Stochastic Networks

The introduction of uncertainty to mathematical programs greatly increases the size of the resulting optimization problems. Specialized methods that exploit program structures and advances in computer technology promise to overcome the computational complexity of certain classes of stochastic programs. In this paper we examine the progressive hedging algorithm for solving multi-scenario generalized networks. We present computational results demonstrating the effect of various internal tactics on the algorithm's performance. Comparisons with alternative solution methods are provided.

The introduction of uncertainty to mathematical programs greatly increases the size of the resulting optimization problems. Specialized methods that exploit program structures and advances in computer technology promise to overcome the computational complexity of certain classes of stochastic programs. In this paper we examine the progressive hedging algorithm for solving multi-scenario generalized networks. We present computational results demonstrating the effect

We describe and compare stochastic network optimization models for investment planning under uncertainty. Emphasis is placed on multiperiod a sset allocation and active portfolio management problems. Myopic as well as multiple period models are considered. In the case of multiperiod models, the uncertainty in asset returns filters into the constraint coefficient matrix, yielding a multi-scenario program formulation. Different scenario generation procedures are examined. The use of utility functions to reflect risk bearing attitudes results in nonlinear stochastic network models. We adopt a newly proposed decomposition procedure for solving these multiperiod stochastic programs. The performance of the models in simulations based on historical data is discussed.

We develop a multi-objective model for the time-cost trade-off problem in a dynamic PERT network using an interac- tive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network

Abstract—The maximum traffic arrival rate at the network for a given delay guarantee (delay constrained throughput) has been well studied for wired channels. However, few results are available for wireless channels, especially when multiple antennas are employed at the transmitter ...

The scenario aggregation algorithm is specialized for stochastic networks. The algorithm determines a solution that does not depend on hindsight and accounts for the uncertain environment depicted by a number of appropriately weighted scenarios. The solution procedure decomposes the stochastic program to its constituent scenario subproblems, thus preserving the network structure. Computational results are reported demonstrating the algorithm's convergence behavior. Acceleration schemes are discussed along with termination criteria. The algorithm's potential for execution on parallel multiprocessors is discussed.

We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for Brownian control problems \citehar, associated with a broad family of stochastic networks, follows as a consequence.

Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an importan...

As an alternative effort for quantifying recurrent traffic dynamics caused by network variations and analyzing the impact on the network performance from information provision, we describe in this paper a new equilibrium modeling scheme for stochastic networks with a finite number of states, which takes into account the behavioral inertia.  A finite-dimensional variational inequality model is formulated to describe the cross-state equilibrium conditions among heterogeneous travelers with different inertial degrees and knowledge structures.  Our model allows for traveler’s partial understanding and inertial effect in perceiving varying network conditions and provides a different perspective (from existing stochastic and Markovian network equilibrium approaches) to describe traffic flow variations across multiple network scenarios.  A disaggregate simplicial decomposition algorithm is suggested to solve the variational inequality problem.  Numerical results from a few stochastic network examples demonstrate the validity and effectiveness of our methodology in modeling the inertia phenomenon within route choice behavior and the efficacy of using traveler information systems to eliminate the inertia effect.

This paper contributes to further understanding the economic performance of Portuguese and Spanish regions, using a stochastic network approach. The empirical analysis is made at the territorial level of NUT 3 regions and covers the period 1995-2008. The performance of regions is based on GDP per capita at Purchasing Power Standards. The network analysis is based on a metric space

The goal of this research is to identify response mechanisms in online learning networks. We ask whether actors choose their response partners at random or whether certain special mechanisms are at work. In that case, we would like to discover what mechanism is most descriptive of the networks. While previous studies checked a few selective attributes of the networks, in this research, we capture their rich complex feature space by mapping them into a high-dimensional feature space. A Multi-way Support Vector Machine algorithm is used to classify 35 observed response networks of online learners into a set of five representative stochastic network generation models. The result shows that all the response networks were classified into a preferential response model in which actors tend to respond to partners who are a-priori equipped with response attraction power. We provide a possible explanation for this behavior, based on the nature and goal of the online learning networks, and dis...

Purpose–With rapid advances in wireless portable devices, ubiquitous computing seems becoming a reality everyday. The paper aims to explore the possibility of offering real-time content adaptation on set of data streams using the active pervasive network infrastructure ...

Variations in the durations of activities are commonplace in the construction industry. This is due to the fact that the construction industry is influenced greatly by variations in weather, productivity of labour and plant, and quality of materials. Stochastic network analysis has been used by previous researchers to model variations in activities and produce more effective and reliable project duration estimates. A number of techniques have been developed in previous literature to solve the uncertain nature of networks, these are: PERT (program evaluation and review techniques), PNET (probabilistic network evaluation technique), NRB, (narrow reliability bounds methods) and MCS (Monte Carlo simulation). Although these techniques have proved to be useful in modelling variations in activities, dependence of activity duration is not considered. This can have a severe impact on realistically modelling projects. In this context, the objective of the present research is to develop a methodology that can accurately model activity dependence and realistically predict project duration using a risk management approach. A simulation model has been developed to encapsulate the methodology and run experimental work. In order to achieve this, the following tasks are tackled: identify risk factors that cause activity variations using literature reviews and conducting interviews with contractors; model risk factors and their influence on activity variations through conducting case studies and identifying any dependence between them; develop a computer based simulation model that uses a modified Monte Carlo technique to model activity duration and dependence of risk factors; and run experimental work to validate and verify the model.