investigate the infuence of traffic shaping at the edge nodes, as introduced by optical burst generation algorithms, on the packet drop rate at the core nodes.
Impact of Edge Traffic Aggregation on the Performance of FDL-Assisted Optical Core Switching Nodes Ahmad Rostami and Adam Wolisz Telecommunication Networks Group (TKN) Technical University of Berlin, Germany Email: {rostami|wolisz}@tkn.tu-berlin.de Abstract— In this paper we consider optical burst/packet switching networks with core nodes in which contentions are resolved by means of a hybrid scheme incorporating FDL buffering and wavelength conversion. For such a network we investigate the infuence of traffic shaping at the edge nodes, as introduced by optical burst generation algorithms, on the packet drop rate at the core nodes. In particular we focus our attention on the impact of the algorithms that generate fixed-size optical bursts, i.e., volume-based burst assembly. The simulative investigation reveals that the total number of burst flows multiplexed at the core node under consideration as well as the assembly threshold are the two most influential factors, and that the influence of these factors on the drop rate could be as high as several orders of magnitude. Additionally, it is discussed that the assembly process can negatively influence the performance of the so-called void-filling channel scheduling algorithms.
I. I NTRODUCTION Since the introduction of wavelength division multiplexing (WDM) technology in 70’s, several proposals have been investigated to utilize the increased capacity of optical links in an efficient and cost-effective manner. Nevertheless, the rather slow growth of optical switching elements has resulted in a mismatch between transmission speed of optical links and switching speed of optical devices. As a result, directly switching IP packets in the optical domain, i.e., optical packet switching (OPS), can introduce very large switching overheads. A natural solution would be to generate jumbo packets – bursts – by aggregating small-size packets. This is the main idea of optical burst switching (OBS) technique, which has been introduced and followed over the last couple of years ([1], [2]). By increasing the size of data units, the aggregation process makes it possible to relax the requirements on the speed of optical switching. Traffic aggregation, which is a key factor distinguishing OBS from OPS, has a tendency to regulate and smooth the traffic process, the amount of which depends on the policy used for burst assembly. This however changes the statistical characteristics of the input traffic that, in turn, influence the performance of the network. Therefore, it is crucial to take the impact of the assembly process into account when studying performance of an OBS network. 1 This work was supported in part by the European Commission within the Network of Excellence e-Photon/ONe+.
On the other hand, performance of a core switching node depends very much on the contention resolution strategy that is implemented in that node. In general, there are three major techniques to resolve contentions among data bursts, which frequently occur on the output ports of the core nodes. Namely, wavelength conversion, optical buffering and deflection routing [3]. In this paper our focus is on a combinational scheme that incorporates the first two techniques. Using wavelength conversion technique, the contention probability is reduced by allowing a packet arriving on a certain wavelength to be transmitted on a different wavelength, i.e., wavelengths are shared among the packets. Performance evaluation studies have widely acknowledged that wavelength conversion could very effectively reduce the loss rate; however, the performance of a node with a reasonable number of wavelength channels and converters is still far from being considered as acceptable. Accordingly, this technique has to be used in tandem with other means of contention resolution such as optical buffering. Optical buffers are usually realized by combining fixedsize fiber delay lines (FDLs) of different lengths ([4], [5]). The common outcome of recent studies has been that FDL buffering combined with wavelength conversion could be a promising approach for dealing with contention problem in burst/packet switching networks, e.g., see [3]. What is still missing in the available literatures is analysis of the impacts of traffic aggregation on the effectiveness of contention resolution techniques. In fact the same contention resolution strategy may be applied to both OBS and OPS networks, however, as mentioned before due to the traffic aggregation in the former one, characteristics of traffic inside the two networks are different. Nevertheless, most of the performance studies in the literature ignore the impact of burst assembly and assume that burst-level traffic has the same statistical characteristics as packet-level traffic – in fact it is usually assumed that bursts arrive at an OBS core node according to the Poisson process with burst lengths exponentially distributed. In [8], authors analyze the impact of burst assembly process on the performance of a bufferless OBS core node and discuss that the shaping effect of the assemblers can reduce the loss rate; however, the gain that is achieved in this way is not noticeable. Following our earlier work in [9], in this paper we inves-
