traffic and this information is also used by the scheduling algorithm. ... strategy in terms of multiplexing gain for reasonable values of cell loss ratio and ... utilisation of network resources when deterministic allocation, based on peak rate, is considered. To .... of cells at the generic step n+k is predicted with a linear law from the ...
A Multiplexing Scheme Using a Prediction Based Scheduling Strategy for Self-Similar Traffic R.G. Garroppo, S. Giordano, S. Miduri {garroppo, giordano, miduri}@iet.unipi.it
Department of Information Engineering University of Pisa - Italy Via Diotisalvi 2 Pisa, I-56126 Tel. +39 50 568511 Fax +39 50 568522
ABSTRACT: The flexibility given by ATM networks permits to reach high network resources utilisation when the traffic is managed considering its actual statistical behaviour. A dynamic managing of network resources (i.e. bandwidth and buffer space) improves the utilisation when considering heterogeneous sources corresponding to multimedia services. In this scenario the paper presents a multiplexing scheme which permits to dynamically allocate the bandwidth using an ad hoc scheduling discipline and a push out management of the buffer. The capacity assigned to each source depends on its predicted offered traffic and this information is also used by the scheduling algorithm. The prediction is linear and the design of the prediction filter is based on the self-similar modelling of the ingoing traffic, considering the statistical nature of traffic observed during measurements sessions. The performance of the proposed strategy in terms of multiplexing gain for reasonable values of cell loss ratio and queueing delay have been studied considering actual and synthetic traces with different Hurst parameter. Keywords: ATM, linear prediction, Long Range Dependence, self-similarity, statistical multiplexing.
1 INTRODUCTION Recent traffic studies have highlighted high peak to mean ratio of traffic sources, which leads to underutilisation of network resources when deterministic allocation, based on peak rate, is considered. To reach an efficient network utilisation guaranteeing the requested Quality of Service for each user, a deep statistical analysis of offered traffic is needed. Among the statistical features showed by the measured data acquired in different network contexts during the active sessions of different service typology, the burstiness is the most critics one for the performance of the network elements. It worth pointing out that traffic is considered bursty when the arrivals are clustered and then the activity levels are alternating between periods with high and low values. This behaviour is related to a long memory feature of traffic, known as Long Range Dependence (LRD), which has been highlighted in different traffic studies [1]. In particular its presence has been confirmed for the multimedia traffic by means of measurements carried out on 10 Mbps Ethernet LAN, during multi-user videoconferencing service, at the Telecommunication Networks Laboratory of the University of Pisa. These analyses have pointed out self-similar traffic models as emerging realistic mathematical representation of multimedia sources. The relevance of the self-similar modelling is mainly related to the ability of such processes to capture in a parsimonious manner the LRD of actual traffic and the related burstiness. The parameter describing the degree of selfsimilarity (i.e. Hurst parameter, H) represents a measure of the LRD (due to the autocorrelation structure of these processes) and thus of the burstiness. In particular, observing the data pattern obtained with selfsimilar generators it can be noted that, for fixed value of the peak to mean ratio, higher values of H correspond to higher values of burstiness. As pointed out by previous studies on queueing performance, LRD and related high burstiness have a deep impact on queueing behaviour, leading to worse performance compared with those obtained loading the system with short memory processes [2][3][4]. In this scenario a low utilisation of network resources is required in order to operate with acceptable values of Cell Loss Ratio (CLR) and Mean Waiting Time (MWT). The proposed multiplexing scheme is based on a linear prediction filter, defined using the parameters that describe the self-similar traffic model (i.e. mean, variance and H). The predicted values are utilised to determine the bandwidth instantaneously assigned to each source and to set a priority level to each cell. The buffer management with a push out discipline permits if necessary to eliminate cells that are scheduled with a low priority in transmission.
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The remainder of this paper is organised as follows: Section 2 presents some definitions on the selfsimilar modelling of LRD traffic, Section 3 summarises the measurement scenario and the acquired data analysis. Section 5 describes, in detail, the proposed multiplexing scheme and its Scheduling algorithm, based on the prediction filter mentioned in Section 4. Finally considering CLR, MWT and multiplexing gain like reference performance parameters, Section 6 analyses the behaviour of proposed multiplexing strategy by means of discrete event simulations. The advantages of the proposed solution are highlighted in the Conclusions Section.
