Tibor Gyires

Lévy flights and fractal modeling of internet traffic

The relation between burstiness and self-similarity of network traffic was identified in numerous papers in the past decade. These papers suggested that the widely used Poisson based models were not suitable for modeling bursty, local-area and wide-area network traffic. Poisson models were abandoned as unrealistic and simplistic characterizations of network traffic. Recent papers have challenged the accuracy of these results in todays networks. Authors of these papers believe that it is time to reexamine the Poisson traffic assumption. The explanation is that as the amount of Internet traffic grows dramatically, any irregularity of the network traffic, such as burstiness, might cancel out because of the huge number of different multiplexed flows. Some of these results are based on analyses of particular OC48 Internet backbone connections and other historical traffic traces. We analyzed the same traffic traces and applied new methods to characterize them in terms of packet interarrival times and packet lengths. The major contribution of the paper is the application of two new analytical methods. We apply the theory of smoothly truncated Levy flights and the linear fractal model in examining the variability of Internet traffic from self-similar to Poisson. The paper demonstrates that the series of interarrival times is still close to a self-similar process, but the burstiness of the packet lengths decreases significantly compared to earlier traces.

Does the Internet Still Demonstrate Fractal Nature

The self-similar nature of bursty Internet traffic has been investigated for the last decade. A first generation of papers, approximately from 1994 to 2004, argued that the traditionally used Poisson models oversimplified the characteristics of network traffic and were not appropriate for modeling bursty, local-area, and wide-area network traffic. Since 2004, a second generation of papers has challenged the suitability of these results in networks of the new century and has claimed that the traditional Poisson-based and other models are still more appropriate for characterizing today’s Internet traffic. A possible explanation was that as the speed and amount of Internet traffic grow spectacularly, any irregularity of the network traffic, such as self-similarity, might cancel out as a consequence of high-speed optical connections, new communications protocols, and the vast number of multiplexed flows. These papers analyzed traffic traces of Internet backbone collected in 2003. In one of our previous papers we applied the theory of smoothly truncated Levy flights and the linear fractal model in examining the variability of Internet traffic from self-similar to Poisson. We demonstrated that the series of interarrival times was still close to a self-similar process, but the burstiness of the packet lengths decreased significantly compared to earlier traces. Since then, new traffic traces have been made public, including ones captured from the Internet backbone in 2008. In this paper we analyze these traffic traces and apply our new analytical methods to illustrate the tendency of Internet traffic burstiness. Ultimately, we attempt to answer the question: Does the Internet still demonstrate fractal nature?

Methodology for modeling the impact of traffic burstiness on high-speed networks

Recent results published by Leland, Taqqu, Willinger and Wilson (1994), Addie, Zukerman and Neame (see IEEE Communications Magazine, p.88-95, 1998), and by Taqqu, Teverovsky and Willinger (1995) prove that high-speed network traffic is more bursty and its variability cannot be predicted as assumed previously. According to the authors, network traffic has similar statistical properties in a certain amount of time called self-similarity. One of the consequences is that combining the various flows of data, as it happens for example in ATM virtual paths, does not result in the smoothing of traffic. Combining bursty data streams will also produce bursty combined data flow. The studies imply that the methods and models used in traditional network design require modifications. This paper presents a new methodology that estimates and measures the impact of bursty traffic on network links and network devices applying discrete event simulation techniques. By using the new methodology, we can get more accurate results in measuring the momentarily utilization of links, response time, and the queuing performance of switches and routers in a large network. We illustrate the methodology with a Comnet model.

Extension of Multiprotocol Label Switching for long-range dependent traffic: QoS routing and performance in IP networks

Abstract This paper presents an extension to the Multiprotocol Label Switching (MPLS) traffic engineering in IP networks with long-range dependent traffic. The extension provides the ability to diverge traffic flows away from the shortest path calculated by the traditional IP routing protocols into a less congested area of the network. When the traffic burstiness of a packet flow exceeds a predefined threshold, the extension calculates the cost of the traffic distribution and the effectiveness of Label Switching Routers (LSPs) to minimize the number of discarded packets. The simulation results demonstrate that the extension significantly improves the overall network performance in link utilization, port processor utilization, message delay, number of dropped packets, and buffer usage level.