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tigate impacts of the aggregation process on the performance of an OBS core node equipped with small FDL buffers and wavelength converters, and compare the results with those of an OPS node. In particular we focus our attention on the impact of the algorithms used to generate fixed-size optical bursts, i.e., volume-based burst assembly. Our simulationbased performance analysis reveals that shaping the packetlevel traffic at the edge of the network could have a sizeable positive impact – as high as several orders of magnitude – on the drop rate. Additionally, we identify that the amount of the impact depends on parameters such as the number of multiplexed burst flows, the assembly threshold, the burst size variations and the buffering capacity of the core node. The rest of this paper is structured as follows. In section II the assembly process is introduced and its impact on traffic characteristics of a single burst flow is analyzed. In section III several simulation experiments are performed, whose results demonstrate that the impact of the assembly process on the burst drop rate is really high. The work is concluded in section IV by presenting final comments. II. B URST A SSEMBLY Aggregating small-size packets into bursts through burst assembly can greatly influence performance of the network since it shapes the traffic that is injected into the network. Burst assembly is performed at every ingress node as follows. First, arriving packets, which are usually collected from low-speed links, are classified based on their destination address (and possibly the quality of service (QoS) class that they belong to). Therefore, there should be several assembly buffers to which packets are forwarded after having been classified. Then a controller has to take care of deciding when to assemble a burst out of the packets in every assembly buffer and send it out. To generate bursts, the controller treats every assembly buffer independently. In this way the traffic generated by every assembly buffer forms a separate flow of bursts whose egress nodes in OBS network are the same. In general, the controller that is responsible for generating bursts, does so by monitoring either length of the assembly buffer or the delay experienced by the packet at the head of the buffer or both of them. In this paper, we focus on the volume-based burst assembly, in which a new burst will be generated as soon as the aggregate volume of packets in the buffer exceeds a predefined threshold LT h , see Fig. 1. This threshold is usually selected with respect to maximization of utilization of resources over the network [7]. We make the usual assumptions that packets arrive to the assembly buffer according to the Poisson process with packet lengths being exponentially distributed. The assumption of
Poisson packet arrivals can be justified taking into account that burst assemblers multiplex packet-level traffic of a large number of independent micro flows. There are also some recent measurements suggesting that at sub-second time scales packet arrivals in the core network follow the Poisson process [10]. We note here that, the time scale associated with the burst assembly is usually far below a second. Additionally, it is known that the long-range dependency has very little impact on the performance of a network with small buffering capacity [11], which is indeed the case for the OBS network under study. As for the exponential assumption for distribution of input packets length, it is obvious that it has almost no impact on the burst length distribution under volume-based assembler. Furthermore, in [12] it is shown that the discrepency between interdeparture time distribution of bursts with exponentially distributed input packets length and that with trimodal input packets length of the same mean – obtained through real measurement in the Internet – is negligible. In [12], we showed that for a volume-based assembler with the assembly threshold LT h , burst length and burst interdeparture time density functions are respectively given by f (l) = µe−µ(l−LT h ) (l ≥ LT h ). f (t) =
∞ λ(λt)n −λt (µLT h )n −µLT h e . e . n! n! n=0
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where λ is the packet arrival rate and µ−1 is the average packet size. Let us now consider (1) and (2) and discuss how the assembly process changes the characteristics of packet-level traffic. Generally speaking, burst assembly has a tendency towards smoothing and regulating the traffic. The smoothing effect comes from the fact that contentions among the packets belonging to different micro flows with the same destination and QoS class are resolved by the assembly buffer. To quantify the regulating effect of the assembly buffer we compute the coefficient of variation (CoV) [13] of burst traffic at the output of a single burst assembler. By definition, coefficient of variation of a given distribution is the ratio of its standard deviation to its mean, and is a measure of variability of that distribution. Coefficients of variation of burst length and burst interdeparture time are depicted in Figs. 2 and 3, respectively, at the output of a volume-based burst assembler, with the aggregate input traffic rate of 100 Mbit/s and the average input packet size of 500 Bytes. In both graphs the assembly threshold varies from 2 KBytes to 100 KBytes. One might expect to have a pure deterministic burst size under the volume-based algorithm; however, burst lengths still show little variability, because the granularity of input IP packets is usually not fine enough to generate bursts of exactly LT h bytes long. For a packetlevel traffic the coefficients would be equal to one due to the exponential assumption. The regulating effect of the assembly process is clearly seen in the figures. For samll values of LT h the variation of both bursts length and bursts interdeparture