2 NOTES ON SELF-SIMILAR TRAFFIC MODELLING The data traffic driving the simulations represent the number of cells transmitted during a fixed time interval (Tu=100 msec.). These sequences of observations can be seen as a sample path of a second order, discrete-time and discrete-state, wide sense stationary process { X n } n∈Ν . This process presents LRD if the normalised autocorrelation function, indicated as r( k ) , is characterised by a hyperbolic decay, i.e.: r(k) ∝ k -β as k→∞ defining the power spectral density as S ( e jω ) =
+∞
∑ r( k ) e
− jω k
(2.1) , for a process with LRD the slow decay of
k = −∞
the autocorrelation function implies its non summability which leads to a divergent power spectral density at low frequencies: (2.2) S(f) ∝ f - γ as f → 0 Referring to a self-similar modelling, the LRD can be simply captured considering the relation β=2-2H, where H is the Hurst parameter, or equivalently γ=2H-1 [5]. Thus the Hurst parameter can be used as a measure of the long memory properties of actual traffic. Another important feature of LRD is related to the statistical behaviour of the aggregated process { X n(m) }n∈Ν , obtained by averaging the original series over non-overlapping intervals of length m: X n( m ) =
m = 2,3,......., M 1 (X nm −m +1 + + X nm ) n = 1,2,3,........,+∞ m
(2.3)
Unlike SRD processes, the aggregated series extracted from LRD data are characterised by a slowly decaying variance which is given by (at least asymptotically): (2.4) σ m2 ∝ m -β, as m→∞ For a self-similar process { X n } n∈Ν the H parameter can be evaluated considering the asymptotic autocorrelation decay (2.1) or equivalently the power spectral density (2.2) or the decay of the variance of aggregated processes (2.4). The synthetic traces driving the simulations are generated according to the discrete time process Fractional Gaussian Noise (FGN) Y(n) which is exactly second order self-similar, completely described by three parameters: mean, variance and the Hurst parameter. Its autocorrelation function is given by [6]: 1 (2.5) r(k) = ( k - 12H - 2 k 2H + k + 12H ) 2
3 EXPERIMENTAL MEASUREMENTS AND DATA ANALYSIS In this section the measurement test-bed and the analysis of the traffic offered by a specific multimedia application for multiuser videoconferencing to a broadband network infrastructure, represented by a 140 Mbit/s DQDB (Distributed Queue Dual Bus) MAN known as “Tuscan MAN”, are summarised; more details can be found in [7]. The interest was directed to desktop conferencing tools for common PCs performing software coding of voice and video signals. The traffic was collected by a UNIX workstation and forwarded (on a multicast tunnel) to another multimedia workstation located at a remote site connected to the MAN via an SMDS (Switched Multimegabit Data Service) server. The videoconferencing sessions were implemented over this broadband infrastructure considering only two nodes of the MAN (figure 3.1), connected respectively via a LAN bridging access (local site) and an SMDS access (remote site). The video and voice packets were generated by a group of four PCs at the local site and software coded by the CU-SeeMe application (a widely used public domain Internet software developed by Cornell University). Consequently, the encoded data was sent as unicast packets
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to a multipoint communication unit, called reflector, which transmitted them as multicast IP packets to the remote site. On the remote site the receiver was represented by a multicast videoconferencing Station, running video (NV) and audio (VAT) applications, which can be configured to be compatible with CUSeeMe. This station had multimedia capability and exchanged video and audio signals with the multicast reflector redistributing them to the PCs in the local site.
10 Mbps Ethernet
LAN bridge /SMDS Gateway Traffic Traffic Measurements Measurements
10 Mbps Ethernet
140 Mbps DQDB V.C. station
DSU
Power MAC Central Multicast Reflector
34 Mbps DQDB
SMDS 2 Mbps
10 Mbps Ethernet DSU
Multiprotocol Router
CGW
SMDS Router
Fig 3.1. Measurement testbed
As stated in the previous section the acquired traces represent the number of bytes on disjoint intervals of duration Tu=100 msec collected over the Ethernet LAN, as described in the figure 3.1. The acquired data have been converted in the number of cells transmitted in the Tu dividing the observed bytes by 48 (this represents a very coarse segmentation of Ethernet frame in ATM cells). In figure 3.2, a portion of the data measured on May 29th, 1996 is shown pointing out persistency phenomenon (i.e. local trends can differ significantly from the global behaviour) typical of LRD traffic. 300
250
Cells/Tu
200
150
100
50
0 0
500
1000
1500 Time unit (Tu)
2000
2500
3000
Fig 3.2 Pattern of acquired data
For this trace the average number of cells per Tu and the peak value observed are 95.81 and 300 respectively, while the standard deviation is 54.92. The autocorrelation function and the V-T plot (i.e. the variance of aggregated processes versus the aggregation level) for the considered trace are shown in figures 3.3 and 3.4 respectively. Figure 3.3 highlights the hyperbolic decay of the autocorrelation function which, as stated by (2.1), points out the LRD nature of the process.
