E P S A
Table 3.1: The rule structure for the NFCAC
in Table 3.1 was obtained by using GA in the self-organized learning phase. When the fuzzy logic rules were found, the NFCAC controller entered the supervised learning phase, in which the membership functions were adjusted optimally.
Three different values of η were used for the variables Ca, y, pl, and ˆz. η was set to zero for plbecause the membership functions were specified by the QoS constraint and should not be modified. η = 0.001 was used for y because the membership functions of y were initially optimized. As for Ca and ˆz, their initial membership functions were heuristically set and required further optimization in the supervised learning phase. Thus, η = 0.01 was used.
The use of different η may drastically reduce the training time required in the supervised learning phase. The learned membership functions of the linguistic variables for type-1 and type-2 traffic were shown in the right-hand side of Fig. 3.4(a) and Fig. 3.4(b), respectively.
For type-1 traffic in Fig. 3.4(a), it can be found that the differences of the membership functions before and after learning are: For the membership functions of Ca, the mean value m(I)11 of the membership function of N E was properly modified from -0.4 to -0.27. Similarly, the mean value m(I)12 of the membership function of E was properly modified from 0.16 to -0.02. There is a drastically change for membership functions of Ca, and the phenomenon can also be found in the membership functions of y. It is because we heuristically set their initial values and we used only two terms to describe Ca or y. The change of the position of one term of Caand y will squeeze the other term but receive less counteraction from the other one term (compared to ˆz described later). Membership functions of pl are not changed since
η for pl was chosen to be zero. For the membership function of ˆz, however, the mean m(O)1 of the membership function of R is slightly increased from 0 to 0.05, representing that the effect of “Reject” is decreased. Also, the mean m(O)3 of the membership function of W A is slightly increased from 0.67 to 0.72, representing that the effect of “Weak Accept” is increased. The small change is because we used four terms to describe ˆz. The change of the position of one term of ˆz will squeeze the other three terms but receive more counteraction from the three terms. Therefore, the change of position would be confined in a smaller range. The changes of membership functions of ˆz imply that the NFCAC controller prefers to accept new calls. This phenomenon demonstrates that the NFCAC controller intends to recover some system bandwidth which the equivalent capacity method wastes due to over-estimation, while keeping the QoS contract. It may be the reason for the utilization improvement of the proposed NFCAC controller, which will be shown below. Similar results could be found for type-2 traffic in Fig. 3.4(b).
We compare the NFCAC scheme with the effective-band-width-based CAC (EBCAC) scheme proposed in [10], the fuzzy-logic-based CAC (FLCAC) scheme proposed in [18], the neural-net-based CAC (NNCAC) scheme proposed in [23], and the radial-basis-function-based CAC (RBFCAC) scheme from the aspects of the cell loss ratio (CLR), the system utilization, and/or the training time under the constraint of QoS guarantee. The EBCAC scheme is a hybrid technique combining the conventional techniques of the Gaussian ap-proximation and the bufferless analysis; it is an improved version of the equivalent capacity method [8]. Simulation of the EBCAC scheme is simply to calculate the required bandwidth of a new connection. The new connection request is accepted if the total bandwidth re-quired by the new connection and the existing connection is less than the system capacity.
Otherwise, it is rejected. The FLCAC scheme is a fuzzy implementation of the equiva-lent capacity admission control method; details for the FLCAC scheme can be referred to
[18]. The NNCAC and RBFCAC schemes are neural-net implementation of the equivalent capacity admission control method, where the NNCAC adopts the multi-layer perceptron (MLP) structure with 30 hidden nodes, while the RBFCAC uses radial basis function net-work (RBFN) with 30 hidden nodes. Details for the NNCAC scheme can be referred to [23].
In the simulations, the FLCAC, NNCAC, or RBFCAC controller is equipped with the same three peripheral processors as those used in the NFCAC controller shown in Fig. 3.1. The sizes of training set and test set are all equal to 200, the number of repeated experiments is 20, and the standard deviation is less than 5%.
