A. Erramilli, J. Gordon, and W. Willinger, "Applications of fractals in engineering for realistic traffic processes, " in Proceedings of the ITC-14, vol. 1a, pp. 35--44, Elsevier, Amsterdam, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....al. 6] Heyman, Tabatabai and Lakshman [7] and Grunenfelder et al. 8] Also, a different approach has been used to characterize traffic based on the notion of long term correlations. This approach is based on the theory of self similarity (see Leland et al. 9] Erramilli, Gordon and Willinger [10] and Duffield, Lewis and O Connel [11] and references therein) To compound the problem of choosing an appropriate model for ATM traffic, the ATM forum decided to standardize the following parameters: peak rate, sustainable rate, cell delay variation for the peak rate, and maximum burst length. ....

A. Erramilli, J. Gordon, and W. Willinger. Applications of Fractals in Engineering for Realistic Traffic Processes. In Proceedings of 14th International Teletraffic Congress (ITC), 35--44, 1994.

....be distorted in many practical cases and it may have no information for practical usage. 1. Introduction During the last half decade a number of extensive studies of high resolution traffic measurements from a wide range of packet networks (Ethernet LANs, CCSN SS7, ISDN, ATM) have been reported [1,3,6,9,10,15,14]. An interesting finding of these studies is the fractal nature of aggregate packet traffic which has opened a new venue in the teletraffic research. The most frequently identified properties are long range dependence and selfsimilarity. Roughly speaking a weakly stationary process is called ....

A. Erramilli, J. Gordon, and W. Willinger. Applications of fractals in engineering for realistic traffic processes. In Proc. 14th ITC, pages 35--44, Antibes Juan-les-Pins, France, 1994.

....of packets or bytes arriving in an interval of length t grows faster than O(t) as t ##. As indicated in the papers discussing tra#c measurements, the data tend to be inconsistent with the familiar tra#c models. This has led to the development of new tra#c models, e.g. involving fractals; see [18]. Within the context of existing models, an important question is: How can the models better reflect the data Toward that end, we ask: When will a stochastic fluid model have a long tail bu#er content distribution as in (1) or (3) The purpose of this paper is to show that long tail ....

A. Erramilli, Application of fractals in engineering for realistic tra#c processes, Proceedings 14th Int. Teletra#c Congress, 1994, 35--44.

.... of both classes for these four cases (solid lines) and verifies the results with simulation (shown as crosses) It should be noted that simulation of queues with regularly varying properties must be approached with great care [7] and that such simulations converge very slowly, for instance see [11] and [16] Typically the simulation results below are based on 10 million departures, and required about 1 hour to converge sufficiently, whereas the algorithm described in this paper took less than 10 seconds. We have used the version of the Pareto distribution given by 1 F x j (x) # j ....

A. Erramilli, J. Gordon, and W. Willinger. Applications of fractals in engineering for realistic traffic processes. In Jaques Labetoulle and James W. Roberts, editors, Proceedings of the 14th International Teletraffic Congress - ITC 14, volume 1a, pages 35--44. Elsevier, Amsterdam, 1994.

....the same queue, then an excessively low limit may have to be placed on the amount of aggregate traffic so that all traffic types meet their respective requirements. Even though the areas of traffic characterization and traffic mix optimization have been actively researched in the past, e.g. 1] [15]) the work on mixing traffic of different types has often been characterized by the limited setting for the investigation (e.g. shared Ethernet LANs in [1] and [2] ring LAN in [3] Also, models used for data and video traffic were not always in concordance with their actual characteristics, as ....

.... investigation (e.g. shared Ethernet LANs in [1] and [2] ring LAN in [3] Also, models used for data and video traffic were not always in concordance with their actual characteristics, as revealed by a number of measurements studies conducted for video (e.g. 8] 10] and data traffic (e.g. 11] [15]) Accordingly, the main goal of this study is to identify which traffic types can be mixed together in the same queue without incurring a significant loss in throughput; based on this identification, an appropriate mapping of traffic types to service classes When enough classes are provided, ....

A. Erramilli, J. Gordon, and W. Willinger, "Application of Fractals in Engineering for Realistic Traffic Processes," Proceedings of ITC-14, June 1994.

....FRPs and their variants should never be used in simulation, but merely that great care be taken in their use. This is of course the case whenever simulating systems in which heavy tails play a part. It is known for example that heavy tails can have drastic effects on the convergence of estimates [5, 7]. We have noted here that because the FRP generates correlations through large events, we must keep track of the number of events at each scale in order to know whether correlations on that scale are represented in the data. It follows that if we are interested in measuring any phenomena at all on ....