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1 0.9 0.8
Autocorrelation coefficients
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
200
400
600
800
1000
Lag (k)
Fig 3.3 Autocorrelation function
Log10(Variance)
10000
1000
100 1
10
100 Log10(k)
Fig 3.4 Variance-Time plot. The dotted line represents the best fitting line to evaluate the H parameter.
Figure 3.4 confirms the LRD nature of acquired data and permits to evaluate a Hurst parameter around 0.9, considering the slope β of the best fitting line, in the asymptotic region of the plot, and the relation
H =1−
β 2
, accordingly to (2.4).
4 LINEAR PREDICTION FILTER The Dynamic Bandwidth Allocation scheme used in the proposed multiplexing system is based on a linear prediction of the input traffic [8]. The prediction filter is realised by means of a Minimum Mean Square Error (MMSE) technique and is described by the following equation:
x (n + k ) =
p −1
∑ w(i )x(n − i ) i =0
(4.1)
where p represents the predictor order, {w(i)}i = 0 are the filter coefficients, x ( n) and x ( n) are respectively p −1
forecasted and the actual value of the number of arrivals during the n-th time interval. Hence, the number of cells at the generic step n+k is predicted with a linear law from the knowledge of the samples at steps n, n-1, ..., n-p+1. Using the notation: T w = [w(0), w(1),, w( p − 1)] (4.2) T x (n ) = [x (n ), x (n − 1),, x (n − p + 1)] the error function can be written as: e(n ) = x (n + k ) − xˆ (n + k ) = x (n + k ) − w T x (n ) (4.3) The optimum MMSE predictor is obtained minimising, with respect to the w(i ) coefficients, the Mean Square Error. In matrix form, this leads to the following linear system whose solution gives the optimum filter coefficients (Weiner-Hopf linear equation): (4.4) R x w = P(k )
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with
rx (1) rx (0) r (1) rx (0 ) x Rx = rx ( p − 1) rx ( p − 2 )
rx ( p − 1) rx ( p − 2 ) rx (0 )
(4.5)
P(k ) = [rx (k ) rx (k + 1) rx (k + p − 1)]
T
with rx (k ) = E{x (n )x (n + k )}. The matrix Rx and the vector P(k) can be easily determined by the knowledge of the autocorrelation function of the FGN process, (2.5), which represents a proper model of
actual data [7]. The filter coefficients {w(i )}i =0 can be evaluated simply resolving equation (4.4). p −1
5 THE MULTIPLEXING SCHEME The functional architecture of the proposed multiplexer, implemented with a particular FIFO scheduling discipline, is shown in Figure 5.1. The predicted number of cells evaluated by each prediction filter is passed to the priority logic management unit of the multiplexer which uses these data to state the priority of each incoming cell by means of the algorithm described in figure 5.2. The priority level permits to manage the scheduling of cells accordingly to the following strategy: • the rate reserved to each source depends on the linear prediction of the incoming traffic; • the service is strictly FIFO (First In First Out), meaning that the priority is not considered for the queueing order; • discarding of cells is made on the basis of priorities. The priority information used by the buffer management can be transferred using an internal flag added to each cell into the multiplexing system. This solution permits to maintain the functionality reserved for the CLP bit in the header of each cells.
