Timothy C. Matisziw

Modeling s-t path availability to support disaster vulnerability assessment of network infrastructure

The maintenance of system flow is critical for effective network operation. Any type of disruption to network facilities (arcs/nodes) potentially risks loss of service, leaving users without access to important resources. It is therefore an important goal of planners to assess infrastructures for vulnerabilities, identifying those vital nodes/arcs whose debilitation would compromise the most source-sink (s-t) interaction or system flow. Due to the budgetary limitations of disaster management agencies, protection/fortification and planning for the recovery of these vital infrastructure facilities is a logical and efficient proactive approach to reducing worst-case risk of service disruption. Given damage to a network, evaluating the potential for flow between s-t pairs requires assessing the availability of an operational s-t path. Recent models proposed for identifying infrastructure vital to system flow have relied on enumeration of all s-t paths to support this task. This paper proposes an alternative model constraint structure that does not require complete enumeration of s-t paths, providing computational benefits over existing models. To illustrate the model, an application to a practical infrastructure planning problem is presented.

On the use of ZIP codes and ZIP code tabulation areas (ZCTAs) for the spatial analysis of epidemiological data

BackgroundWhile the use of spatially referenced data for the analysis of epidemiological data is growing, issues associated with selecting the appropriate geographic unit of analysis are also emerging. A particularly problematic unit is the ZIP code. Lacking standardization and highly dynamic in structure, the use of ZIP codes and ZIP code tabulation areas (ZCTA) for the spatial analysis of disease present a unique challenge to researchers. Problems associated with these units for detecting spatial patterns of disease are explored.ResultsA brief review of ZIP codes and their spatial representation is conducted. Though frequently represented as polygons to facilitate analysis, ZIP codes are actually defined at a narrower spatial resolution reflecting the street addresses they serve. This research shows that their generalization as continuous regions is an imposed structure that can have serious implications in the interpretation of research results. ZIP codes areas and Census defined ZCTAs, two commonly used polygonal representations of ZIP code address ranges, are examined in an effort to identify the spatial statistical sensitivities that emerge given differences in how these representations are defined. Here, comparative analysis focuses on the detection of patterns of prostate cancer in New York State. Of particular interest for studies utilizing local, spatial statistical tests, is that differences in the topological structures of ZIP code areas and ZCTAs give rise to different spatial patterns of disease. These differences are related to the different methodologies used in the generalization of ZIP code information. Given the difficulty associated with generating ZIP code boundaries, both ZIP code areas and ZCTAs contain numerous representational errors which can have a significant impact on spatial analysis. While the use of ZIP code polygons for spatial analysis is relatively straightforward, ZCTA representations contain additional topological features (e.g. lakes and rivers) and contain fragmented polygons that can hinder spatial analysis.ConclusionCaution must be exercised when using spatially referenced data, particularly that which is attributed to ZIP codes and ZCTAs, for epidemiological analysis. Researchers should be cognizant of representational errors associated with both geographies and their resulting spatial mismatch, especially when comparing the results obtained using different topological representations. While ZCTAs can be problematic, topological corrections are easily implemented in a geographic information system to remedy erroneous aggregation effects.

Comparative Approaches for Assessing Network Vulnerability

A common theme in analysis and evaluation of network-based critical infrastructure is the assessment of system vulnerability. Graph theoretic, simulation, and optimization-based techniques have played a significant role in examining potential network vulnerabilities given the insights they can provide for mitigating facility loss and prioritizing fortification efforts. Central to these approaches is the concept of facility (arc—node) importance or criticality to system survivability. Assessments of network vulnerability can dramatically differ based on how facility importance is characterized. In this review, various approaches for assessing facility importance and network vulnerability are examined. The key differences in these approaches are the ways in which a facilitys role in maintaining network operability is evaluated given arc—node disruption. Comparative results suggest significant differences exist among measures of facility importance and network performance. Furthermore, the subsequent incongruities in these measures and their implications need to be clearly understood to support interdiction risk and vulnerability assessment for critical infrastructures.

Critical network infrastructure analysis: interdiction and system flow

Effective management of critical network infrastructure requires the assessment of potential interdiction scenarios. Optimization approaches have been essential for identifying and evaluating such scenarios in networked systems. Although a primary function of any network is the distribution of flow between origins and destinations, the complexity and difficulty of mathematically abstracting interdiction impacts on connectivity or flow has been a challenge for researchers. This paper presents an optimization approach for identifying interdiction bounds with respect to connectivity and/or flow associated with a system of origins and destinations. Application results for telecommunications flow are presented, illustrating the capabilities of this approach.

