This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

Stochastic Network Optimization with Application to Communication and Queueing Systems

Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner in order to support information transfer. In this text we will present abstract models that capture the cross-layer interaction from the physical to transport layer in wireless network architectures including cellular, ad-hoc and sensor networks as well as hybrid wireless-wireline. The model allows for arbitrary network topologies as well as traffic forwarding modes, including datagrams and virtual circuits. Furthermore the time varying nature of a wireless network, due either to fading channels or to changing connectivity due to mobility, is adequately captured in our model to allow for state dependent network control policies. Quantitative performance measures that capture the quality of service requirements in these systems depending on the supported applications are discussed, including throughput maximization, energy consumption minimization, rate utility function maximization as well as general performance functionals. Cross-layer control algorithms with optimal or suboptimal performance with respect to the above measures are presented and analyzed. A detailed exposition of the related analysis and design techniques is provided.

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Resource Allocation and Cross Layer Control in Wireless Networks

Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson (1967), Kerdock (1972), Preparata (1968), Goethals (1974), and Delsarte-Goethals (1975). It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z/sub 4/, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z/sub 4/ domain implies that the binary images have dual weight distributions. The Kerdock and "Preparata" codes are duals over Z/sub 4/-and the Nordstrom-Robinson code is self-dual-which explains why their weight distributions are dual to each other. The Kerdock and "Preparata" codes are Z/sub 4/-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z/sub 4/, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the "Preparata" code and a Hadamard-transform soft-decision decoding algorithm for the I(Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z/sub 4/, but extended Hamming codes of length n/spl ges/32 and the Golay code are not. Using Z/sub 4/-linearity, a new family of distance regular graphs are constructed on the cosets of the "Preparata" code. >

The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes

1. Introduction 2. Background 3. Performance evaluation process algebra 4. Modelling study: multi-server multi-queue systems 5. Notions of equivalence 6. Isomorphism and weak isomorphism 7. Strong bisimilarity 8. Strong equivalence 9. Conclusions Bibliography Index.

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A Compositional Approach to Performance Modelling

Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals. It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z_4, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the Z_4 domain implies that the binary images have dual weight distributions. The Kerdock and "Preparata" codes are duals over Z_4 -- and the Nordstrom-Robinson code is self-dual -- which explains why their weight distributions are dual to each other. The Kerdock and "Preparata" codes are Z_4-analogues of first-order Reed-Muller and extended Hamming codes, respectively. All these codes are extended cyclic codes over Z_4, which greatly simplifies encoding and decoding. An algebraic hard-decision decoding algorithm is given for the "Preparata" code and a Hadamard-transform soft-decision decoding algorithm for the Kerdock code. Binary first- and second-order Reed-Muller codes are also linear over Z_4, but extended Hamming codes of length n >= 32 and the Golay code are not. Using Z_4-linearity, a new family of distance regular graphs are constructed on the cosets of the "Preparata" code.

The Z_4-Linearity of Kerdock, Preparata, Goethals and Related Codes

According to several studies, the power consumption of the Internet accounts for up to 10% of the worldwide energy consumption, and several initiatives are being put into place to reduce the power consumption of the ICT sector in general. To this goal, we propose a novel approach to switch off network nodes and links while still guaranteeing full connectivity and maximum link utilization. After showing that the problem falls in the class of capacitated multi-commodity flow problems, and therefore it is NP-complete, we propose some heuristic algorithms to solve it. Simulation results in a realistic scenario show that it is possible to reduce the number of links and nodes currently used by up to 30% and 50% respectively during off-peak hours, while offering the same service quality.

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Reducing Power Consumption in Backbone Networks

According to several studies, the power consumption of the Internet accounts for up to 10% of the worldwide energy consumption and is constantly increasing. The global consciousness on this problem has also grown, and several initiatives are being put into place to reduce the power consumption of the ICT sector in general. In this paper, we face the problem of minimizing power consumption for Internet service provider (ISP) networks. In particular, we propose and assess strategies to concentrate network traffic on a minimal subset of network resources. Given a telecommunication infrastructure, our aim is to turn off network nodes and links while still guaranteeing full connectivity and maximum link utilization constraints. We first derive a simple and complete formulation, which results into an NP-hard problem that can be solved only for trivial cases. We then derive more complex formulations that can scale up to middle-sized networks. Finally, we provide efficient heuristics that can be used for large networks. We test the effectiveness of our algorithms on both real and synthetic topologies, considering the daily fluctuations of Internet traffic and different classes of users. Results show that the power savings can be significant, e.g., larger than 35%.

Minimizing ISP network energy cost: formulation and solutions

Power consumption of ICT is becoming more and more a sensible problem, which is of interest for both the research community, for ISPs and for the general public. In this paper we consider a real IP backbone network and a real traffic profile. We evaluate the energy cost of running it, and, speculating on the possibility of selectively turning off spare devices whose capacity is not required to transport off-peak traffic, we show that it is possible to easily achieve more than 23% of energy saving per year, i.e., to save about 3GWh/year considering today's power footprint of real network devices.

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Energy-Aware Backbone Networks: A Case Study

In this paper, promising technologies and a network architecture are presented for future optical packet switched networks. The overall network concept is presented and the major choices are highlighted and compared with alternative solutions. Both long and shorter term approaches are considered, as well as both the wide-area network and multiple-area networks parts of the network. The results presented in this paper were developed in the frame of the research project DAVID (Data And Voice Integration over DWDM) project, funded by the European Commission through the IST-framework.

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The European IST project DAVID: a viable approach toward optical packet switching

We develop a general methodology, mainly based upon Lyapunov functions, to derive bounds on average delays, and on queue size averages and variances of complex systems of queues. We then apply this methodology to input-buffered, cell-based switch and router architectures. These architectures require a scheduling algorithm to select at each slot a subset of input-buffered cells which can be transferred towards output ports. Although the stability properties (i.e., the limit throughput) of input-buffered, cell-based switches was already studied for several classes of scheduling algorithms, no analytical results concerning cell delays or queue sizes are yet available in the technical literature. We concentrate on purely input-buffered switches that adopt a maximum weight matching scheduling algorithm, that was proved to be the scheduling algorithm providing the best performance. The derived bounds proved to be rather tight, when compared to simulation results.

Fabio Neri

Papers

Reducing Power Consumption in Backbone Networks

Minimizing ISP network energy cost: formulation and solutions

Energy-Aware Backbone Networks: A Case Study

The European IST project DAVID: a viable approach toward optical packet switching

Bounds on average delays and queue size averages and variances in input-queued cell-based switches