Source 1
Source 2
Linear Predictor
Linear Predictor
Priority Logic
Source N
Linear Predictor
MULTIPLEXER
Fig 5.1 Multiplexing structure
The priority management strategy (for a generic Virtual Connection labelled by i), presented in figure 5.2, consists of the following steps: • at the beginning of each Tu, the arrival counter Ai is set to 0 and the threshold Pi is set equal to the predicted value of cells number that will arrive in the considered Tu; • at the arrival of a new cell from the considered input stream, Ai is incremented by 1; • the new value Ai is compared with the threshold Pi: if (Ai > Pi) Cell Priority = 1; • if the previous condition is not matched, the overall number of arrivals (for all the input streams) is then compared to the link capacity C: N
if ( ∑ Ai > C ) Cell Priority = 1; i =1
else Cell Priority = 0; • the cell is then sent to the queue As mentioned above the priority is used to manage cell discarding: at the arrival of a high-priority cell (i.e. priority = 0), if the buffer is full, the new cell is queued in the last position of the buffer provided
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that at least one low-priority cell is currently stored (otherwise it must be rejected). The free space in the buffer is obtained by discarding the older low-priority cell. Low priority arrivals are simply refused if the buffer is full, irrespective of the priority of cells in the buffer. New Arrival
Ai = Ai + 1
yes
A i > Pi
Prio = 1
no
∑ Ai
> C yes
Prio = 1
i
no Prio = 0 Mux. Queue
Fig 5.2 Priority Management Strategy
6 EXPERIMENTAL RESULTS To evaluate the performance of the proposed multiplexing architecture several trace driven simulations have been carried out. As reference performance parameters CLR, MWT and multiplexing gain have been chosen. CLR and MWT are considered both for the global multiplexed traffic and for each source. The latter analysis has been carried out in order to test the fairness of the analysed scheduling algorithm. The data traffic used to drive simulations was both the acquired data and synthetic FGN traces generated with the Random Midpoint Displacement (RMD) algorithm [9]. This method permits to generate selfsimilar sample paths with determined value of mean, variance and Hurst parameter, which completely characterise the FGN process. In more details simulations have been conducted under the following working conditions: • each input trace represents the number of arrivals per Tu; • the interarrival time between cells is assumed to be uniformly distributed over Tu; • the waiting queue length has been defined to guarantee a maximum delay of 100 msec. The value for the maximum delay has been chosen assuming the transport of real-time traffic, namely videoconferencing, video-telephony etc. which LRD behaviour has been proved in [7] [10]. 0.125 K=5 K = 10
Normalised Mean Square Error
0.12
0.115
0.11
0.105
0.1
0.095
0.09 2
4
6
8 10 Predictor order p
12
14
Fig 6.1 Mean Square Error
An order p=10 and a number of steps ahead k=5 have been used for the MMSE predictor. In particular the chosen value of k corresponds to an adjournment time of half second. This value is sufficient to manage the computational load necessary to the filter for determining the forecasted value. The order p permits to achieve a negligible mean square error with a limited complexity of the linear filter, as
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described in the figure 6.1, where the normalised mean square error of the linear prediction is represented versus the order p. In particular the parameter represented in the Y axis has been obtained dividing the mean square error (the error is defined in 4.3), by the mean square value of the considered trace; it represents a measure of SNR (Signal to Noise Ratio) [8]. As the picture highlights a greater order than 10 does not lead to a significant improvement of the predictor performance. In the same figure it is shown that higher value of k gives worse behaviour of the predictor. In the following, the simulation results driven by the acquired data traffic are presented highlighting a better utilisation of resources of the proposed scheduling discipline than an algorithm based on a fixed resource reservation for each ingoing traffic flow. In the second subsection the analysis of the proposed algorithm is extended to different H parameters of the ingoing traffic, supposing homogeneous sources. 6.1 Acquired data simulation analysis The proposed multiplexing scheme is characterised by a dynamic allocation of the network resources (bandwidth and buffer space) permitting to utilise the bandwidth unused by a source with low activity by sources whose activity level is momentary high. The prediction mechanism permits to establish if a source is in the high or low activity level and predicting the quantity of information that it will emit in the next Tu. These informations are used by the priority logic and the buffer management in order to share as well as possible the available resources. The efficiency of this multiplexing scheme is proved in this section comparing it with a classical scheduling discipline based on a fixed allocation of the available bandwidth. In this case for each input flow an output capacity proportional to its peak value is assigned, and a classical Weighted Round Robin algorithm has been adopted. In other words, for each incoming flow the maximum number of cells that can be sent per Tu, was fixed and proportional to its peak value. The simulation are driven considering the trace presented in Section 3 and others two sequences, whose statistical features have been analysed in [7]. In figure 6.2 the comparison among the CLR for the two strategies is plotted versus the normalised offered load (i.e. offered load to service time ratio, indicated as ρ) of the multiplexing system. 0.1
0.01
CLR
0.001
0.0001
1e-05
1e-06 50
48
46 44 Normalised Traffic Load
42
40
Fig 6.2 CLR with linear prediction (continuos line) and fixed rate allocation (hatch line).
The curves show that the dynamic multiplexing strategy give rise to significantly better performance than those achievable with the fixed rate allocation. This result is confirmed by the analysis of MWT (one of the relevant parameters when dealing with real-time applications), shown in figure 6.3. To quantify the gain of the proposed scheme with respect to the fixed allocation one, it is possible to consider the following example. Values of the MWT around 10 msec are observed when the normalised load is equal to 0.61 and to 0.85 for the fixed and proposed strategy respectively. Thus, in the case of the prediction based strategy, the same MWT can be reached with a higher network utilisation with respect to the fixed allocation.