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time sharply reduce with the assembly threshold, however, at the higher values of LT h the CoVs reduce at a slower rate. In general, the assembly threshold tends to shape the packet-level traffic to a semi-periodic one, and in the extreme case – where LT h is selected extremely high – a single burst flow might be well approximated by a constant bit rate (CBR) traffic model. III. M ULTIPLEXING S EVERAL B URST F LOWS In the last section we showed how the assembly process changes the characteristics of a traffic flow generated by a single burst assembler. In this section we analyze the performance of a core node fed by aggregation of several burst flows, and discuss the impacts of key parameters such as the assembly
Our performance analysis is carried out on a single output port of a core switching node with W wavelength channels of rate C Gbit/s. Fig. 4 shows an abstract model for the switch under consideration. Aimed at improving the loss rate of the system, the switch supports full wavelength conversion capability, and each output port of the switch is equipped with a small-size WDM FDL buffer. The buffering unit is employed in a dedicated single-stage feed-forward architecture [4], and as shown in the figure arriving packets/bursts may undergo wavelength conversion – performed by tunable wavelength converters (TWC) – before entering the buffer, that is, every data unit that goes through the buffer makes use of the same wavelength in FDL unit and over the outgoing link. FDL buffer comprises M + 1 delay lines as (D0 , D1 , D2 , ..., DM ), with D0 = 0 and the ith delay line providing delay of i × D with (1 ≤ i ≤ M ), where D is the so-called buffer granularity. There are N ingress traffic sources that feed the considered output port. When fully loaded, each source can deliver traffic of the rate Clow Mbit/s. To facilitate studying performance of the system under different number of traffic flows, Clow is changed for each simulation experiment in a way that the aggregated traffic applied to the considered port – at the full load – is always equal to W ×C Gbit/s, i.e., Clow = W ×C × 1000/N . In order that – per wavelength – load offered to the link is ρ, loads of traffic sources are uniformly distributed in the range [2ρ − 1, 1]. In practice the total number of flows that can concurrently inject traffic into an output port of a core switch depends both on the total number of traffic sources, i.e., ingress nodes, as well as on the size of the switch itself. Nevertheless, here we assume that size of the switch does not limit the number of flows. Traffic generated by each source has the same characteristics as described in the last section, and packets are assembled into the bursts using the volumebased algorithm with the assembly threshold LT h . It is also assumed that all bursts generated by the assembler have the same offset time value. Specifically, we assume zero offset time, that allows us to only focus on the impact of the traffic aggregation and to compare the system with an OPS system. Accordingly, we neglect the pre-transmission delay that bursts may experience in burst buffers. B. Performance Analysis The model has been simulated with discrete event simulator OMNeT++ [14] by developing and incorporating additional functionalities required for OBS. To implement burst traffic generators we have used the emulators that were developed in [12]. In simulation results shown below, the method of batch means [15] has been used to estimate the mean values of drop rates. We have estimated 90% confidence intervals for the results; however, in the cases they are too narrow, they have been excluded from the curves to improve readability of the figures.
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To evaluate the impact of aggregation process on performance of the system, we have performed two sets of experiments. In both sets the performance metric that is considered is data drop (loss) rate, which is calculated as the fraction of total generated bits that are dropped at the port due to contentions. In experiment I, we suppose that total offered load to the link is 0.7, there are 8 wavelength channels each operating at 2.5 Gbit/s, the buffer granularity D is set to the average burst size1 , and arriving data units are scheduled over the channels using the latest available unscheduled channel (LAUC) scheduling algorithm [7]. We analyze the impact of varying LT h , N and M. In experiment II, we suppose that the assembly threshold is 10 KBytes, the number of multiplexed burst flows is 150 and M=2. We evaluate the system performance varying FDL buffer granularity and offered load when a void filling scheduling algorithm (LAUC-VF) [7] is used. In the following we present the results of both experiments. C. Experiment I Figs. 5-7 (a) depict drop rates of the system as a function of number multiplexed flows N for different values of the assembly threshold LT h and number of delay lines M . The results for each value of M have been compared with the drop rate of the same output port when fed by a Poisson stream of fixed-size packets, denoted in the figures by Poisson. First, it is seen that the number of multiplexed flows could have a big impact on the performance, so that the less the number of flows, the better the performance. This implies that decreasing the number of traffic flows through aggregating traffic into flows with higher capacities at the edge of the network can greatly improve the loss rate. We also observe that the positive impact of reduction in the number of flows increases with the FDL buffer capacity; i.e., decreasing the number of flows from 1000 to 50 while M=1 (Fig. 5(a)) improves the performance for around an order of magnitude, 1 Our simulations results have shown that this value of the buffer granularity results in the optimum performance for the setup considered here.
