In this paper, improved algorithms for radix-4 and radix-8 FFT are presented. This is achieved by re-indexing a subset of the output samples resulting from the conventional decompositions in the radix-4 and radix-8 FFT algorithms. These modified radix-4 and radix-8 algorithms provide savings of more than 33% and 42% respectively in the number of twiddle factor evaluations or accesses to the lookup table compared to the corresponding conventional FFT algorithms without imposing any additional complexity.

Improved radix-4 and radix-8 FFT algorithms

A method and system are provided for modeling network traffic in which an artificial neural network architecture is utilized in order to intelligently and adaptively model the capacity of a network. Initially, the network traffic is decomposed into a plurality of categories, such as individual users, application usage or common usage groups. Inputs to the artificial neural network are then defined such that a respective combination of inputs permits prediction of bandwidth capacity needs for that input condition. Outputs of the artificial neural network are representative of the network traffic associated with the respective inputs. For example, a plurality of bandwidth profiles associated with respective categories may be defined. An artificial neural network may then be constructed and trained with those bandwidth profiles and then utilized to relate predict future bandwidth needs for the network.

Methods and system for modeling network traffic

Nowadays, data centers are becoming increasingly dynamic due to the common adoption of virtualization technologies. Systems can scale their capacity on demand by growing and shrinking their resources dynamically based on the current load. However, the complexity and performance of modern data centers is influenced not only by the software architecture, middleware, and computing resources, but also by network virtualization, network protocols, network services, and configuration. The field of network virtualization is not as mature as server virtualization and there are multiple competing approaches and technologies. Performance modeling and prediction techniques provide a powerful tool to analyze the performance of modern data centers. However, given the wide variety of network virtualization approaches, no common approach exists for modeling and evaluating the performance of virtualized networks.
The performance community has proposed multiple formalisms and models for evaluating the performance of infrastructures based on different network virtualization technologies. The existing performance models can be divided into two main categories: coarse-grained analytical models and highly-detailed simulation models. Analytical performance models are normally defined at a high level of abstraction and thus they abstract many details of the real network and therefore have limited predictive power. On the other hand, simulation models are normally focused on a selected networking technology and take into account many specific performance influencing factors, resulting in detailed models that are tightly bound to a given technology, infrastructure setup, or to a given protocol stack.
Existing models are inflexible, that means, they provide a single solution method without providing means for the user to influence the solution accuracy and solution overhead. To allow for flexibility in the performance prediction, the user is required to build multiple different performance models obtaining multiple performance predictions. Each performance prediction may then have different focus, different performance metrics, prediction accuracy, and solving time.
The goal of this thesis is to develop a modeling approach that does not require the user to have experience in any of the applied performance modeling formalisms. The approach offers the flexibility in the modeling and analysis by balancing between: (a) generic character and low overhead of coarse-grained analytical models, and (b) the more detailed simulation models with higher prediction accuracy.

The contributions of this thesis intersect with technologies and research areas, such as: software engineering, model-driven software development, domain-specific modeling, performance modeling and prediction, networking and data center networks, network virtualization, Software-Defined Networking (SDN), Network Function Virtualization (NFV). The main contributions of this thesis compose the Descartes Network Infrastructure (DNI) approach and include:

• Novel modeling abstractions for virtualized network infrastructures. This includes two meta-models that define modeling languages for modeling data center network performance. The DNI and miniDNI meta-models provide means for representing network infrastructures at two different abstraction levels. Regardless of which variant of the DNI meta-model is used, the modeling language provides generic modeling elements allowing to describe the majority of existing and future network technologies, while at the same time abstracting factors that have low influence on the overall performance. I focus on SDN and NFV as examples of modern virtualization technologies.
• Network deployment meta-model—an interface between DNI and other meta- models that allows to define mapping between DNI and other descriptive models. The integration with other domain-specific models allows capturing behaviors that are not reflected in the DNI model, for example, software bottlenecks, server virtualization, and middleware overheads.
• Flexible model solving with model transformations. The transformations enable solving a DNI model by transforming it into a predictive model. The model transformations vary in size and complexity depending on the amount of data abstracted in the transformation process and provided to the solver. In this thesis, I contribute six transformations that transform DNI models into various predictive models based on the following modeling formalisms: (a) OMNeT++ simulation, (b) Queueing Petri Nets (QPNs), (c) Layered Queueing Networks (LQNs). For each of these formalisms, multiple predictive models are generated (e.g., models with different level of detail): (a) two for OMNeT++, (b) two for QPNs, (c) two for LQNs. Some predictive models can be solved using multiple alternative solvers resulting in up to ten different automated solving methods for a single DNI model.
• A model extraction method that supports the modeler in the modeling process by automatically prefilling the DNI model with the network traffic data. The contributed traffic profile abstraction and optimization method provides a trade-off by balancing between the size and the level of detail of the extracted profiles.
• A method for selecting feasible solving methods for a DNI model. The method proposes a set of solvers based on trade-off analysis characterizing each transformation with respect to various parameters such as its specific limitations, expected prediction accuracy, expected run-time, required resources in terms of CPU and memory consumption, and scalability.
• An evaluation of the approach in the context of two realistic systems. I evaluate the approach with focus on such factors like: prediction of network capacity and interface throughput, applicability, flexibility in trading-off between prediction accuracy and solving time. Despite not focusing on the maximization of the prediction accuracy, I demonstrate that in the majority of cases, the prediction error is low—up to 20% for uncalibrated models and up to 10% for calibrated models depending on the solving technique.
In summary, this thesis presents the first approach to flexible run-time performance prediction in data center networks, including network based on SDN. It provides ability to flexibly balance between performance prediction accuracy and solving overhead. The approach provides the following key benefits:
• It is possible to predict the impact of changes in the data center network on the performance. The changes include: changes in network topology, hardware configuration, traffic load, and applications deployment.
• DNI can successfully model and predict the performance of multiple different of network infrastructures including proactive SDN scenarios.
• The prediction process is flexible, that is, it provides balance between the granularity of the predictive models and the solving time. The decreased prediction accuracy is usually rewarded with savings of the solving time and consumption of resources required for solving.
• The users are enabled to conduct performance analysis using multiple different prediction methods without requiring the expertise and experience in each of the modeling formalisms.
The components of the DNI approach can be also applied to scenarios that are not considered in this thesis. The approach is generalizable and applicable for the following examples: (a) networks outside of data centers may be analyzed with DNI as long as the background traffic profile is known; (b) uncalibrated DNI models may serve as a basis for design-time performance analysis; (c) the method for extracting and compacting of traffic profiles may be used for other, non-network workloads as well.

