Energy management in communication networks: a journey through modelling and optimization glasses

The widespread proliferation of Internet and wireless applications has produced a significant increase of ICT energy footprint. As a response, in the last five years, significant efforts have been undertaken to include energy-awareness into network management. Several green networking frameworks have been proposed by carefully managing the network routing and the power state of network devices. Even though approaches proposed differ based on network technologies and sleep modes of nodes and interfaces, they all aim at tailoring the active network resources to the varying traffic needs in order to minimize energy consumption. From a modeling point of view, this has several commonalities with classical network design and routing problems, even if with different objectives and in a dynamic context. With most researchers focused on addressing the complex and crucial technological aspects of green networking schemes, there has been so far little attention on understanding the modeling similarities and differences of proposed solutions. This paper fills the gap surveying the literature with optimization modeling glasses, following a tutorial approach that guides through the different components of the models with a unified symbolism. A detailed classification of the previous work based on the modeling issues included is also proposed

Measuring Marginal Congestion Costs of Urban Transportation: Do Networks Matter?

In determining the marginal cost of congestion, economists have traditionally relied upon directly measuring traffic congestion on network links, disregarding any “network effects,” since the latter are difficult to estimate. While for simple networks the comparison can be done within a theoretical framework, it is important to know whether such network effects in real large-scale networks are quantitatively significant. In this paper we use a strategic transportation planning model (START) to compare marginal congestion costs computed link-by-link with measures taking into account network effects. We find that while in aggregate network effects are not significant, congestion measured on a single link is a poor predictor of total congestion costs imposed by travel on that link. Also, we analyze the congestion proliferation effect on the network to see how congestion is distributed within an urban area.marginal congestion costs, congestion pricing, urban networks

Imprecise Markov Models for Scalable and Robust Performance Evaluation of Flexi-Grid Spectrum Allocation Policies

The possibility of flexibly assigning spectrum resources with channels of different sizes greatly improves the spectral efficiency of optical networks, but can also lead to unwanted spectrum fragmentation.We study this problem in a scenario where traffic demands are categorised in two types (low or high bit-rate) by assessing the performance of three allocation policies. Our first contribution consists of exact Markov chain models for these allocation policies, which allow us to numerically compute the relevant performance measures. However, these exact models do not scale to large systems, in the sense that the computations required to determine the blocking probabilities---which measure the performance of the allocation policies---become intractable. In order to address this, we first extend an approximate reduced-state Markov chain model that is available in the literature to the three considered allocation policies. These reduced-state Markov chain models allow us to tractably compute approximations of the blocking probabilities, but the accuracy of these approximations cannot be easily verified. Our main contribution then is the introduction of reduced-state imprecise Markov chain models that allow us to derive guaranteed lower and upper bounds on blocking probabilities, for the three allocation policies separately or for all possible allocation policies simultaneously.Comment: 16 pages, 7 figures, 3 table

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported

Network modeling and design : a distributed problem solving approach

This dissertation is concerned with developing new solution algorithms for network modeling and design problems using a distributed problem solving approach. Network modeling and design are fundamental problems in the field of transportation science, and numerous transportation applications such as urban travel demand forecasting, congestion pricing, defining optimal toll values, and scheduling traffic lights all involve some form of network modeling or network design. The first part of this dissertation focuses on developing a distributed scheme for the static traffic assignment problem, based on a spatial decomposition. The objective of the traffic assignment problem is to estimate traffic flows on a network and the resulting congestion considering the mutual interactions between travelers. A traffic assignment model takes as input the network topology, link performance functions, and a demand matrix indicating the traffic volume between each pair of origin-destination nodes. There are efficient algorithms to solve the traffic assignment problem, but, as computational hardware and algorithms advance, attention shifts to more demanding applications of the traffic assignment problem (bilevel programs whose solution often requires the solution of many traffic assignment problem instances as subproblems, accounting for forecasting errors with Monte Carlo simulation of input parameters, and broadening the geographic scope of models to the statewide or national levels.) In Chapter 2, we propose a network contraction technique based on the theory of equilibrium sensitivity analysis. In the proposed algorithm, we replace the routes between each origin-destination (OD) pair with a single artificial link. These artificial links model the travel time between the origin and destination nodes of each OD pair as a function of network demands. The network contraction method can be advantageous in network design applications where many equilibrium problems must be solved for different design scenarios. The network contraction procedure can also be used to increase the accuracy of subnetwork analysis. The accuracy and complexity of the proposed methodology are evaluated using the network of Barcelona, Spain. Further, numerical experiments on the Austin, Texas regional network validate its performance for subnetwork analysis applications. Using this network contraction technique, we then develop a decentralized (distributed) algorithm for static traffic assignment in Chapter 3. In this scheme, which we term a decentralized approach to the static traffic assignment problem (DSTAP), the complete network is divided into smaller networks, and the algorithm alternates between equilibrating these networks as subproblems, and master iterations using a simplified version of the full network. The simplified network used for the master iterations is based on linearizations to the equilibrium solution for each subnetwork obtained using sensitivity analysis techniques. We prove that the DSTAP method converges to the equilibrium solution on the complete network, and demonstrate computational savings of 35-70% on the Austin network. Natural applications of this method are statewide or national assignment problems, or cities with rivers or other geographic features where subnetworks can be easily defined. The second part of this dissertation, found in Chapter 4, deals with network design problems. In a network design problem, the goal is to optimize an objective function (minimize the travel time, pollution, maximize safety, social welfare, etc.) by making investment decisions subject to budget and feasibility constraints. Network design is a bi-level problem where the leader chooses the design parameters, and travelers, as followers, react to the leader’s decision by changing their route. These problems are hard to solve, and distributed problem solving approach can be used to develop an efficient framework for scaling these problems. In the proposed distributed algorithm for network design problems, different planning agencies may have different objective functions and priorities, while a regional agent (state or federal officials) allocates the finding between the urban cities. In this model, the urban planning agencies do their own planning and design independently while capturing the system-level effects of their local decisions and plans. The regional agent has limited and indirect authorities over the subnetworks through budget allocation. In addition to computational advantages for traditional bi-level network design problems, the proposed algorithm can be used to model the linkage between different entities for multi-resolution applications. We develop a solution algorithm based on a sensitivity-analysis heuristic, and test our algorithm on two case studies: a hypothetical network composed of two copies of Sioux Falls network, and the Austin regional network. We evaluate the correctness of the decentralized algorithm, and discuss the benefits of the algorithm in modeling the global impacts of local decisions. Furthermore, the implementation of distributed algorithm on Austin regional network demonstrates a computational saving of 22%.Civil, Architectural, and Environmental Engineerin