Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks

This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models

Feedback Control of the National Airspace System

This paper proposes a general modeling framework adapted to the feedback control of traffic flows in Eulerian models of the National Airspace System. It is shown that the problems of scheduling and routing aircraft flows in the National Airspace System can be posed as the control of a network of queues with load-dependent service rates. Focus can then shift to developing techniques to ensure that the aircraft queues in each airspace sector, which are an indicator of the air traffic controller workloads, are kept small. This paper uses the proposed framework to develop control laws that help prepare the National Airspace System for fast recovery from a weather event, given a probabilistic forecast of capacities. In particular, the model includes the management of airport arrivals and departures subject to runway capacity constraints, which are highly sensitive to weather disruptions.National Science Foundation (U.S.) (Contract ECCS-0745237)United States. National Aeronautics and Space Administration (Contract NNA06CN24A

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds

Computational optimization of networks of dynamical systems under uncertainties: application to the air transportation system

To efficiently balance traffic demand and capacity, optimization of air traffic management relies on accurate predictions of future capacities, which are inherently uncertain due to weather forecast. This dissertation presents a novel computational efficient approach to address the uncertainties in air traffic system by using chance constrained optimization model. First, a chance constrained model for a single airport ground holding problem is proposed with the concept of service level, which provides a event-oriented performance criterion for uncertainty. With the validated advantage on robust optimal planning under uncertainty, the chance constrained model is developed for joint planning for multiple related airports. The probabilistic capacity constraints of airspace resources provide a quantized way to balance the solution’s robustness and potential cost, which is well validated against the classic stochastic scenario tree-based method. Following the similar idea, the chance constrained model is extended to formulate a traffic flow management problem under probabilistic sector capacities, which is derived from a previous deterministic linear model. The nonlinearity from the chance constraint makes this problem difficult to solve, especially for a large scale case. To address the computational efficiency problem, a novel convex approximation based approach is proposed based on the numerical properties of the Bernstein polynomial. By effectively controlling the approximation error for both the function value and gradient, a first-order algorithm can be adopted to obtain a satisfactory solution which is expected to be optimal. The convex approximation approach is evaluated to be reliable by comparing with a brute-force method.Finally, the specially designed architecture of the convex approximation provides massive independent internal approximation processes, which makes parallel computing to be suitable. A distributed computing framework is designed based on Spark, a big data cluster computing system, to further improve the computational efficiency. By taking the advantage of Spark, the distributed framework enables concurrent executions for the convex approximation processes. Evolved from a basic cloud computing package, Hadoop MapReduce, Spark provides advanced features on in-memory computing and dynamical task allocation. Performed on a small cluster of six workstations, these features are well demonstrated by comparing with MapReduce in solving the chance constrained model

Road network equilibrium approaches to environmental sustainability

Environmental sustainability is closely related to transportation, especially to the road network, because vehicle emissions and noise damage the environment and have adverse effects on human health. It is, therefore, important to take their effect into account when designing and managing road networks. Road network equilibrium approaches have been used to estimate this impact and to design and manage road networks accordingly. However, no comprehensive review has summarized the applications of these approaches to the design and management of road networks that explicitly address environmental concerns. More importantly, it is necessary to identify this gap in the literature so that future research can improve the existing methodologies. Hence, this paper summarizes these applications and identifies potential future research directions in terms of theories, modelling approaches, algorithms, analyses, and applications.postprin

A Convex Framework for Epidemic Control in Networks

With networks becoming pervasive, research attention on dynamics of epidemic models in networked populations has increased. While a number of well understood epidemic spreading models have been developed, little to no attention has been paid to epidemic control strategies; beyond heuristics usually based on network centrality measures. Since epidemic control resources are typically limited, the problem of optimally allocating resources to control an outbreak becomes of interest. Existing literature considered homogeneous networks, limited the discussion to undirected networks, and largely proposed network centrality-based resource allocation strategies. In this thesis, we consider the well-known Susceptible-Infected-Susceptible spreading model and study the problem of minimum cost resource allocation to control an epidemic outbreak in a networked population. First, we briefly present a heuristic that outperforms network centrality-based algorithms on a stylized version of the problem previously studied in the literature. We then solve the epidemic control problem via a convex optimization framework on weighted, directed networks comprising heterogeneous nodes. Based on our spreading model, we express the problem of controlling an epidemic outbreak in terms of spectral conditions involving the Perron-Frobenius eigenvalue. This enables formulation of the epidemic control problem as a Geometric Program (GP), for which we derive a convex characterization guaranteeing existence of an optimal solution. We consider two formulations of the epidemic control problem -- the first seeks an optimal vaccine and antidote allocation strategy given a constraint on the rate at which the epidemic comes under control. The second formulation seeks to find an optimal allocation strategy given a budget on the resources. The solution framework for both formulations also allows for control of an epidemic outbreak on networks that are not necessarily strongly connected. The thesis further proposes a fully distributed solution to the epidemic control problem via a Distributed Alternating Direction Method of Multipliers (ADMM) algorithm. Our distributed solution enables each node to locally compute its optimum allocation of vaccines and antidotes needed to collectively globally contain the spread of an outbreak, via local exchange of information with its neighbors. Contrasting previous literature, our problem is a constrained optimization problem associated with a directed network comprising non-identical agents. For the different problem formulations considered, illustrations that validate our solutions are presented. This thesis, in sum, proposes a paradigm shift from heuristics towards a convex framework for contagion control in networked populations

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Quick Link Selection Method by Using Pricing Strategy Based on User Equilibrium for Implementing an Effective Urban Travel Demand Management

This paper presents a two-stage model of optimization as a quick method to choose the best potential links for implementing urban travel demand management (UTDM) strategy like road pricing. The model is optimized by minimizing the hidden cost of congestion based on user equilibrium (MHCCUE). It forecasts the exact amount of flows and tolls for links in user equilibrium condition to determine the hidden cost for each link to optimize the link selection based on the network congestion priority. The results show that not only the amount of total cost is decreased, but also the number of selected links for pricing is reduced as compared with the previous toll minimization methods. Moreover, as this model just uses the traffic assignment data for calculation, it could be considered as a quick and optimum solution for choosing the potential links.</p

Congestion-aware Multi-modal Delivery Systems Utilizing Drones

Multi-modal delivery systems are a promising solution to the challenges posed by the increasing demand of e-commerce. Due to the potential benefit drones can have on logistics networks such as delivery systems, some countries have taken steps towards integrating drones into their airspace. In this paper we aim to quantify this potential by developing a mathematical model for a multi-modal delivery system composed of trucks and drones. We propose an optimization formulation that can be efficiently solved in order to design socially-optimal routing and allocation policies. We incorporate both societal cost in terms of road congestion and parcel delivery latency in our formulation. Our model is able to quantify the effect drones have on mitigating road congestion, and can solve for the path routing needed to minimize the chosen objective. To accurately capture the effect of stopping trucks on road latency, we use SUMO simulations and derive a mathematical latency function for roads shared by trucks and cars. Based on this, we show that the proposed framework is computationally feasible to scale due to its reliance on convex quadratic optimization techniques