Strategic route extension in transit networks

This study proposes a methodology through which transportation analysts and policy makers can use spatial optimization to support strategic planning, with the goal of extending existing service networks. Based on modeling objectives common to many service industries, an approach is developed for integrating geographic information systems (GIS) and spatial optimization modeling in order to extend an existing transit system through prioritizing route and stop additions. Development of a strategic methodology such as this is vital for agencies interested in extending transit networks to accommodate urban growth and development. This is especially true in public transit applications, such as bus route planning, as the future of bus-based public transportation depends on the success of route expansion and modification. The developed approach is applied to the transit system in Columbus, Ohio.

Connectivity change in habitat networks

Habitat management is essential for safeguarding important flora and fauna. Further, habitat connectivity is a crucial component for maintaining biodiversity given that it is known to have implications for species persistence. However, damage to habitat due to natural and human induced hazards can alter spatial relationships between habitats, potentially impacting biodiversity. Therefore, the susceptibility of spatial relationships to patch loss and associated connectivity degradation is obviously an important factor in maintaining existing or planned habitat networks. Identifying patches vital to connectivity is critical both for effectively prioritizing protection (e.g., enhancing habitat connectivity) and establishing disaster mitigation measures (e.g., stemming the spread of habitat loss). This paper presents a methodology for characterizing connectivity associated with habitat networks. Methods for evaluating habitat network connectivity change are formalized. Examples are presented to facilitate analysis of connectivity in the management of biodiversity.

Spatio-temporal fluctuations in the global airport hierarchies

Abstract The global air transportation network is responsible for moving millions of domestic and international passengers each year. Not surprisingly, relationships between airports vary widely, due to a myriad of geographic, economic, political and historical determinants. Further, given the dynamic nature of the many influences acting on the air transportation system, inter-airport relationships and the structure of the global air network as a whole are also constantly changing. The purpose of this paper is to explore such spatio-temporal variations in the structure of the global airport hierarchies. Here, we show how the concept of nodal regions can be applied to measure the extent of these variations. To facilitate this analysis, a database of nearly 900 airline carrier schedules and 4650 worldwide origins and destinations, representing a nearly complete record of commercial air travel over a six-year period, is examined. Given this dataset, nodal regions are derived for all airports represented. In general, results suggest that regions associated with individual airports are often relatively dynamic at the yearly as well as quarterly level. Los Angeles International Airport (LAX) is utilized as a local case-study to provide a detailed examination of these dynamics.

Downscaling spatial structure for the analysis of epidemiological data

Abstract Many widely accessible forms of socio-economic and public health data have been subjected to some form of spatial aggregation. Polygonal units, such as US Census tabulation areas, political boundaries, transportation analysis zones and ZIP codes, are often used to represent the spatial extent of these data. While convenient, this type of spatial aggregation, not only ignores the underlying variability of the data of interest, but also the spatial relationships between observations. Although privacy concerns are certainly an important issue in this context, spatial data aggregation can negatively influence one’s ability to accurately surveil disease and identify locations (or clusters of locations) with increased disease incidence. The purpose of this paper is to explore the use of supplementary spatial data, particularly street networks, for downscaling the spatial structure of polygonal units. Spatial statistical tests are then used to identify clusters of disease incidence for the downscaled study area. Results suggest that the downscaled spatial structure of polygonal units provides valuable information on the spatial distribution of disease and can facilitate a more detailed spatial analysis of epidemiological data. Prostate cancer data aggregated to ZIP codes for a region of New York State are used to illustrate this concept.

Robustness elasticity in complex networks

Network robustness refers to a network’s resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems.

A Geocomputational Heuristic for Coverage Maximization in Service Facility Siting

Siting service facilities in order to maximize regional coverage is important when budget resources are limited. Various approaches exist for addressing this particular planning problem for discrete or continuous representations of potential facility sites and demand to be served. In cases where both candidate facility sites and service demand are continuous, approaches for maximizing regional coverage have only examined the siting of a single facility. In this article, a geocomputational approach is proposed for addressing multiple facility siting when demand is continuously distributed and facilities may be located anywhere in the region. Emergency warning siren location is used to highlight the developed approach.