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1
Mean Waiting time (sec)
0.1
0.01
0.001
0.0001 0.65
0.7
0.75 Normalized Offered Load
0.8
0.85
Fig 6.3 Comparison based on Mean Waiting Time with linear prediction (continuos line) and fixed rate allocation (hatch line).
On the other hand, in this particular case of actual traffic the simulation results highlighted that even with the fixed rate allocation, an output link capacity around 50% of the overall peak rate (corresponding to a normalised load equal to 0.67), is sufficient to avoid losses. This can be explained observing that, though persistence manifests itself with the different activity levels, the highest peaks of the analysed traces are relatively short in duration. Hence, in the considered scenario, the multiplexer can manage the peaks thanks to the queue buffer, without introducing any cell loss. The results of the previous simulations have been validated also using “shuffled” traces [4] with the same autocorrelation structure of the original data, confirming in this way the dependence of network performance on long-term correlation. Even a particular rearrangement of the traces, leading to the coincidence of the three peaks, it does not introduce significant differences in queueing performance. Indeed, the multiplexing strategy efficiently handles the incoming traffic: in steady-state conditions, the number of queued cells is equal to the prediction error and so the probability that a sudden spike finds a relatively empty buffer is quite high. This behaviour absorbs traffic peaks without increasing the loss probability. The various simulations showed that a higher resource utilisation can be reached when the number of multiplexed sources increases, as highlighted in table I. Number of multiplexed MWT CLR ρ Sources (sec.) 3 dynamic allocation 0.7 1.6E-3 0 3 fixed allocation 0.7 19E-3 9.3E-5 3 dynamic allocation 0.8 0.01 1.3E-4 3 fixed allocation 0.8 0.102 6.6E-3 6 dynamic allocation 0.7 6E-4 0 6 fixed allocation 0.7 16E-3 1E-3 6 dynamic allocation 0.8 5E-3 6.5E-5 6 fixed allocation 0.8 62E-3 12E-3 Table I – Simulations results for the global traffic
As in previous simulations, the results are “robust” with respect to trace shuffling (provided that LRD is preserved). Moreover, since in a static peak-rate allocation strategy the bandwidth is determined by the sum S of the peak values of all the input streams, the multiplexing gain grows as the ratio between S and the mean activity level increases. This confirms the efficiency of the proposed multiplexing scheme and the adopted multiplexing strategy.
Source 1 2 3
Proposed Scheme Fixed Strategy CLR MWT CLR MWT ρ=0.75 ρ =0.80 ρ =0.75 ρ =0.80 ρ =0.75 ρ =0.80 ρ =0.75 ρ =0.80 0 1.04e-04 0.0036 0.0102 5.07e-04 1.30e-02 0.022 0.0528 0 8.11e-05 0.0023 0.0062 7.23e-04 1.82e-02 0.058 0.208 0 4.41e-05 0.0014 0.0042 3.30e-04 9.57e-03 0.012 0.0126 Table II - Simulations results for single source
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Table II shows the simulation results obtained for the single multiplexed sources highlighting a substantially fair behaviour of both strategies. In particular it can be observed that CLR and MWT maintains values of the same order of magnitude, though the sources, as highlighted by their analysis presented in [7], are characterised by quite different statistical features, in terms of mean bandwidth as well as of burstiness. 6.2 Synthetic data simulation analysis Considering the better performance obtained with the proposed strategy with respect to the fixed one, in this section the proposed scheme is deeply analysed in order to evaluate its behaviour for different H parameter values. Each simulation refers to the multiplexing of homogeneous sources. In this set of simulations the driving traces are synthetically generated setting the value of mean and variance equal to 100 cells/Tu and 2500 cells2/Tu2 respectively for all traces; these values has been adopted according to the statistics of the considered real-data trace analysed in section 3. Moreover for each source the peak to mean ratio has been set equal to 3. Figure 6.4 shows the simulation results comparing the CLRs of global multiplexed traffic for different values of H and normalised offered load. The curves related to decreasing values of H lead to lower values of CLR. This behaviour is reasonable taking into account that, considering a fixed distribution of data traffic, a greater value of H corresponds to a higher degree of burstiness, as stated in the Introduction section. The results obtained for the MWT, depicted in figure 6.5, confirms the trends obtained for the CLR. Moreover the analysis of this figure emphasises an MWT value lower than the imposed maximum delay of about one order of magnitude. 0.01 H=0.6 H=0.7 H=0.8 H=0.9
CLR
0.001
0.0001
1e-05
1e-06 0.8
0.78
0.76
0.74 0.72 0.7 Normalised Offered Load
0.68
0.66
0.64
Figure 6.4 Cell Loss Ratio vs. ρ 0.1 H=0.6 H=0.7 H=0.8 H=0.9
MWT
0.01
0.001
0.0001 0.8
0.78
0.76
0.74 0.72 0.7 Normalised Offered Load
0.68
0.66
0.64
Fig. 6.5 Comparison based on Mean Waiting Time vs. ρ
The difference among the values of CLR with respect to H leads to decreasing Multiplexing Gain for increasing values of H, as shown in table III. In particular the Multiplexing Gain has been evaluated estimating the bandwidth, BNL, necessary to guarantee no losses for all sources managed with the proposed multiplexing scheme, and evaluating the ratio between the sum of the peak cell rate of each source and BNL. The BNL has been estimated by means of simulations.