whereas doing the same while M=3 (Fig. 7(a)) results in a performance improvement of more than two orders of magnitude. Also notice that the drop rate of the system with assembled bursts is not a linear function of the number of multiplexed flows. That is, at small values of N , particularly for N ≤ 200, a small reduction in the number of flows can greatly improve the performance, however, when N increases beyond 500, the loss rate could be hardly improved by small reductions of N . Comparing the results with the case of Poisson arrivals, it is seen that the performance of multiplexed burst flows is much better than that of Poisson packet arrivals. This is an important message, implying that in an FDL-assisted architecture, burst switching outperforms packet switching. Nevertheless, when we increase the number of flows, the loss rate of the OBS system asymptotically approaches that of the Poisson model. Second, we observe that the assembly parameter also influences the loss rate of the system. Specifically, as the assembly parameter increases, the drop rate decreases. The impact is again profound at small number of multiplexed flows, where the loss rate could be affected by more than one order of magnitude, however, as we multiplex more flows, the impact reduces. Let us now discuss the reasons why assembly parameter and number of flows influence the drop rate. We observed in the last section that the assembly process affects the corresponding burst flow in two different ways. First, it resolves contentions among different packets of the same burst flow, thus makes the arrival process become smoother. Second, it reduces the variability of the burst sizes. In order to quantify the smoothing effect of the burst generation process as well as the multiplexing effect, we consider the variability of traffic as seen by the core switch. For this purpose, we have estimated the Lexis ratio [15] of distribution of number of burst arrivals at different time intervals, i.e., time scales. Lexis ratio of number of arrivals at time scale t, which serves as a measure of smoothness of the arrival process, is computed as the ratio of variance to mean of total number of burst arrivals to the system during time intervals of length t. That is, it has the same meaning for a discrete distribution that CoV does for a
continous one. To select the appropriate time scales we take into account that the number of bursts that could be absorbed by an FDL buffer depends on the number of delay lines M and wavelength channels W . That is, for the system under study, at M = 1, 2, 3 at most 8, 16 and 24 bursts could be absorbed by the buffer at high loads, respectively. On the other hand, the system has the capacity to absorb W bursts without relying on the FDL buffer. Therefore the limit of the capacity of the system can be computed as (M + 1) × W bursts. Accordingly, to estimate the Lexis ratios we select the time scales to be proportional to the system capacity. Specifically, for different values of M , the time scales are set to be equal to the times required to transmit (M + 1) × W bursts of average size. The results are depicted in Figs. 5-7 (b). Referring to the figures, it is seen that Lexis ratio of the aggregated traffic is always less than that of the Poisson traffic, which is always equal to one. This indicates that the traffic process resulted from multiplexing several burst flows is still smoother than the Poisson process. This is in accordance with some earlier works in the context of ATM networks demonstrating that superposition of periodic cell streams requires much less buffering capacity in comparison with a Poisson cell stream, e.g., see [16] and [17]. In fact, both number of multiplexed flows as well as the assembly parameter influence the smoothness of the arrival process. Specifically, for small number of flows, the assembly parameter has a significant effect on the smoothness of the arrival process, however, the impact of LT h diminishes as the level of multiplexing increases. The impact of the assembly parameter on the smoothness can be also understood intuitively by recalling that when we increase the threshold, the relative variation of the time that is required until enough packets arrive to the assembly buffer decreases. Another important issue to be considered here is the implications of smoothing burst sizes, as depicted in Fig. 2. We will investigate this in detail in the next subsection and see that a stream of fixed-size packets achieves a better performance than the same stream with variable size packets. This can explain the reason why in Figs. 5 and 6 (a) performance of the aggregated traffic for a very small range of N and LT h drops below that of the Poisson stream despite the fact that the Lexis ratio of the arrival process of the former one is smaller, see Figs. 5 and 6 (b). In fact, in the simulation model pure-fixed size packets have been generated for the Poisson model. D. Experiment II In the first experiment we considered impacts of burst assembly process on the performance of a core node with a non-void-filling scheduling algorithm. This setup allowed us to compare the performance of an OBS core node with an OPS one. Nevertheless, another important difference between the two architectures is that in an OBS network a void filling scheduling algorithm may be used in order to improve the performance of the so-called delayed reservation [1]. Void filling can also improve performance of an FDL-assisted OBS node.
