R. G. Garroppo, S. Giordano and M. Pagano { garroppo, giordano,

Transcription

1 ($685((76Ã29(5Ã7+(Ã83,6$Ã&$386Ã(7:25. 75$)),&Ã$'Ã48(8(,*Ã$$/<6,6 R. G. Garroppo, S. Giordano and M. Pagano { garroppo, giordano, pagano}@iet.unipi.it Department of Information Engineering University of Pisa Via Diotisalvi Pisa - Italy Tel , Fax $EVWUDFW The paper presents the analysis of traffic data acquired at ATM cell level in the access link of Engineering Faculty to the network backbone of University of Pisa. The analysis results highlight interesting issues in traffic modelling of LAN-to-LAN interconnection service. In particular, starting from an ON/OFF modelling approach, the study, carried out considering cell interarrival times, has emphasised a very significant feature: the sequences of the ON and OFF periods lengths do not follow renewal hypothesis. Indeed they present a non negligible correlation that leads to a fractal nature of the counting process (at least over several time scales). Thus, renewal hypothesis in the ON/OFF model leads to a very optimistic evaluation of queueing performance, as highlighted by the results obtained by means of the discrete event simulation of a single server queueing system. Ã,QWURGXFWLRQ The evolution of network technologies and the development of innovative services raises up new research challenges for the teletraffic engineers. Their efforts are aimed to take advantage of the high flexibility offered by packet networks, which permit to manage in an efficient way services with very different features, both in terms of resources and Quality of Service requirements. In this complex scenario new traffic control schemes are needed and traffic characterisation and modelling represent basic tools for their design. Teletraffic literature presents a lot of traffic models based on Markovian assumptions, which often permit analytical tractability in the performance evaluation of quite complex control schemes. Unfortunately, their use in traffic modelling often does not derive from the observation of actual data, but it is simply justified by sometimes unrealistic assumptions. On the other hand, most of the latest traffic studies are marked by a growing interest toward traffic data acquired in operating networks, particularly in the framework of the new services enabled by B-ISDN network, based on the ATM transfer mode. Since their beginning, these studies highlighted the bursty nature of traffic and its deep impact on network design and control. The main results were the physical interpretation of the fractal nature of traffic [Willinger97] evidenced by analysis of measured data and the foundation of a new fractal queueing theory, which recently has led to the definition of analytical bounds [Narayan][Norros]. It is worth mentioning that, for historical reasons, the pioneering studies following a measurement based approach dealt with network technologies different from ATM. In this scenario, self similarity was emphasised both in LANs as well as in WANs. Our past contribution in this field was the analysis of multimedia traffics offered by a set of departmental LANs to the LAN Bridging interface, provided by the DQDB (Distributed Queue Dual Bus) Tuscany MAN offering a connectionless service. The analysis was carried out either at frame as well as at DQDB segment level. At frame level, we could confirm the self similarity of the traffic observed in the link access to the MAN [Cinotti]. On the other hand, DQDB slot level analyses have raised up interesting issues related to the ON/OFF modelling of the acquired traffic [Giordano][Garroppo99A]. In particular, the OFF periods lengths was characterised by a wide range of variability, with a not negligible number of observations one or two order of magnitude higher than the mean value. This feature highlighted the heavy tailed nature of the inactive periods distribution and led us to consider an ON/OFF model characterised by a discrete version of Pareto distribution for the OFF periods. Analytical investigation led us to establish a simple relation between the distribution of sojourn times in each state and the Long Range Dependence of observed traffic [Garroppo99B]. In this paper we present a similar traffic analysis, but now the underlying network technology is changed. Indeed the Tuscany MAN is no more operative for the scientific community, and our Faculty LAN networks are connected to other University and Research Centres in Pisa and to the Gateway towards the Internet Community by means of a

