neural modelling of ethernet traffic over atm networks - CiteSeerX

Proceedings of the fourth International Conference on Engineering Applications of Neural Networks (EANN’98), Gibraltar, June, 1998, pp. 304-307

NEURAL MODELLING OF ETHERNET TRAFFIC OVER ATM NETWORKS E. Casilari, A. Alfaro, A.Reyes, A. Díaz-Estrella, F. Sandoval Dpto. Tecnología Electrónica, E. T. S. I. Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071 Málaga. E-mail: [email protected] Abstract The purpose of this paper is to present a method of modeling a superposition of individual Ethernet sources over an Asynchronous Transfer Mode (ATM) network through neural networks. It is proposed the two-state MMPP model (Markov Modulated Poisson Process) to approximate the aggregated ATM traffic because of its simplicity and analytical tractability. The neural network is able to calculate the MMPP model of real Ethernet traffic over a 155 Mbps ATM network, avoiding, through this adaptive and real-time technique, complex analytic solutions. Besides, to match long-time dependence, it is studied the two-level MMPP model, that considers several time scales. Introduction Accurate traffic modelling is a key issue in the design and performance evaluation of Broadband Integrated Service Digital Networks (B-ISDN) based on ATM (Asynchronous Transfer Mode) technology. Traffic modelling is necessary for theoretical analysis as well as for simulation purposes. Normally, a model is defined by a reduced number of parameters, included in a "traffic descriptor", which must be chosen to match a set of statistical characteristics of the real traffic. For the case of ATM, where heterogeneous multimedia sources are multiplexed on the same link, models must also consider the approximation of aggregate traffic. One of the most popular models for superposed ATM traffic is the two-state MMPP (Markov Modulated Poisson Process) model. MMPP [1] is especially adequate for its simplicity and analytical tractability, in opposition to other modelling strategies, such as empirical, nonparsimonious or self-similar models. The main problem when designing a MMPP model [2] is to determine the parameters that define it as a function of the traffic descriptor to fit. On the other hand, MMPP has been normally validated by the bibliography considering just synthetic traffic, generated by simplistic source models, such as On-Off process. In this work we propose to use a neural network to calculate the MMPP model that best matches the statistical descriptor of real ATM sources. In particular, we utilise a multilayer perceptron [3] to calculate the MMPP parameters that adjust the behaviour of actual Ethernet traffic conveyed on an ATM link. With this neural approach, which is adaptive and able to work in real time applications, more complex analytical solutions are avoided. Finally, to improve the queuing performance the model is extended to two time scales, resulting in a two layer model which accurately approximates delay, jitter and losses. Proposed scheme A two-state MMPP consists of a double stochastic process in which, for each state (1 and 2), traffic is generated following a Poisson distribution of means λ1 and λ2, respectively. Sojourn times are -1 -1 exponentially distributed with means r1 and r2 . So, the model, as its name indicates, can be considered as a Poisson process whose mean value is modulated by a Markov chain of two states. As it has been -1 -1 pointed out in the previous section, these four parameters (λ1, λ2, r1 , r2 ) are calculated in such a way that the model exhibits the same statistical properties of the real traffic. Several traffic descriptors have been proposed by the bibliography. In this paper, we take into consideration the proposal by Heffes [1]. This descriptor defines he following statistics: (1) 1.- The mean arrival rate: m = M (t ) = N (0 , t ) t

where N(0,t) is the number of cell arrivals in the interval (0,t).


2.-The short term variance-to-mean ratio of the number of cell arrivals in (0,t1). v1 = I ( t1 ) =

Var( N (0, t1 )) M(t1 )

(2)

3.-The long term variance-to-mean ratio of the number of arrivals. v2 = I ( ∞) = lim t →∞

Var( N (0, t )) M (t )

(3)

4.- The skewness index in (0, t2) defined as the third central moment-to-mean ratio

[

μ3 (0, t2 ) E [ ( N (0, t2 ) − E( N (0, t2 )] s = S( t2 ) = = M(t2 ) M(t2 )

3

]

(4)

where μ3 is the third central moment -1 -1 The model parameters (r1 , r2 , λ1, λ2). must be properly calculated to fit the descriptor (m, v1, v2, s). In [1] this adjustment is performed solving a system of four non-linear equations. In this paper we propose to substitute this complex solution, which even requires iterative calculations, by the neural scheme depicted in figure 1. Individual Traffic Sources

ATM Node

Aggregate Traffic

Pattern Generation Generation of {r1,r2,λ1,λ2}

{m,v1,v2,s}= f{r1,r2,λ1,λ2}

m

{m,v1,v2,s}

x1

Estimation of Statistics

r1

v(t1)

λ1 v(t2)

Error

λ2

-

x2 xj

r2

+

Neural Module

s(t3)

MMPP Model {r’1,r’2,λ’1,λ’2}

xM

Figure 1. Proposed scheme

Figure 2. Neural Module

From figure 1 it can be observed that the relationship between the traffic descriptor and the model parameters is established via a three-layer perceptron. The descriptor is directly measured in the ATM link where Ethernet traffic is multiplexed. The learning patterns are generated from random combinations -1 -1 of r1 , r2 , λ1 and λ2. The statistical descriptors for these combinations are easily computed from the formulation of the MMPP model, also described in [1]. The learning phase is performed through an accelerated backpropagation algorithm which uses RPROP improvement [4]. RPROP speeds up the convergence by adjusting the weights with a variable learning coefficient which is increased or decreased as a function of the error gradient. In order to improve the neural learning a different perceptron is devoted to the estimation of each parameter, as it is indicated in figure 2. Two-level model To cope with the long-range-dependence existing in multimedia traffic [5], the previous MMPP model is extended to two time scales [6]. For this purpose, traffic traces are split into two different series, representing low and high loaded periods, respectively. This division is accomplished through an averaging process of the traces through a moving average filter with a window size of W slots. The resulting signals are divided into two levels, depending on the averaged traffic load. A threshold equal to the mean bit rate is defined as a classification criterion for the averaged traces. Once they have been separated, each series is modelled by a different MMPP model, representing the short-term traffic behaviour. Consequently, the two-level model, which is represented in figure 3, consists