More precisely, void filling not only improves the performance but also simplifies the FDL buffer design by making the loss curve become a smoother function of the buffer granularity [18]. In [19], dimensioning of FDL buffers for OBS networks in the presence of void filling has been studied; however, the analysis is performed under the assumption that burst lengths follow an exponential distribution and the arrival process is Poisson. In this subsection we focus on the same system as introduced before assuming that the link scheduling algorithm enjoys void filling capability, i.e., LAUC-VF. Of our interest is to figure out possible implications of burst length smoothing. Drop rate curves of the system with void-filling (VF) and without that (NVF) at the rather high load of 0.8 as a function of D are shown in Fig. 8, denoted by ”Assembled150, Det”. For the sake of comparison, in the same figure we have depicted the results for the case that the arrival process is Poisson and the burst lengths are either fixed or exponentially distributed, respectively denoted by ”Poisson, Det” and ”Poisson, Exp”. Referring to Fig. 8, the drop rate of exponentially distributed bursts with void filling is a decreasing function of the buffer granularity. More precisely, the loss rate decreases with D to a cut-off point, and then it becomes almost insensitive to the buffer granularity. In the system presented here, value of the cut-off point is between two and three times the average burst size. On account of this, the author in [19] argues that ”FDL delays in the range of a few mean burst transmission times yield close to optimal performance for all architectures and reservation strategies at high load”. Nevertheless, we observe that this could not be a correct choice for the case of assembled traffic. That is, in contrast to that of exponentially distributed burst length, the loss rate of assembled burst traffic is not a monotone function of the buffer granularity. Specifically, at small values of D the loss rate of the assembled bursts decreases sharper than that of exponentially distributed bursts. However, in the former case, after the drop rate reaches a minimum, increasing D has a detrimental effect on the performance. Further simulation experiments – though not shown here – suggest that depending on the number of wavelength channels and FDL buffer capacity, this phenomenon can deteriorate the performance by up to several orders of magnitude. Let us now explore the reasons of performance fluctuations under assembled burst traffic. When a delay line is used to resolve a contention between two bursts, the one that arrives later will go through a delay that is usually larger than the contention period; hence, a gap would be created between the time that last bit of the first burst is transmitted over the channel and the time the second burst starts its service. In a system with a non-void-filling strategy, gaps degrade the system performance by keeping the channels idle during some periods of time despite there are some bursts for transmission. This negative effect is sometimes referred to as the excess load. Starting from a small delay line, increasing length of the line on one hand could improve the performance, because a longer delay line could resolve contentions of longer periods, and on
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the other hand, it could deteriorate the performance, because the longer the delay line, the longer the gaps. This explains the existence of a value of D that leads to the minimum drop rate with a non-void-filling scheduling algorithm, Dnvf,opt . The exact location of Dnvf,opt. usually depends on the load [20]. With the objective of improving the link utilization, a voidfilling scheduler tries to further utilize the gaps after they have been created, by filling them with some new arrivals. To do so, a new burst of an appropriate length has to arrive to the system during the life time of a gap. This requires a match between distribution of gap size and that of burst size. That combined with the fact that duration of the gaps is a function of delay line length, imply that for fixed-size bursts no instance of void filling could occur while D < 1, as it is seen in Fig. 8. However, this is not the case for bursts with exponentially distributed lengths. Therefore, it is seen that for the setup considered here bifurcation of VF and NVF curves of exponentially distributed bursts occurs at D 0.3. The reason lies in the fact that exponentially distributed bursts have the flexibility to fill even very small size gaps. This flexibility allows them to overcome the negative effect of the gaps and to have a very smooth drop rate curve. In contrast, far smaller variation of size of assembled bursts results in a poor gap utilization. Moreover, comparing the VF and NVF curves in Fig. 8, we observe that with the assembled burst traffic, the value of D at which void filling starts to occur, i.e., Dvf 1, coincides with Dnvf,opt. . If the load is further increased, Dvf can even exceed Dnvf,opt. . This means