Network Robustness Index – Next Steps: Addressing Trip Importance, Travel Demand, and Scalability AUTHORS: Novak, Sullivan, Aultman-Hall

ABSTRACT  In previous work, we outline the motivation for the development of the Network Robustness Index (NRI) and the Network Trip Robustness (NTR) performance measures and test both metrics on hypothetical networks to demonstrate their use and functionality. We clearly show that our methodological approach using the NRI yields different planning and management priorities than existing approaches (Scott et al., 2006). We have also successfully applied both metrics to real-world transportation networks using planning agency travel demand models consisting of traffic analysis zones (TAZs) and arterial roads (Sullivan et al., 2009a, Sullivan et al., 2009b). We have explored how changing the operational capacity on a given link can impact the rank-ordering of all the links in a network and have observed that relationships between operational capacity and network connectivity (a measure of redundancy in a network) are non-linear and not necessarily intuitive.

Our future work is an extension of the NRI and the NTR. We outline three specific objectives: 1)  To develop a universally applicable, flexible, and detail-oriented travel demand proxy

model (TDPM) to substitute for existing travel demand models. The TDPM can be comprehensively generated for any study area and for any subset of travel modes using available spatial (GIS) data even in cases where existing travel demand forecasting models do not exist.

2)  To incorporate a measure of the relative importance of a trip into the calculation of the NRI. This improvement will improve the NRI and allow decision makers to consider variations in the costs associated with travel time delays between discretionary and non-discretionary passenger trips, as well as the costs associated with travel time delays to freight. Currently, the NRI treats all trips and all travel time delay equally – regardless of trip purpose or use category.

5)  To evaluate the scalability of the NTR metric and to investigate alternative mathematic formulations of the metric to ensure that the NTR is scalable across all types of networks, regardless of physical size, topology (the physical spatial layout of the network), connectivity, and demand levels.

Our goal is to develop a more detailed and flexible travel demand modeling approach using the TDPM and to improve upon the NRI and NTR metrics. The suggested improvements will provide substantial benefits to existing management practices. We also feel that our methods can serve as a foundation for future research in the areas of travel demand modeling and network disruption / critical infrastructure modeling.

ACKNOWLEDGMENTS Funding sources for the previous research related to the NRI include: the US Department of Transportation (USDOT), Federal Highway Administration (FHWA) awarded through the University of Vermont Transportation Research Center and the New England University Transportation Consortium at MIT.

We currently have several outstanding proposals under review at the National Science Foundation (NSF) and the USDOT.

BACKGROUND Our project builds upon recent research that addresses the need to better define and measure transportation system performance concepts such as flexibility and reliability by refining two network performance metrics: 1) the Network Robustness Index (NRI), and 2) the Network Trip Robustness (NTR). We define network robustness as the degree to which the transportation network can function correctly in the presence of some type of capacity disruption on component links. The link-specific NRI allows the individual links in a network to be rank-ordered based on how critical they are to the overall performance or functionality of the entire network. A link is more critical if its removal results in a high increase in the network-wide travel time compared to the removal of a less critical link which results in a low increase (or no increase) in the overall system travel time. The network-specific NTR is a measure of the aggregate travel-time change per trip and provides a scalable measure of network robustness that can be used to directly compare physically disparate networks, different sized networks, and networks with differing levels of connectivity and varying demand. The ease with which the NRI and NTR can be calculated using existing algorithms in planning software such as TransCAD® makes them ideal for actual implementation and use in real-world planning networks. The data currently contained within the travel-demand forecasting model within any city or region can be directly applied in this approach to obtain a list of system-critical links for consideration by policy makers. The Chittenden County Metropolitan Planning Organization (CCMPO) of Vermont has shown considerable interest in this methodological approach and the NRI has been used to rank-order the most important links in the CCMPO planning network.

The NRI is the increase in total vehicle-hours of travel (VHT) on the transportation network resulting from the disruption of an individual link. Disruption in this context is complete or partial capacity reduction. Therefore, the NRI metric is link-specific. First, total VHT is calculated for the base-case operational scenario (no links are disrupted): c = ∑iЄI tixi. Where ti is the travel time across link i, in hours per trip, and xi is the flow on link i at equilibrium. I is the set of all links in the network. Second, total VHT is calculated after link a is disrupted and system traffic has been re-assigned, including re-routing in a traffic assignment model: ca = ∑iЄI/a ti

(a)xi(a). Where ti

(a) is the new travel time across link i when link a has been disrupted, and xi(a)

is the new flow on link i. Notice the disruption of link a has the potential to affect travel time on all links in the network and not just on link a. The NRI of link a is calculated as the increase in total VHT over the base case: NRIa = ca – c.