-1

-1

-1

-1

of 10 parameters: 8 to define the two MMPPs (λ12, λ12, r11 , r12 , λ21, λ22, r21 , r22 ) for high and low -1

-1

traffic load, and two sojourn times (r1 , r2 ) for each state in the long term level. Level 1 r11-1

r12-1

λ11

λ1

r21-1

r22-1

λ21

λ2

2

State 11

State 12

2

State 21

r1-1

r2-1 λ1

State 1

State 21

Level 2

λ2 State 2

Figure 3. Two-level model Simulation Results

ATM cells

To prove the performance of the neural scheme we consider a set of actual ATM samples consisting of half a minute traces from a 155 Mbps ATM link connecting two Fast Ethernet (100 Mbps) LANs. A sample path of a trace has been depicted in figure 4. The figure represents the number of ATM cells measured in the link during intervals of 1000 slots (a slot is the time required for transmitting an ATM cell which, for a 155 Mbps link, is 2.7 μsec.). The neural network was simulated using ANSI C programming language. The training was performed until it was reached an acceptable mean quadratic error. For the two-level model W was chosen to be 1250000 slots (3.5 second approximately).

Con formato

Time (in thousands of slots)

Figure 4. Sample path The MMPP models obtained by the propose procedure are checked to know their accuracy. Their behaviour in a simulated queue is compared with that of the real traces. Thus, the model will be as accurate as it can approximate some parameters that normally determine the quality of an ATM communication. These parameters are: the cell delay (average waiting time of a cell in the queue, considering infinite queue size), the jitter (regarded as the standard deviation of the delay) and the cell loss probability. This comparison is depicted in figures 5 and 6 for cell loss probability and mean delays, respectively. Similar results can be obtained for the jitter. These figures shows the improvement that is achieved when two activity levels are considered, while simple MMPP underestimates losses and delays for large buffers sizes or high channel utilisation.

Con formato


10

0 4

Channel Occupation: 51%

3

x 10

Real Traffic

10

10

Simple MMPP

-1

2.5

2-level MMPP

Delay in slots

Cell Loss probabilty

10

-2

Real Traffic Simple MMPP

2

2-level MMPP

1.5

1

-3

0.5

10

-4

0

1000

2000

Buffer size (in cells)

Figure 4. Losses

3000

0 65

60

55

50 45 40 Channel Utilization (%)

35

30

25

Figure 5. Delays

Conclusions A neural procedure to model aggregate ATM traffic has been developed. In particular, the proposed scheme designs the MMPP models that best approximates the behaviour of real ATM traffic traces, just considering a traffic descriptor. In order to improve the queuing performance a two-level MMPP model is proposed. The utilisation of neural networks in model design avoid the complexity of analytical solutions. Furthermore, because of its adaptive nature, the neural scheme could be extended to other traffic descriptors and other traffic models apart from MMPP. Acknowledgements This work has been partially supported by the Spanish Comisión Interministerial de Ciencia y Tecnología (CICYT), Project No. TIC96-0743. . We also wish to express our gratitude to Telefónica I+D for releasing the ATM traces. References [1] Heffes, H., y Lucantoni, D.M. “A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance”. IEEE Journal Selected Areas in Communications, Vol. 4, No. 6, pp. 856-868, September, 1986. [2] Arvidsson, Ä., y Lind, C. “Using Markovian Models to Replicate Real ATM Traffics”. Documento postcript accesible vía Internet, http://www.itm.hk-r.se/~akear/bursty.html Department of Telecommunications and Mathematics, University of Karlskrona/ Ronneby, S-371 79 Karlskrona, Sweden. [3] Casilari, E., Jurado A., Pansard G., Díaz-Estrella A., y Sandoval, F. “Modelling Aggregate Heterogeneous ATM Sources Using Neural Networks”, Electronic Letters, Vol,. 32, No. 4, pp. 363365, January, 1996. [4] Schiffmann, W., Joost, M., y Werner, R. “Optimization of the Backpropagation Algorithm for Training Multilayer Perceptrons”, Internal Report, University of Koblenz, Institute of Physics, Germany, 1992. [5] Leland, W.E., Taqqu, M.S., Willinger, W., y Wilson, D.V. “On the self-similar nature of Ethernet traffic” (Extended Version). IEEE/ACM Transactions on Networking Communications, Vol. 2, pp. 115, 1994. [6] Karlsson, P., y Arvidsson, Ä. “Modelling of traffic with high variability over long time scales with MMPPs”. Postcript document, available in Internet: http://www.itm.hk-r.se/~akear/bursty.html, Department of Telecommunications and Mathematics, University of Karlskrona/Ronneby, S-371 79, Karlskrona, Sweden.


Abstract Number: 98169 EANN Conference SEA PL 953 (Humalistonkatu) 20101 Turku 10 Finland -Finlandia