2 campus network. In particular, considering that almost all departmental networks are very heterogeneous legacy LANs, the transport of their traffics over the ATM network is guaranteed by the MPOA (MultiProtocol Over ATM) service. In this new network scenario, we have acquired data traffic in the access link of Engineering Faculty to the ATM network, and we analyse them at two different level: AAL5-PDU and ATM cells. For sake of brevity we do not report the statistical background for Long Range Dependence features highlighted in the analysis Section; an extended collection of references can be found in [Willinger96]. Ã HDVXUHPHQWÃ6FHQDULR The measurement scenario considered in the acquisition of traffic data is represented by an access link to the backbone of the campus network of the University of Pisa. In particular, we observed the traffic offered by the Engineering Faculty to other faculties and Internet community, and vice versa. The backbone, located at SER.R.A Centre (the board managing the network services at University of Pisa), is composed by Layer 2 and Layer 3 switches (OmniStack and Omni 5 of Xylan) connected to the different Faculty networks by optical links. As it can be seen from figure 2., two faculties are connected to the SER.R.A Centre in ATM; in particular a completely meshed ATM network permits the access of the faculties of Medicine and Engineering to the SER.R.A Centre, and, thus, to the campus backbone and Internet. 524 Layer 3 Switch SMF Optical Link Different Faculty s networks Translators SMF / UTP 32 C Layer 2 Switch SMF Optical Link Ethernet LAN Router Servers Router Fast Ethernet LAN Different Departmental LANs Centillion 5 N x BaseT OMNI 5 5BH SMF Optical Link ATM Network SER.R.A Center Centillion Router Different Departmental LANs Router Ethernet LAN Fast Ethernet LAN Engineering Faculty Network Medicine Faculty Network Figure 2. Measurement Scenario of Campus Network ATM nodes are three different Nortel Networks switches. In particular: at SER.R.A Centre, there is a 5BH with 4 ports OC-3C at 55 Mbps and 4 ports Fast Ethernet connected to the ATM blackplane. These ports permit the connection of the ATM switch with the Layer 2 and Layer 3 switches of the campus network. Moreover the 5BH has Route Server functionality and presents the MPOA Server and the MPOA Client, which permit the logical connection among heterogeneous network architectures and the implementation of the MPOA service in the ATM network; at the Engineering Faculty, there is a Centillion C5 with 2 ports OC-3C at 55 Mbps and 4 ports Fast Ethernet connected to the ATM blackplane. Moreover the switch presents the MPOA Client; at the Medicine Faculty, there is one Centillion C with 2 ports OC-3C at 55 Mbps and 6 ports Ethernet connected to the ATM blackplane. Also this switch presents the MPOA Client. As it can be deduced from the network infrastructure, the ATM meshed network permits the transport of IP traffic by means of the MPOA service. 2