Flexible Modeling of Data Center Networks for Capacity Management

An improved radix-16 decimation-in-frequency (DIF) FFT algorithm is proposed by introducing new indices for some of the output sub-sequences resulting from the conventional radix-16 DIF decomposition of the DFT. This improved radix-16 DIF FFT algorithm achieves savings of more than 46% in the number of twiddle factor evaluations or accesses to the lookup table and address generations compared to the conventional radix-16 DIF FFT algorithm. These savings are achieved without imposing any additional computational or structural complexity in the algorithm.

An improved radix-16 FFT algorithm

Dynamic admission control is a very important mechanism that aims, not only to check resources availability, but also to verify QoS constraints satisfaction. In this paper, we propose a new admission control mechanism in MPLS-based packet-switched networks. This admission control mechanism satisfies delay constraints for all the network connections. The admission control mechanism is based on solving a mixed linear programming model which is shown NP-hard. As real instances are relatively small sized (20 to 30 nodes), an exact resolution using the CPLEX software suite can be done. Numerical results are then given and discussed.

A Mathematical Model for the Admission Control Problem in MPLS Networks with End-to-End delay guarantees

On-line traffic, including conversational calls, videoconference calls, and live video, is becoming an important type of traffic in the Internet. The traffic traces of on-line traffic are not pre-recorded, which means little information on the on-line traffic is known in advance. Hence, on-line traffic is hard to characterize by existing traffic models, such as D-BIND. In order to anticipate and capture the burstiness property of on-line traffic, we introduce a new confidence-level-based statistical bounding interval-length dependent (S-BIND) traffic model and a statistical admission control algorithm, based on the S-BIND traffic model: the GammaH-BIND algorithm. Our simulation results show that by using the S-BIND traffic model as inputs, the GammaH-BIND algorithm can achieve the maximum valid network utilization for both low-bursty and high-bursty on-line traffic, which is 50%/spl sim/70% higher than the achievable network utilization under the D-BIND traffic model.

A new traffic model and statistical admission control algorithm for providing QoS guarantees to on-line traffic

Memory reference in digital signal processors (DSP) is among the most costly operations due to its long latency and substantial power consumption. In this paper, we present a new method to minimize memory references due to twiddle factors for implementing any existing fast Fourier transform (FFT) algorithms on DSP processors. The new method takes advantage of previously proposed twiddle factor reduction method (TFRM) and twiddle-factor-based butterfly grouping method (TFBBGM). It can compute two butterflies in one stage of any FFT diagram by loading only one twiddle-factor. Further memory reference reduction is done by computing butterflies with the same twiddle factor at the same time in different stages of the FFT diagram. We have applied the new method to implement radix-2 DIT FFT algorithm on TI TMS320C64x DSP. While using only 50% memory space for storing twiddle factors compared to the conventional DIT FFT implementation, the new method achieves an average reduction in the number of memory references by 79% for accessing the twiddle factors, and 17.5% reduction in the number of clock cycles.

A new memory reference reduction method for FFT implementation on DSP

In this paper, we present a high-performance implementation for the search function of a graph-based packet classification algorithm, used by networking applications in Internet routers, on the Intel IXP1200 network processor. The implementation uses optimal consolidation of memory reads to reduce the number of expensive SRAM accesses. Also, the implementation inserts instructions after SRAM accesses to hide the memory access latencies and improve processor utilization. Experimental results show the performance of the implemented search function on the IXP1200 using five microengines at 166 MHz can be as high as 1.18 Msps (million searches per second), which satisfies the requirements of packet rates from OC-3 or fast Ethernet and up to OC-12 or Gigabit Ethernet. The methods presented here can also be adapted to other network processors with similar architectures.

Yiyan Tang

Papers

A new traffic model and statistical admission control algorithm for providing QoS guarantees to on-line traffic

A new memory reference reduction method for FFT implementation on DSP

High-performance implementation for graph-based packet classification algorithm on network processor