that, when we increase D, before void filling comes into play and reduces the drop rate, the excess load overrides the positive impact of buffering. Thus, using void filling algorithms, which are also difficult to implement, under these situations makes little sense. Accordingly, in order to utilize the potential of void filling in performance improvement we should either engineer the system in a way that void filling occurs at smaller values of D, e.g., through increasing the burst length variability, or alternatively try to somehow shift Dnvf,opt. to larger values of D. In the following, we only discuss the latter one. As pointed out before, the value of Dnvf,opt. is a function of the offered load to the system. More precisely, contentions among the bursts increase with load, so that for a given system, if we increase the load, the value of Dnvf,opt. decreases. This implies that to shift the Dnvf,opt. to higher values, one can reduce the offered load to the system. To demonstrate the validity of this argument and also to see how doing so might help reducing the fluctuations in the performance, we have estimated the drop rate of the system with LAUC-VF scheduling algorithm at different load values, as depicted in Fig. 9. We observe that decreasing the load can reduce the performance deterioration, so that at load 0.6 the loss curve is almost a monotone function of D over a wide range of values. In all curves of Fig. 9, the void filling manifests its effect in the performance as soon as D reaches D 1, and since negative impact of the excess load is reduced by reducing the load, the
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void filling can really help improving the performance. To conclude this section we discuss that the fluctuations in the performance of an OBS node with void filling at high load can be considered important from different perspectives. First, it makes the design process of the whole system more complex, because the system has to be equipped with an additional mechanism that takes care of the negative effect described above. Second, in an FDL-assisted OBS architecture, this negative effect of burst assembly is translated into the reduced capacity of the network. In other words, working at the optimum operation point of the FDL buffer is usually very difficult in practice, since it depends very much on parameters such as the offered load and the average burst size; as a result, to prevent the fluctuations in the performance and achieve a
target drop rate, the offered load to the system has to be kept low. Alternatively, one might conclude that if the system is to be employed at high load, it makes little sense to use a voidfilling scheduling algorithm, and design of the system could be simplified by using a simple non-void filling algorithm, which is far easier to implement. IV. C ONCLUSION AND F UTURE W ORKS This paper provides new insights into the influence of traffic aggregation at the edge of optical networks on the performance of FDL-assisted core nodes. Specifically, it is demonstrated that the performance of an OBS core node equipped with small FDL buffers can be significantly improved – in the range of orders of magnitude of the drop rate – by decreasing the number of passing-through flows. For example, it was shown that for the system described in the text with 2 delay lines per port, reducing the number of flows from 150 to 50 could result in improvement of the drop rate by around two orders of magnitude. Additionally, we observed that the gain increases with the buffering capacity of the node. This emphasizes on the importance of employing traffic engineering approaches at the edge of the OBS domain to smooth the traffic as much as possible. Taking into account that burst aggregation is the major fundamental difference between OBS and OPS, the results presented in this paper allow us to make a comparison between the two technologies in the presence of FDL buffers. The outcome of such a comparison is that in an FDL-assisted architecture, OBS can outperform OPS owing to the fact that it inherently has a tendency to reduce the number of flows in the core by means of traffic aggregation. Moreover, it was shown that if the void-filling algorithm is employed to schedule the bursts, then additional cares have to be taken as for designing the system, because in that case the performance is very much sensitive to the burst length variations. We discussed that this sensitivity could have several different implications if it is viewed from different perspectives. In this study, we considered the volume-based burst assembly algorithm. To complement the analysis we are working on the hybrid algorithms, in which maximum aggregation delay is controlled by means of an assembly timer. This can change the characteristics of both burst interdeparture time and burst length. Also, we plan to repeat the same experiment with the measurment-based Internet traffic as input to the assembly buffers, in order to evaluate the aggregation gain in that case.
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