3 By summarising the network is obtained connecting the two Centillions to two ports of the 5BH, while the remaining ports of the Centillions are used for backup links, load balancing and load sharing among them and the central 5BH switch. The traffic data have been acquired using the ATM Broadband Test System HP E42B with a 55 Mbps optical interface, which permits to capture cells flowing through ATM links and to reconstruct the Adaptation ATM Layer Protocol Data Unit (AAL-PDU) which cells belong to. So, we could analyse traffic considering Cell level as well as Packet level. As shown in figure 2.2, to observe a meaningful amount of traffic, we inserted the measurement tool in the link connecting the Engineering Faculty with Medicine and modified the ATM campus network appropriately in order to capture all the traffic exchanged by our Faculty and the rest of campus network (either other University locations and Internet). R &HQWLOOLRQà (QJLQHHULQJ )DFXOW\ R &HQWLOOLRQà HGLFLQH )DFXOW\ +3Ã(% Figure 2.2 Connection of measurement instrument during the acquiring of data traffic à $QDO\VLVÃRIÃDFTXLUHGÃGDWDÃWUDIILF During our measurement campaigns, we acquired traffic data over both the TX and RX links, where in TX link we observe the traffic offered by Engineering Faculty to the extern and vice versa in the RX link. The HP42B is able to store in its buffer 372 cells and to reconstruct the corresponding AAL5-PDU. The length of traffic data acquired during each measurement session is not adequate for a deep statistical analysis. The method we employed to overcome this drawback consists in attaching, one after the other, traffic data acquired in successive measurement sessions. In other words, we repeat five times the measurement, storing each time the data contained in the buffer of the HP42B in a file. The obtained traffic data correspond to about 4 s of traffic in each direction of the link access. The almost equivalent measurement period time in the two series is due to an almost equal mean traffic, as highlighted by the mean values presented in the counting process analysis (see Section 3.3). For sake of brevity, all the plots shown in the following are related to the TX trace since very similar results are obtained in RX trace. The raising problem is the effect of the attaching procedure on the accuracy of the analysis results. To support the correctness of our approach, we point out that it logically corresponds to the external shuffling of the underlying traffic process. In other words, we can consider the whole traffic process as a sequence of different blocks; then we perform external shuffling and consider only the first 4 s which corresponds to data blocks we actually acquired. The correctness of this procedure lies in the randomness of the times between two consecutive measurements; however in this hypothesis we have to limit the correlation horizon of the counting process to a fraction of the mean duration of measurement block, i.e. about 6 s. Hence, we only dealt with the process memory under s. On the other hand, the analysis of cell interarrival times is not influenced by shuffling since time dynamics of cells are much lower than the length of a single acquisition block. Furthermore, the stationarity hypothesis, assumed for the traffic process during the whole time of the data acquisition in each direction, is fundamental for the robustness of analysis. To support this hypothesis, we observe that the time needed to acquire and store the successive 5 cells blocks was of about 2 min and hence it is reasonable to assume that the overall statistics of the traffic do not change over such a time interval. Ã$7Ã&HOOVÃ$QDO\VLV The first analysis is directed to recognise the presence of different time scales in the sequences describing interarrival times of acquired ATM cells. To this aim we consider textured plots obtained printing cells arrivals in consecutive time intervals of size Tu (for each Tu we plot the difference between the actual arrival time and the beginning of the considered interval). Figure 3. presents this analysis for Tu= µs, which highlights the clustered arrivals of cells, alternated by periods of traffic inactivity with length of the order of ms; this ON/OFF behaviour will be investigated in more details in Section 3.4. Figure 3.2 reports the textured analysis with Tu= µs, which confirms the ON/OFF behaviour and at the same time evidences a regular emission of cells during the transmission of AAL5-PDU. In particular, we can observe that the cell interarrival times during the ON periods are almost constant and equal to the cell transmission time in the OC-3C link. This is due to the absence of traffic policing in the switches which simply manage MPOA traffic using UBR traffic category. 3

4 Time (s) Time (s) Figure 3. Textured plot with Tu= µs Figure 3.2 Textured plot with Tu= µs The same analysis obtained with a Tu of ms is shown in figure 3.3. It evidences packets arrivals by means of segments representing burst arrivals of cells belonging to the same or contiguous AAL5-PDUs. The absence of stripes filling the entire plot highlights the presence of a packet time scale and, in general, of an activity period lower than ms, confirmed in the ON/OFF and in the AAL5-PDU analysis presented in the following Sections Time (sec.) Figure 3.3 Textured plot with Tu= ms To identify the distribution of cells arrivals within a single AAL5-PDU, we extract all the interarrival times lower than µs and we evaluate their histogram (see figure 3.4). The latter clearly shows an high concentration of cell interarrival times near to 2.7 µs, which corresponds to cell transmission time in the OC-3C link. Moreover we can observe samples with a slightly different values (exact values are 3. and 3.2 µsec.) which can be related to a different position of cells with respect to the overhead section of OC-3C frame. Other observations are located at around two and three times the cell time (i.e. at 5.4 and 8. µsec.)..... TRCOND.DDP e-5 2e-6 3e-6 4e-6 5e-6 6e-6 7e-6 8e-6 9e-6 Time (s) Figure 3.4 Histogram of Cells Interarrival Times within a µs time period 4