Fig. 3.5 shows the CLRs of an ATM traffic controller employing the NFCAC scheme, and the EBCAC, FLCAC, NNCAC, RBFCAC schemes. It is found that the QoSs for both types of traffic are indeed guaranteed for all of these control schemes. Fig. 3.6 shows that the system utilization of the NFCAC scheme and the four schemes. We can find that the utilization of the NFCAC scheme is slightly greater than that of the NNCAC and the RBFCAC schemes; the system utilizations of NFCAC, NNCAC, and RBFCAC are 91%, 90.5%, and 89%, respectively; and the NFCAC scheme offers about 32% and 11%
greater system utilization than the EBCAC scheme and the FLCAC scheme. It is because NFCAC can incorporate the domain knowledge obtained from both the analytical-based method (the equivalent capacity scheme [8] is employed in the bandwidth estimator) and the measurement-based method (the system statistics of the queue length, the change rate of the queue length, and the CLR are considered in the congestion controller). Also, the reason for the performance improvement is that NFCAC possesses the learning capability of the neural network.
Fig. 3.7 shows the training time required for the NFCAC scheme and the NNCAC, RBFCAC schemes. Here, a widely used back-propagation learning algorithm was employed to adjust the membership functions (i.e. represented in terms of weights) of the multi-layer
neural fuzzy network and neural network for the NFCAC and NNCAC schemes, while the RBFCAC scheme is basically trained by the hybrid learning rule: unsupervised learning in the input layer and supervised learning in the output layer. It is found that NFCAC has training time of 7 (4) epochs, while RBFCAC and NNCAC have training time of 103 (40) and 5 × 104 (6 × 102), respectively, for type-1 (type-2) traffic. The NFCAC has higher learning speed than the RBFCAC and NNCAC. One reason is that the neural fuzzy network is a structured network, thus the NFCAC controller can easily adopt the domain knowledge of conventional control methods to construct the initial rule structure and the parameters of the membership functions, providing an excellent initial guess in adjusting its weights;
on the contrast, the neural network is a non-structured network, which cannot incorporate domain knowledge about system. The other reason is that the neural fuzzy network has simpler structure than the neural network; the number of tunning parameters used in the neural fuzzy network is quite small, as compared to the neural network such as MLP and RBFN considered here. In this chapter, there are only 16 weighting parameters used in NFCAC, while there are 150 and 480 weighting parameters required for the RBFCAC and NNCAC, respectively. It is also noted that the RBFCAC scheme has less learning time than the NNCAC scheme. This is because the RBFCAC scheme can have the proper initial setting of means and variances for the Gaussian activation functions during unsupervised learning according to the prior knowledge, and it has only one layer of connection needed to be trained by supervised learning.
As usually noted, RBFCAC can have faster training speed than NNCAC but cannot achieve the same accuracy as the back-propagation NNCAC. In the simulations, we first adopted the same set of data used to train NFCAC and NNCAC for RBFCAC. However, it was found that RBFCAC finally violated the QoS contracts due to its error decision of accepting more users than it should be. In order to provide QoS guarantee for RBFCAC, we
have to prepare much more training data, especially those around the acceptance/rejection boundary. This will increase the training time of RBFCAC in each epoch than those required by NFCAC and NNCAC. Moreover, the overall processing time of RBFCAC is greater than that needed by either NFCAC or NNCAC because RBFCAC uses more nodes (compared with NFCAC) and a more complicated activation function (compared with NNCAC). All these would degrade the performance of RBFCAC in real application.
3.4 Concluding Remarks
This chapter has proposed a neural fuzzy approach for connection admission control in high-speed multimedia networks. The neural fuzzy connection admission control (NFCAC) scheme combines the linguistic control capability of a fuzzy logic controller and the learning ability of a neural network. This type of integrated neural fuzzy system can automati-cally construct a rule structure by learning from training examples and can self-calibrate parameters of membership functions. It not only provides a robust framework to mimic experts’ knowledge embodied in existing traffic control techniques but also constructs intel-ligent computational algorithms for traffic control. It can be easily trained and enhances system utilization. Simulation results show that the proposed NFCAC scheme provides sys-tem utilization about 32% and 11% higher than the EBCAC and FLCAC schemes proposed in [10] and [18], respectively, and the NFCAC scheme requires only a fraction of the 103 order and the 101 order of training cycles, consumed by the NNCAC scheme proposed in [23] and RBFCAC scheme, respectively. An NFCAC scheme such as the one introduced here may be the answer to the problem of designing a coherent call admission controller for ATM systems.
Figure 3.5: Cell loss ratio for (a) type-1 traffic, (b) type-2 traffic
Figure 3.6: System utilization
Figure 3.7: Training cycles needed for (a) type-1 traffic, (b) type-2 traffic