In this paper, we develop a three-stage stochastic network-based optimization model for the provision of 5G services with Unmanned Aerial Vehicles (UAVs) in the disaster management phases of: preparedness, response and recover/reconstruction. Users or devices on the ground request services of a fleet of controller UAVs in flight and the requested services are executed by a fleet of UAVs organized as a Flying Ad-Hoc Network and interconnected via 5G technology. A disaster scenario can create difficulties for the provision of services by service providers. For this reason, in the first stage, service providers make predictions about possible scenarios in the second stage. Therefore, the first stage represents the preparedness phase, the second stage represents the response phase, followed by the recovery/reconstruction phase, represented by the third stage. In each of the three stages, service providers seek to maximize the amount of services to be performed, assigning each service a priority. They also aim to, simultaneously, minimize the total management costs of requests, the transmission and execution costs of services, the costs to increase the resources of the pre-existing network and, if need be, to reduce them in the recovery/reconstruction phase. For the proposed multi-stage stochastic optimization model, we provide variational formulations for which we investigate the existence and uniqueness of the solution. Finally, a detailed numerical example is solved in order underline some of the key aspects of the model. This paper adds to the literature on the rigorous mathematical modeling of advanced technologies for disaster management.

Abstract This paper presents a panoramic view of research on economic and financial networks in the journal Networks, since its inception half a century ago. This paper focuses on both the breadth and depth of the journal articles, and within the context of earlier contributions, as well as more recent related ones in other scientific publications. From network optimization to game theory and a plethora of equilibrium concepts, along with novel dynamical systems frameworks, the journal has led the way in advancing economic and financial network models, algorithms, and applications. Moreover, Networks has helped to attract researchers in a variety of disciplines to the science of networks and the formulation and solution of associated problems drawn from the real world.

In this paper we consider an alternative possibility for routing money in the Internet ecosystem based on a spot market for interconnection service that operates alongside, or in addition to, the traditional contract service model. Recent work by others showed that under certain assumptions, enabling transit providers (i.e., networks that carry packets between networks) to sell their excess capacity on a best-effort basis improves both provider profit and consumer surplus. While prior work only focused on pricing strategies, we explore the technical feasibility of such a market in this paper. We consider what is needed to make such a spot market possible and focus on the interaction between technical and economic considerations. In particular, we describe two approaches that demonstrate how economic software defined exchanges (ESDXs) can be used as trusted intermediaries to tie the forwarding service to the flow of money.

There has been a great interest in defining a new network architecture that can meet the needs of a future Internet. One of the main challenges in this context is how to realize the many different technical solutions that have developed in recent years in a single coherent architecture. In addition, it is necessary to consider how to ensure economic viability of architecture solutions. In this work, we discuss how to design a network architecture where choices at different layers of the protocol stack are explicitly exposed to users. This approach ensures that innovative technical solutions can be used and rewarded, which is essential to encourage wide deployment of this architecture.

Abstract This report highlights some recent developments in Network Economics based on papers presented at the Computing in Economics and Finance (CEF 2002) Conference held in Aix en Provence, France.

In this paper, we develop a dynamic model of financial behavior in the case of multiple sectors and multiple instruments in the presence of financial futures, which demonstrates the evolution of the underlying networks through time. The dynamic model is formulated as a projected dynamical system whose set of stationary points coincides with the set of solutions to a variational inequality problem. We identify the network structure of the individual sectors' portfolio optimization problems out of equilibrium and then prove that the equilibrium solution can be reformulated as the solution to a network optimization problem, in which the network represents a merger of the individual networks. We subsequently provide a discrete time algorithm for the solution of the continuous time financial model, which exploits the network structure, and provide convergence results. The model and algorithm are then illustrated through numerical examples. © 1999 John Wiley & Sons, Inc. Networks 33: 93–108, 1999

In this paper, we developed a new general financial equilibrium model with transaction costs which considers multiple sectors of an economy, each of which seeks to determine its optimal composition of instruments held as assets and as liabilities in its portfolio. The governing equilibrium conditions are shown to satisfy a variational inequality problem, which is then studied in terms of existence and other qualitative properties. A decomposition algorithm is proposed which exploits the underlying generalized network structure of the problem and convergence results obtained. Finally, the algorithm is applied to compute the equilibrium asset, liability, and price pattern in several numerical examples. © 1996 John Wiley & Sons, Inc.

Abstract In this paper, we consider the price formulation—rather than the quantity formulation—of spatial network equilibria and introduce a projected dynamical system, whose set of stationary points corresponds to the set of solutions of the governing variational inequality problem. We then interpret the dynamical system as a tatonnement process in which the commodity prices and shipments are updated simultaneously. We propose an Euler‐type method for the computation of the commodity prices and trade patterns, provide convergence results, and demonstrate that the algorithm can be implemented on massively parallel architectures. The notable feature of the algorithm is that the prices and shipments can be computed independently and in closed form. Finally, we illustrate the performance of the implemented algorithm on the Thinking Machine's CM‐2 and CM‐5 architectures.

Abstract This article develops a general network model of financial flow of funds accounting that explicitly incorporates feedback and can be used to calculate reconciled values of all outstanding financial instruments, tangible assets, and net worth. The model captures, as special cases, distinct data‐specific problem scenarios and permits the estimation of sector holdings of both assets and liabilities, total outstanding instrument volumes, and total sector holdings. A decomposition algorithm is then proposed that resolves the network problem into simpler network subproblems, each of which can then be solved exactly in closed form. The algorithm is applied to a dataset derived from the Federal Reserve Board data for 1989. The reconciled dataset can then be used as a base line for an empirical general equlibrium model and for macromonetary policy analysis.

Abstract In this article, we consider an asymmetric market disequilibrium model in a spatial setting in the case of rigid prices and/or controls. In this problem, the markets need no longer clear. We show that the disequilibrium problem can be reformulated as an equilibrium problem over an abstract network with special structure. We then propose a network decomposition algorithm for the computation of the solution that exploits the structure and establishes convergence results using the theory of variational inequalities. Our computational results demonstrate the suitability of this approach for large‐scale market problems.

The authors introduce a general parallelizable computational method called the splitting equilibration algorithm for solving the entire class of constrained matrix problems. The empirical performance of the algorithm is investigated on the largest quadratic constrained matrix problems reported to date using the IBM 3090-600E at the Cornell National Supercomputer Facility in a serial and in a parallel environment. The goals are to compare the relative efficiency of the splitting equilibration algorithm to both the earlier equilibration algorithm and the much-cited Bachem and Korte algorithm, (1978) and to investigate the speedups obtained with parallelization of the splitting equilibration algorithm.>

Abstract This paper presents a general dynamic spatial price network equilibrium model with gains and losses, which contains as special cases both dynamic and static models studied earlier. This framework through the use of multipliers has the capability of handling directly agricultural markets for perishable commodities and financial markets. Alternative variational inequality formulations are given and then exploited (akin to the work for dynamic problems without gains and losses) to construct a Gauss–Seidel‐type decomposition scheme. Computational experience for this scheme and for an equilibration multiplier method is given for a variety of large‐scale problems.