5 In figure 3.5 we can observe the histogram of the remaining interarrival times, i.e. those greater than µs. These are related to the interarrival times among AAL5-PDUs, which can be divided in two different subsets: consecutive (their histogram is shown in figure 3.6, which represents a zoom of figure 3.5) and non consecutive (see figure 3.5) AAL5- PDUs. The 86% of interarrival times are under µs corresponding to the percentage of cells transmitted with a speed near PCR = 55 Mbps. On the other hand, a meaningful percentage of remaining cells are sent with interarrival times of the order of. ms (from figure 3.6 we can note a lot of observations with a percentage of %), which correspond to a transmission rate of few Mbps.. TRCOFFD.DDP. TRCOFFD.DDP.... e Time (s). 5e Time (s) Figure 3.5 Histogram of Cells Interarrival Times greater than µs Figure 3.6 Zoom of histogram of Cells Interarrival Times greater than µs The analysis of the Normalised Autocovariance Function (NAF) of interarrival times, plotted in Log-Linear scale in figure 3.7, emphasises the presence of a certain degree of correlation that does persist for many lags, and thus it can not be neglected. As can be noted the autocovariance assumes values near to -2 very quickly, but maintains this values too for far samples. This, as shown later, will have an implication on the correlation structure of the counting process, and it is a direct consequence of the bursty nature of observed traffic. Normalised Autocovariance Function.... e-5 "trcint.cor" e Lag, n Figure 3.7 Autocovariance Function of Cells Interarrival Times Ã$$/3'8Ã$QDO\VLV In this subsection we present results of the analysis at AAL5-PDU level. Tables 3. and 3.2 present some statistical indexes related to AAL5-PDU lengths and interarrival times respectively. In particular in Table 3. we can observe that the maximum AAL5-PDU length is strictly related to the Maximum Transfer Unit (MTU) of Ethernet LAN and the structure of LAN Emulation (LANE) header. Indeed 56 bytes is the sum of 5 (MTU of legacy Ethernet LAN) and 6 (header of LANE frame). The histogram of AAL5-PDU lengths is reported in figure 3.8, where we can observe an high percentage of AAL5-PDU with length in the interval [62, 56], which correspond to the minimum and the maximum packet size allowed in Ethernet legacy LAN (it is relevant to note that the length of legacy Ethernet frame is reduced by two bytes when is transported over LANE). On the other hand few samples under 62 bytes are also observed 5

6 (the exact values are 8, 2, 6 and 24) which are related to signalling information; indeed they use only the virtual channel /5 and /8, which are active also when no user data are transported. Trace Num. Samples Mean (s) Dev std Min (s) Max (s) TX RX Table 3. Statistical Indexes of AAL5-PDU Length.... e-5 Trace Mean (s) Dev std Min (s) Max (s) TX * RX * Table 3.2 Statistical Indexes of AAL5-PDU Interarrival Times PDULEN.DDP AAL5-PDU size (Bytes) Figure 3.8 Histogram of AAL5-PDUs Lenghts.... e-5 PDUINT.DDP Interarrival Time (s) Figure 3.9 Histogram of AAL5-PDUs Interarrival Times Table 3.2 shows a minimum interarrival time of 3 µs, i.e. close to the cell transmission time. Hence, we can relate this observation to single cell AAL5-PDUs, which are transmitted consecutively to another. In the same table, we can observe the relatively large value of the maximum interarrival time, which determines, as emphasised by the textured analysis in the previous section, OFF periods of around ms. Figure 3.9, showing the histogram of AAL5-PDU interarrival times, presents the same behaviour of figure 3.5, as can be easily deduced considering that cell interarrival times higher than ms correspond to arrivals of EOM (End of Message) and BOM cells (Beginning of Message) of successive AAL5-PDUs. Ã&RXQWLQJÃ3URFHVVÃ$QDO\VLV The counting process is obtained considering the number of cell arrivals observed during nonoverlapping times intervals, Tu, of different size:, and ms. In figures 3. and 3., we show the pattern of counting process with Tu equal to and ms respectively. In the first figure, which shows only a portion of the entire data trace, we can observe a pattern characterised by periods where the number of acquired cells presents higher values with respect to the mean. This behaviour is a clear evidence of the bursty nature, that at higher time scale does not decrease. This statement is supported by figure 3., which shows as at higher time scales the traffic pattern is not smoother, but maintains its bursty feature. Number of Cells TRCMSU.TXT Time (Tu= ms) Figure 3. Counting Process with Tu= ms 6 Number of Cells TRCMS Time (Tu= ms) Figure 3. Counting Process with Tu= ms