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Multiplexing Gain
H = 0.6 H = 0.7 H = 0.8 H = 0.9 Actual Trace 1.54 1.45 1.32 1.26 2.20 Table III – Multiplexing Gain
From table III a higher multiplexing gain is shown when dealing with actual traces. This result can be explained taking into account that in this case the three traces are quite heterogeneous (i.e. they are characterised by different values of mean, variance, H and peak to mean ratio). Moreover the statistical analysis of actual data emphasises a marginal distribution different from the gaussian one of the considered FGN model. This feature together with the high variance to mean ratio of actual data imply the occurrence of higher peaks with a lower frequency leading to better resource utilisation. Finally, as in the previous subsection, the analysis of performance parameters (CLR and MWT) carried out for each source shows a fair behaviour of the proposed algorithm. Indeed the results of simulations, driven by traces characterised by a H value of 0.9 and summarised in Table IV, highlight the same order of magnitude of the two considered performance parameters for each of the three sources and for different load conditions.
Source 1 Source 2 Source 3
ρ=0.70 ρ=0.75 ρ=0.80 CLR MWT CLR MWT CLR MWT 1.33E-4 1.9E-3 6.75E-4 5.87E-3 2.28E-3 1.15E-2 1.13E-4 1.94E-3 5.92E-4 5.88E-3 1.24E-3 1.15E-2 1.03E-4 1.95E-3 8.21E-4 5.88E-3 2.8E-3 1.15E-2 Table IV - Simulations results for single source
7 CONCLUSIONS Recent measurement studies have emphasised LRD and related burstiness as key element in traffic modelling. These features can be captured in a parsimonious manner by means of models based on selfsimilar processes. Starting from these statistical features, the objective of the paper is to highlight the advantages, over the conservative method of peak allocation for each source, of a more efficient dynamic bandwidth allocation strategy with a proper Scheduling discipline in a multiplexing scheme. The proposed multiplexing architecture is able to manage the peaks and the burstiness of each traffic flow using the channel capacity left unused by the other sources, as suggested by statistical multiplexing concept adopted in ATM networks. The main advantage of the proposed scheme is its structural and algorithmic simplicity, based on the use of an extremely agile logic. The simulation studies have emphasised the efficiency of the proposed architecture in guaranteeing low value of CLR and MWT even for high level of system utilisation. In more details the analysed multiplexing scheme permits to reach high multiplexing gain, namely from a minimum value of 26% up to a maximum of 54% when dealing with homogeneous sources. Better results are obtained when loading the system with heterogeneous traces corresponding to actual data traffic. The proposed scheme has proved to be particularly efficient to manage real-time traffic due to a limited MWT introduced by resources contention. Finally the scheduling discipline has highlighted a fair behaviour among the multiplexed sources, guaranteeing them almost identical CLR and MWT values independently to the utilisation level of the system. This work represents a starting point for a deeper investigation in the field of statistical multiplexing schemes based on the use of traffic forecasting; in particular it is important to point out that more studies have to be conducted to analyse how the performance are influenced by the choice of the dimension of Tu. Further works have to be also directed in investigating the possibility of implementing different prediction strategy such as time varying and adaptive filters. ACKNOWLEDGEMENTS This work has been partially carried out in the framework of the PETERPAN (Provisioning of an Enhanced transport by Exploiting reservation in iP and Atm Networks) project, founded by the European Community commission under the ACTS research programme.
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