Ashok Erramilli, James Gordon, and Walter Willinger. Applications of fractals in engineering for realistic traffic processes. In Jaques Labetoulle and James W. Roberts, editors, Proceedings of the 12 14th International Teletraffic Congress - ITC 14, volume 1a, pages 35--44. Elsevier, Amsterdam, 1994.

....be distorted in many practical cases and it may have no information for practical usage. 1 INTRODUCTION During the last half decade a number of extensive studies of high resolution traffic measurements from a wide range of packet networks (Ethernet LANs, CCSN SS7, ISDN, ATM) have been reported [1, 3, 6, 9, 10, 14, 15]. An interesting finding of these studies is the fractal nature of aggregate packet traffic which has opened a new venue in the teletraffic research. The most frequently identified properties are long range dependence and self similarity. Roughly speaking a weakly stationary process is called ....

A. Erramilli, J. Gordon, and W. Willinger. Applications of fractals in engineering for realistic traffic processes. In Proc. 14th ITC, pages 35--44, Antibes Juan-les-Pins, France, 1994.

....is involved, as in practice such distributions must be truncated to finite variance approximations, leading to results which can be markedly truncation level dependent. Simulations must therefore be constructed very carefully, and run over long periods of time before they converge, a fact noted in [9] and [14] When, in addition, the simulation is intended to study the tail of a queue, additional care must be taken, and even longer runs are required, because the discussed difficulties are exaggerated in the tail. The main contribution of this paper is the provision of a numerical method for ....

Ashok Erramilli, James Gordon, and Walter Willinger. Applications of fractals in engineering for realistic traffic processes. In Jaques Labetoulle and James W. Roberts, editors, Proceedings of the 14th International Teletraffic Congress - ITC 14, volume 1a, pages 35--44. Elsevier, Amsterdam, 1994.

....are made for JPEG and MPEG video sequences. Obviously, it is the tail portion of F L (x) not P L ( to have substantial impact on bandwidth allocation. One important property explored in many recent traffic measurement studies is the so called self similar or fractal like behavior (refer to [9, 11, 18] for the pioneer work) A fractal power spectral function is asymptotically proportional to 1 r as frequency 0 for 0 r 1. It characterizes the traffic correlation over an infinite range of timescale. One may refer to [24, 25] for the excellent theoretical queueing analysis of fractal ....

A. Erramilli and W. Willinger, "Applications of Fractals in Engineering for Realistic Traffic Processes," in The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks (Proc. of ITC-14, France, June 1994), J. Labetoulle and J. W. Roberts (Eds.), Elsevier, Amsterdam, 1994, pp. 35-44.

....and an analysis of This research was supported by the Natural Science and Engineering Research Council of Canadian under Operating grant No. A 8450 packet traffic measurements from the Common Channel Signaling Networks(CCSN) which uses the SS7 protocol(operating at a speed of 56 Kbps)[4]. The self similar feature of traffic has serious implications for design, control and analysis of high speed networks[1,4] Merging and splitting are two basic networking operations, owing to common sharing of the resources and routing decisions. For example, ATM multiplexers perform a merging ....

....under Operating grant No. A 8450 packet traffic measurements from the Common Channel Signaling Networks(CCSN) which uses the SS7 protocol(operating at a speed of 56 Kbps) 4] The self similar feature of traffic has serious implications for design, control and analysis of high speed networks[1,4]. Merging and splitting are two basic networking operations, owing to common sharing of the resources and routing decisions. For example, ATM multiplexers perform a merging operation and demultiplexers carry out a splitting operation. ATM switching or crossconnect nodes perform both merging and ....

A. Erramilli, J. Gordon and W. Willinger, "Applications of Fractals in Engineering for Realistic Traffic Processes", Proc. of ITC-14, 1994, pp. 35-44

.... due to the drastical difference in nature between self similarity and currently held Markovian assumptions [6, 14, 28] These studies, however, have looked at somewhat isolated QOS related problems such as experimental queueing analysis [6, 10] traffic modeling [14] and parameter estimation [5] with sometimes inadequate knowledge of the statistical characteristics of self similar traffic. Little attention has yet been paid to (i) gaining a better understanding of the statistical behavior of self similar traffic [23] and (ii) determining which aspects of self similar traffic would indeed ....

A. Erramilli, J. Gordon, and W. Willinger. Applications of fractal in engineering for realistic traffic processes. In Proc. ITC-14, 1994.