7 The bursty nature of traffic over 3 different time scales can be strictly related to the correlation properties of acquired data. We cannot analyse higher time scales since the relative low number of data acquired, while analysis on scales lower than ms is less meaningful since these are influenced by the elementary data unit transported by the network, which is logically represented by a LAN packet. Normalised Autocovariance Function TRCMS.COR Lag, n Figure 3.2 Normalised Autocovariance Function of counting process with Tu= ms Normalised Autocovariance Function TRCMS.COR Lag, n Figure 3.3 Normalised Autocovariance Function of counting process with Tu= ms Figures 3.2 and 3.3, showing the NAF for the counting process with Tu equal to and msec., highlight the presence of a non negligible correlation between samples until an horizon of sec. (lag in figure 3.2 and in figure 3.3). In particular although figure 3.2 seems to show a correlation very close to zero after the lag (i.e. sec.), single values are low but almost always positive: hence they are not negligible and can be a symptom of Long Range Dependence. This is highlighted by figure 3.4, which shows the Variance Time (VT) plot of the considered data trace. From the figure, we clearly observe a slope of VT curve that is different from minus corresponding to Short Range Dependent processes. TRCMS.VT H=.7 Variance. Aggregation level, m Figure 3.4 Variance Time plot of counting process with Tu= ms Figure 3.5 and 3.6 present, in Log-Linear scale, the histograms of counting processes with Tu equal to and ms respectively. From figure 3.5, we can deduce the absence of heavy tailed distribution on time scale of ms and, thus, the slope of Variance Time plot gives directly an estimation of H (considered as a measure of LRD). The result of this analysis lead us to an H parameter equal to.7, which will be also confirmed by the multiscale analysis presented for statistical trace comparisons in the next Section. 7

8 TRCMS.DDP. TRCMS.DDP..... e Cells/Tu Figure 3.5 Histogram of Counting Process for Tu= ms Cells/Tu Figure 3.6 Histogram of Counting Process for Tu= ms In table 3.3 we summarise some statistical indexes estimated from the counting process. In particular we can note the high peak-to-mean ratio observed (equal in two traces to about 5) and a variation coefficient (standard deviation to mean ratio) near to (about.3) which strongly tear down the heavy tailed hypothesis for the marginal distribution. Moreover we can observe a very low link utilisation with peak values of about Mbps, which is very smaller than the 55 Mbps of OC-3C capacity. Trace Mean Num. of Cells in Tu Variance Num. of Cells in Tu Max Number of Cells in Tu Mean Traffic Rate (Kbps) TX RX Table 3.3 Statistical Indexes of Counting Process with Tu= ms Ã2Q2IIÃ$QDO\VLV As shown in textured plots of Section 3., acquired data can be analysed with an ON/OFF approach, where the model is supposed to be in the ON state when cell interarrival times are lower than the double of cell transmission time at the maximum link speed. This threshold permits a tolerance in the definition of ON state that avoids to switch state frequently, in particular also in case of almost consecutive packet arrivals. We tested that this assumption does not introduce sensible variation in the relevant statistical features highlighted in this Section, but affects only mean values. The statement is true also for other threshold values (provided that thresholds of few cell transmission times are assumed), but our assumption presents the advantage of reducing the approximation in the generation of cell arrivals in the ON periods. The ON/OFF interpretation of acquired data leads us to the definition of an apparently simple ON/OFF model for a single traffic flow multiplexed in the access node of an ATM backbone. Complementary Probability.... e-5 e-6 TRCOFF.CP Period Length (s) Figure 3.7 Complementary probability of OFF periods lengths Complementary Probability.... e-5 e-6 TRCON.CP 5e Period Length (s) Figure 3.8 Complementary probability of ON periods lengths Figures 3.7 and 3.8 present the estimated complementary probability (CP) for the OFF and ON periods respectively. The linear behaviour of CP curve in Log-Linear scale highlights a nearly exponential distribution for the OFF periods. 8

