This work is devoted to the study of a class of queueing networks with certain properties, namely those with discontinuous performance measures. An important subclass consists of networks with real-time constraints, where jobs must arrive at their destination within given deadlines, otherwise they are considered lost. Performance in such networks is measured by the probability a job is lost. For a network of K parallel links with a probabilistic routing scheme, consider the problem of optimal routing. Assuming the availability of a closed-form expression for the probability of loss across each link, the problem is solved under general conditions and properties of the optimal flow allocation are given. However, an analytical expression often cannot be derived, in which case other optimization approaches are necessary. One alternative is to use approximate analysis. Two suboptimal heuristic routing schemes are presented and compared. A second alternative involves implementing an on-line gradient-based stochastic optimization algorithm. Such algorithms require performance gradient estimates with respect to the control parameter. The methods of Perturbation Analysis (PA) and the Likelihood Ratio (LR) have been developed to supply the derivative estimates required. Smoothed Perturbation Analysis (SPA) is a specific PA approach suited to gradient estimation problems with discontinuous sample performance functions. SPA overcomes the normal difficulty of discontinuities by defining alternative sample performance functions that are conditioned forms of the original sample functions, such that the discontinuities are smoothed out. Here, a new SPA approach is developed that extends the applicability of SPA to cover additional performance measures including the probability of loss in real-time networks. New SPA gradient estimators are presented for this and other problematic performance measures such as the probability an arriving customer finds an idle server and the network occupancy as seen by an arrival to a tandem network. The convergence rate of SPA and LR gradient estimators are compared experimentally. Furthermore, the effectiveness of SPA gradient estimation in on-line stochastic optimization problems is demonstrated by coupling an SPA algorithm with a sampling-controlled stochastic version of Gallager's algorithm for the routing problem described above.

<p>Crisis response is a time-sensitive problem with multiple concurrent and interacting subprocesses, applied around the world in a wide range of contexts and with access to varying levels of resources. The movement of individuals with their shifting patterns of need and, frequently, disrupted normal support systems pose challenges to responders trying to understand what is needed, where, and when. Unfortunately, crises frequently occur in parts of the world that lack the infrastructure to respond to them and the information to inform responders where to target their efforts. In light of these challenges, researchers can make use of new data sources and technologies, combining the information products with simulation techniques to gain knowledge of the situation and to explore the various ways in which a crisis may develop. These new data sources&mdash;including social media such as Twitter and volunteered geographic information (VGI) from groups such as OpenStreetMap&mdash;can be combined with authoritative data sources in order to create rich, synthetic datasets, which may in turn be subjected to processes such as sentiment analysis and social network analysis. Further, these datasets can be transformed into information which supports powerful agent- based models (ABM). Such models can capture the behavior of heterogeneous individuals and their decision-making process, allowing researchers to explore the emergent dynamics of crisis situations. To that end, this research explores the gathering, cleaning, and synthesis of diverse data sources as well as the information which can be extracted from such synthetic data sources. Further, the work presents a rich, behaviorally complex agent-based model of an evacuation effort. The case study deals with the 2012 Colorado Wildfires, which threatened the city of Colorado Springs and prompted the evacuation of over 28,000 persons over the course of four days. The model itself explores how a synthetic population with automatically generated synthetic social networks communicates about and responds to the developing crisis, utilizing real evacuation order information as well as a model of wildfire development to which the individual agents respond. This research contributes to the study of data synthesis, agent-based modeling, and crisis development. </p>