Internet Traffic Modeling with Lévy Flights

Measurements of local and wide-area network traffic in the 90s established the relation between burstiness and self-similarity of network traffic. Several papers demonstrated that the widely used Poisson based models could not be applied for the past decades network traffic. If the traffic had been a Poisson process, the traffics burst lengths would have been smoothed by averaging over a long time scale contradicting with the observations of the past decades traffic characteristics. Poisson models were abandoned as unsuitable characterizations of network traffic. Recent papers have questioned the direct applicability of these results in networks of the new century. Some authors of these papers demand the revision of previous assumptions on the Poisson traffic models. They argue that as newer and newer network technologies are implemented and the amount of Internet traffic grows exponentially, the burstiness of network traffic might cancel out due to the huge number of aggregated traffic flows. Some results are based on analyses of high-speed Internet backbone links and other traffic traces. We analyzed the same traffic traces and applied novel methods to characterize them in terms of packet interarrival time. We demonstrate that the series of interarrival times is still close to a self-similar process.

Using active networking for congestion control in high-speed networks with self-similar traffic

Various papers have discussed the impact of burstiness on network congestion. Their conclusions are that congested periods can be quite long with packet losses that are heavily concentrated. Several conventional methods have been implemented to avoid congestion, such as traffic shaping, end-to-end feedback congestion control systems, etc. These methods are not responsive enough to the varying bandwidth and network delay caused by bursty traffic. The objective of the paper is to describe a new algorithm to avoid congestion without the negative effects of traditional methods. A model developed under Compuwares COMNET, the discrete event simulation system, illustrates the algorithm. The model is based on real traffic collected in an ATM network.

A heuristic algorithm for distributed control in manufacturing systems

Distributed Problem Solving Networks (DPSN) provide a means for interconnecting intelligent problem solver nodes that can solve only a part of a problem depending on their ability in the problem domain. The decomposition of a problem into subproblems, and the selection of nodes to solve them can be regarded as the generation of an AND/OR tree, and the solution of the problem as a search for a solution tree. Introducing measurements for the cost of a solution tree, we present an algorithm to find one having minimal cost under certain conditions. A Flexible Manufacturing System consisting of a network of flexible workcells is used as an example.

An extension of Integrated Services with active networking for providing quality of service in networks with long-range dependent traffic

Although todays network capacity is increasing exponentially, new applications are demanding higher and higher bandwidth. The available bandwidth always seems to be less than the new applications require. This tendency results in congested networks and packet losses, and we can expect this to continue into the foreseeable future. Congestion can be caused by several factors. The most dangerous cause of congestion is the burstiness of the network traffic. Recent results make it evident that high-speed network traffic is more bursty, and its variability cannot be predicted, as was assumed previously. It has been shown that network traffic has similar statistical properties on many time scales. Traffic that is bursty on many or all time scales can be described statistically using the notion of long-range dependency. Long-range-dependent traffic has observable bursts on all time scales. Factors such as traffic burstiness make providing quality of service (QoS) in high-speed networks increasingly important. QoS implies mechanisms to avoid congestion by allocating network resources optimally, rather than continually increasing network capacities. The objective of our paper is to present an extension of a QoS mechanism called Integrated Services (IntServ) with active networking in networks with long-range-dependent traffic.

A planning algorithm for distributed manufacturing

Distributed manufacturing (DM), downsizing, and outsourcing are becoming increasingly popular. Processes in manufacturing a product may be distributed at different sites. A production plan in such environments consists of various subplans, team coordination schedules, and decision making on task-team assignments. We present a distributed artificial intelligence (DAI) approach that enables people and computers to work cooperatively as teams in decision making. Our model is a set of loosely coupled, autonomous, communicating problem solver nodes representing a functional unit such as design, production, testing, and accounting, that participate in planning, group problem solving and negotiation. A heuristic algorithm assigns subplans to sites to optimize costs.<<ETX>>

Performance prediction of smart permanent virtual circuits in ATM networks with CACI Comnet

As networks become larger and more complex the design and management of systems become more and more difficult. New technologies, such as asynchronous transfer mode, new algorithms, and bandwidth demanding applications are implemented every day. How can network designers decide which combinations of connections, communication speeds, algorithms, and applications are the most appropriate for their business? A widely accepted answer is performance prediction through simulation. A model can be used to: evaluate various design alternatives or various operational policies; explore the behavior of proposed systems and connections before actually building them; and pre-test modifications. We apply simulation techniques to ATM networks. In an ATM network the basic data units, called cells, are routed through switched or permanent virtual circuits. A smart permanent virtual circuit is a connection that looks like a permanent virtual circuit at the local and remote endpoints with a switched virtual circuit in the middle. In an earlier paper the author (1997) presented a search algorithm for managing smart permanent virtual circuits. Our goal is to predict the performance of this search algorithm with the distributed software module of the simulation modeling system CACI Comnet.