9 The moving away from the linear behaviour is observed only for low values of CP, where few samples are available (the amount of ON/OFF periods observed are 9474). On the other hand, the CP for the ON periods have an irregular behaviour, not traceable to any particular distribution model. We can only state that heavy tailed distribution hypothesis is not verified. Normalised Autocovariance Function TRCOFF.COR Lag, n Figure Normalised autocovariance function of OFF periods lengths Normalised Autocovariance Function TRCON.COR Lag, n Figure Normalised autocovariance function of ON periods lengths Hence at cell level, the interarrival time process can be characterised by an ON/OFF model with light tailed distribution of sojourn times in each state. This seems to be in contrast with the LRD behaviour observed for the counting process; as a matter of fact, the latter can be related to correlation in the ON and OFF periods lengths sequences. To confirm this hypothesis, in figure 3.9 and 3.2, we show the NAF of the two considered series, which highlight a relative strong correlation among periods lengths. In particular in both cases periods having distance of 2 samples are correlated in a manner not completely negligible. To analyse the impact of this correlation in the ON and OFF periods lengths sequences on counting process, we carry out a simple experiment. We consider ON and OFF periods lengths sequences and generate a first trace (referred as PR, Pseudo ) where interarrival times in the ON periods are generated approximating the histogram of arrivals observed in the actual trace (first seven points of histogram presented in figure 3.4). In this trace we maintain the correlation in the sequences of ON and OFF periods lengths. Another trace (referred as, No Correlation in ON and OFF Periods lengths sequences) is obtained generating cells arrivals in the ON periods as in PR trace, but in this case we destroy the correlation structure in both periods lengths sequences shuffling their samples (see figures 3.2 and 3.22). Normalised Autocovariance Function "off6shc" Lag, n Figure 3.2 Normalised autocovariance function of shuffled OFF periods lengths Normalised Autocovariance Function "on6shc" Lag, n Figure 3.22 Normalised autocovariance function of shuffled ON periods lengths 9

10 PR H=.5 Variance. Aggregation Level, m Figure 3.23 Comparison of VT statistic among traces The resulting counting processes highlight a very different behaviour of trace with respect to the and PR. The VT analysis, shown in figure 3.23, highlights that, removing the correlation in the ON and OFF periods lengths sequences of ON/OFF model, the LRD of counting process disappears. As a further test for the LRD behaviour of, and PR traffic traces, we consider wavelet analysis which is emerging as one of the most powerful tools for investigating self-similar features. Briefly we recall that the basic idea behind this approach is the assumption of a /f γ (where γ=2h-) decay for the power spectral density, which leads to a direct relation between the amounts of energy associated to the different resolution layers: Γ m =2 mγ Γ where Γ m is the energy at the resolution P, at least over an adequate range of scales [Abry]. The lower resolution layers (higher values of P) contain few transformed coefficients and, consequently, the estimation of Γ m becomes quite noisy; the edge effects (finite length sequences) and the higher correlation between wavelet coefficients [Flandrin] degrade even more the estimate. As far as the lower layers are concerned, the problems are related to the non-ideal (i.e. not /f γ -like) behaviour of spectral density at higher frequencies. This feature is not surprising since LRD property only determines the decay rate of the autocorrelation function UN as N or, equivalently, the behaviour of the power spectral density 6I as I. The estimations (see figure 3.24 for comparisons) have been carried out considering the layers from 4 to 2. The following conclusions can be drawn from wavelet analysis: the trace presents LRD with H.7; PR synthetic trace preserves the same autocorrelation decay, as it could be expected, since it differs from the original trace only for the distribution of cells inside each ON period; the shuffling of the periods lengths kills their correlation and this leads to a SRD sequence (the sojourn times in each period are not heavy tailed distributed that, as shown in previous analysis [Garroppo99B], leads to LRD features). Log2 (Mean Energy) PR Scale Figure 3.24 Wavelet analysis with Daubechies 8 basis