....high frequency characteristics of traffic flow are certainly changed by the queueing system, but whose changes have relatively much less effect on the downstream queueing performance. The significance of low frequency traffic characteristics has also been identified in recent traffic measurement [8, 9]. In this paper, we use Markov Modulated Poisson Process (MMPP) to model the input traffic. A transition rate matrix Q describes the underlying N state Markov chain. The input rate vector fl defines the Poisson input rate in each state. Thus ( fl; Q) describe an MMPP input process. We use ....

....statistics (power spectrum) has a much more significant effect than higher order input statistics on the queueing performance, with the low frequencies exerting the greatest effect. The significance of low frequency traffic characteristics has also been identified in recent traffic measurement [8, 9]. In this paper, we use MMPP to characterize the great diversity of input power spectral properties. The MMPP input process is described by ( fl; Q) Assume that Q is diagonalizable. By spectral decomposition, Q = N Gamma1 X l=0 l g l h l ; 10) half power bandwidth B 0 (rad s) w w ....

A. Erramilli and W. Willinger, "Applications of Fractals in Engineering for Realistic Traffic Processes," in The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks (Proc. of ITC-14, France, June 1994), J. Labetoulle and J. W. Roberts (Eds.), Elsevier, Amsterdam, 1994, pp. 35-44.

....service time distributions can also have significant performance and engineering impacts, even in situations in which classical teletraffic results are known to be highly robust. An example is the blocking performance of a group of servers whose holding times can span many time scales (see [8]) Network scenarios under which this may occur are: circuit switched data applications, full service ATM networks supporting Video on Demand services. The Erlang B and Engset formulas are known to be insensitive to the service time distribution, beyond its mean value. Nevertheless, there are a ....

A. Erramilli, J. Gordon and W. Willinger. Applications of Fractals in Engineering for Realistic Traffic Processes. in: The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks (Proc. of ITC-14, Antibes Juan-les-Pins, France, June

....contributions is to add to the current efforts of gaining a better understanding of queueing performance when the input to the queue is not given by a traditional traffic process but is instead fractal in nature. For recent analytic results and simulation studies in this area, see for example [4, 8, 7, 12, 13, 26, 34]. Given the statistical significance of the finding of selfsimilarity or LRD in measured packet traffic (e.g. in case of the Ethernet data see [26] and its demonstrated significance for queueing performance, stochastic modeling of long range phenomena becomes of crucial importance. Traditional ....

A. Erramilli, J. Gordon and W. Willinger, "Applications of Fractals in Engineering for Realistic Traffic Processes", in: The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks (Proc. of ITC-14, Antibes Juan-les-Pins, France, June 1994), J. Labetoulle and J.W. Roberts (Eds.), Elsevier, Amsterdam, 1994, pp. 35-44.

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A. Erramilli, J. Gordon and W. Willinger, "Applications of Fractals in Engineering for Realistic Tra#c Processes", in: The Fundamental Role of Teletra#c in the Evolution of Telecommunications Networks #Proc. of ITC-14, Antibes Juan-les-Pins, France, June 1994#, J. Labetoulle and J.W. Roberts #Eds.#, Elsevier, Amsterdam, 1994, pp. 35-44.

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A. Erramilli, J. Gordon, and W. Willinger, "Applications of fractals in engineering for realistic traffic processes, " in Proceedings of the ITC-14, vol. 1a, pp. 35--44, Elsevier, Amsterdam, 1994.

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A. Erramilli, J. Gordon, and W. Willinger, "Applications of fractals in engineering for realistic traffic processes," in Proceedings of the 14th International Teletraffic Congress - ITC 14 (J. Labetoulle and J. W. Roberts, eds.), vol. 1a, pp. 35--44, Elsevier, Amsterdam, 1994.

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Ashok Erramilli, James Gordon, and Walter Willinger. Applications of fractals in engineering for realistic traffic processes. In Jaques Labetoulle and James W. Roberts, editors, Proceedings of the 14th International Teletraffic Congress - ITC 14, volume 1a, pages 35--44. Elsevier, Amsterdam, 1994.

No context found.

A. Erramilli, J. Gordon, and W. Willinger, "Applications of fractals in engineering for realistic traffic processes, " in Proceedings of the ITC-14, vol. 1a, pp. 35--44, Elsevier, Amsterdam, 1994.

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A.Erramilli, J.Gordon, W.Willinger, "Applications of Fractals in Engineering for Realistic Traffic Processes.", ITC Vol. 14, PP. 35-44, 1994.

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