11 Ã4XHXHLQJÃ$QDO\VLV In this section we investigate by means of discrete event simulations how the statistical features of traffic data effect the queueing performance. The simulation scenario is represented by a very simplified model, namely a single server queue with deterministic service rate and finite buffer size. In this way we can directly relate meaningful performance parameters (such as cell loss probability and mean queueing delay) to the memory of the queueing system without having to take into account the effects of specific ATM functions. In particular, we considered two different values of the buffer size corresponding to a maximum delay of. and s at a normalised traffic load (NTL) equal to.9, where NTL is defined as the ratio between the cell service time and the mean interarrival time. Figures 3.25 and 3.26 plot the cell loss probability as a function of NTL and a similar analysis for the mean queueing delay in reported in figures 3.27 and Two main conclusions can be drawn from the analysis of these simulation results: The and the PR traces exhibit the same behaviour as a confirm of the little relevance of correlation of cell arrivals inside ON periods (hence, in the following analyses we fed the queue only with the and traces); The effects of the LRD increase with the buffer size (note that for a queue length of s no losses are experienced with the trace) and, at least if the latter is long enough, also with NTL (see the behaviour of the mean delay curves in figure 3.28). Cells Loss Ratio.... e-5 PR Cells Loss Ratio... PR e Normalised Traffic Load Figure 3.25 Buffer Size = ms Normalised Traffic Load Figure 3.26 Buffer Size = s. Mean Delay (s). Mean Delay (s) Normalised Traffic Load Figure 3.27 Buffer Size = ms Normalised Traffic Load Figure 3.28 Buffer Size = s To further highlight the relevance of the correlation inside the ON and OFF periods we also analysed the time evolution of buffer occupancy for three different values of NTL. The differences are particularly remarkable for higher values of NTL and can be analysed according to three different approaches: Temporal behaviour: as shown by figure 3.29, the trace determine higher queue lengths and the presence of relatively long periods in which the queue occupancy level is significatively higher than its mean value; Marginal distribution: the higher values of the queue length with the trace can be easily seen from the different tails of the probability mass function in figure 3.3;

12 Correlation inside the queue lengths: the NAF (see figure 3.3) show an high correlation level when the queue is fed by the trace as a consequence of the persistence properties of LRD traffics (as reported in the previous sections, the input traffic is LRD with H=.7). In other words, the correlation inside the ON and OFF periods lengths sequences is quite relevant and cannot be neglected in the proper modelling of ATM traffic at cell level since it determines the LRD properties exhibited by the counting process and, as a consequence, has a deep impact on queueing behaviour as highlighted by the simulation results described in this section Time (.5 ms) Buffer Size = s - NTL =.3 Trace Time (.5 ms) Buffer Size = s - NTL =.3 - Trace Time (.5 ms) Buffer Size = s - NTL =.5 Trace Time (.5 ms) Time (.5 ms) Buffer Size = s - NTL =.5 - Trace Time (.5 ms) Buffer Size = s - NTL =.8 Trace Buffer Size = s - NTL =.8 Trace Figure Temporal behaviour of the queue length 2

13 .... e e-5 e-6 e Buffer Size = ms - NTL =.3 Buffer Size = s - NTL = e-5 e Buffer Size = ms - NTL =.5 Buffer Size = s NTL =.5... e-5.. e-5. e Buffer Size = ms - NTL =.8 Buffer Size = s - NTL =.8 Figure Probability Mass Function of the queue length 3

14 Noralised Autocovariance Function Noralised Autocovariance Function Noralised Autocovariance Function Lag n (To=.5 ms) Noralised Autocovariance Function Lag n (To=.5 ms) Buffer Size = ms - NTL =.3 Buffer Size = s - NTL = Lag n (To=.5 ms) Noralised Autocovariance Function Lag n (To=.5 ms) Buffer Size = ms - NTL =.5 Buffer Size = s - NTL = Lag n (To=.5 ms) Noralised Autocovariance Function Lag n (To=.5 ms) Buffer Size = ms - NTL =.8 Buffer Size = s - NTL =.8 Figure NAF of the queue length Ã&RQFOXVLRQV This work presents a measurement campaign carried out over the ATM campus network of the University of Pisa under standard working condition. Traffic data have been analysed both at ATM cell and AAL5-PDU level, in order to understand relationships between statistical features at these different levels. Considering the counting process, it is worth mentioning how the traffic generated by our Departmental LANs preserves the same long memory properties previously observed in 994 when the access network was a DQDB MAN [Cinotti], irrespective of increased number of users, the evolution of applications and the change in the network technology. Moreover, the paper experimentally confirms the robustness of the physical interpretation of traffic fractal features in the access of a WAN network [Kurtz]. The analysis at ATM cell levels aims to the ON-OFF characterisation of the offered traffic. As a key result, we highlight the presence of correlation in the sequences describing the sojourn time in each state and its effects over the counting process. Since the distributions of the sojourn times are light tailed, it is the presence of such a correlation that 4

15 determines the LRD behaviour of the counting process over higher time scales. This statement is easily verified by means of the shuffling procedure, as described in the paper. Furthermore, the observed correlation structure has a deep impact on queueing performance, as supported by the comparison of results obtained driven the simulations by the acquired data and synthetic trace, generated destroying the observed correlation by means of a shuffling procedure. As a consequence, renewal theory can be inadequate when dealing with actual broadband traffics. The latter conclusion is quite in contrast with our findings when considering the traffic offered to the DQDB MAN: in that scenario the LRD at Ethernet level implied the heavy-tailed distribution of the OFF periods length, while the renewal assumption was accepted [Garroppo99A]. A physical interpretation of these different behaviours is not easy and requires further investigation. The most reasonable explanation is represented by the effects of the different network structures (ATM vs. DQDB). 5HIHUHQFHV [Abry] P. Abry and D. Veitch, "Wavelet Analysis of Long Range Dependent Traffic", IEEE Transactions on Information Theory, pp. 2-5, Vol. 44, N., January 998 [Cinotti] M. Cinotti, E. Dalle Mese, S. Giordano, F. Russo Long-range dependence in Ethernet traffic offered to interconnected DQDB MANs Proc. of the IEEE ICCS 94 Singapore 4-8 Nov. 994 [Flandrin] P. Flandrin, "Wavelet Analysis and Synthesis of Fractional Brownian Motion", IEEE Transactions on Information Theory, pp. 9-97, Vol. 38, N. 2, March 992 [Garroppo99A] R. G. Garroppo, S. Giordano, M. Pagano Modelling DQDB Multimedia Sources at cell/segment level, in F. De Natale and S. Pupolin eds., Multimedia Communications, pp , Springer-Verlag, London 999 [Garroppo99B] R.G. Garroppo, S. Giordano, M. Isopi, M. Pagano, "On the Implications of the OFF Periods Distribution in two-state Traffic Models" IEEE Communications Letters, Vol. 3, N. 7, pp , July 999 [Giordano] S. Giordano Searching for Fingerprints of Broadband Traffic, Invited Speech in "Hot Topic Session on Traffic Characterization", ITC 5, Washington, DC, June 997 [Kurtz] T.G. Kurtz Limit theorems for workload input models in F.P. Kelly, S. Zachary and I. Ziedins eds., Stochastic networks: Theory and Applications in Telecommunication Networks, Oxford University Press, Oxford, 996 [Narayan] O. Narayan Exact Asymptotic Queue Length Distribution for Fractional Brownian Traffic Advances in Performance Analysis, Vol. N., pp , March 998 [Norros] I. Norros A storage model with self-similar input in Queueing Systems, Vol. 6, pp , 994 [Willinger97] W. Willinger, M.S. Taqqu, R. Sherman, and D.V. Wilson Self-Similarity Through High- Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level (Extended Version), IEEE/ACM Transactions on Networking 5():-6, May 997 [Willinger96] W.Willinger, M.S. Taqqu, A. Erramilli A bibliographical guide to self-similar traffic and performance modelling for modern high speed networks, in F.P. Kelly, S. Zachary and I. Ziedins eds., Stochastic networks: Theory and Applications in Telecommunication Networks, Oxford University Press, Oxford, 996 5