The Network Trip Robustness (NTR) is calculated by summing the NRI values associated with each individual link and dividing that sum by the total demand in the network: NTRn = ∑aЄI NRIa / Dn . Dn is the total demand between all origins and all destinations in network n. Dn represents the total number of trips, so the units for the NTR are expressed as a unit of time per trip.

METHODOLOGY / DATA Travel Demand Modeling: One of the most complete sources of street mapping for the entire United States is the US Census Topologically Integrated Geographic Encoding and Referencing system (TIGER) line layers. The 2009 TIGER/Line files will be used in this research. The TIGER GIS data does not include all network link fields used to calculate the NRI - capacity, free-flow speed, and free-flow travel time. However, the Census Feature Class Codes (CFCC) can be used to infer the capacities and free-flow speeds of the roads in the network. We will use the CFCC data to estimate capacities and free-flow speeds for all links within the TIGER GIS networks. The E911 database for the state of Vermont is a point layer in GIS that represents all residence locations (single locations family homes, multi-family homes, seasonal homes, and mobile homes) and non-residence locations (commercial, industrial, education, government, health care and public gathering) in Vermont. The primary use of the database is for emergency responders to accurately identify the location of distress calls. In Vermont, the E911 database is publicly available through the Vermont Center for Geographic Information. This building-specific data will be used to generate a disaggregate proxy of origin-destination travel demand, assuming that each structure generates and attracts trips. Travel characteristics for residential buildings will be estimated using the new 2008 National Household Travel Survey (NHTS) data and the Origin Destination (OD) travel demand matrices will be derived with a doubly-constrained gravity-model. Use of the TIGER line data will allow us to select regions based on the characteristics that are determined to be most useful or appropriate for our study and not by artificially constrained existing TAZs.

Trip Importance: The trip matrices developed in the TDPM (above) will be broken down into four separate sub-matrices corresponding to trip purposes that are relevant to the value of importance: 1) Discretionary. 2) Non-Discretionary (Mandatory) 2a) Professional/business, 2b) Freight, and 2c) Other. The relative frequency of each of these trip purposes (all except freight) will be derived from the 2008 NHTS (NHTS, 2008). These frequencies will be used to apportion a fraction of the total demand already estimated to each of the trip purposes. A new factor will be introduced to the NRI to incorporate the user’s valuation of travel time, valuation of travel by trip purpose, and valuation of travel time for freight, into the rank-ordering of the links in the network. Each of the trip purposes will be assigned a “value-of-time” taken from the literature. This monetary value, mp, will be converted into an importance-based, unitless “tag”, vp, based on its relationship to the value-of-time for all purposes, P: vp = mp /∑pЄP mp. The system-wide cost, c, will now be: c = ∑iЄI ∑pЄP vptixp such that ∑pЄP xp = xi. Where ti is the travel time across link i, in minutes per trip, xp is the flow on link i due to trip-purpose p at user equilibrium (the sum of the flows for all purposes on link i is xi, the total flow on link I). I is the set of all links in the network. The new variable v will be a purpose-based importance “tag”, with a dollar value per unit time. P is the set of all trip purposes on link i at user equilibrium. The formally used travel-time-based cost factor, xiti, is therefore modified by the importance of each trip purpose on the link. The system-wide cost, ca, after link a is disrupted and system traffic has been re-assigned to a new equilibrium, will be: ca = ∑iЄI∑pЄP vpti

(a)xp(a). Where ti

(a) is the new travel time across link i when link a has been disrupted, and xp(a) is the new flow on link i due to trip-purpose p. The same constraint on link flows applies and the NRI of is calculated in the same way as the

difference between ca and c. Except that now the NRI is in monetary units instead of time units.

Assessing Scalability: The NTR has advantages over other network performance measures because it accounts for network-wide travel demand, link capacities, and traffic re-assignment while other measures only account for static network topology. The formulation of the NTR has been shown to be stable for comparisons of the robustness of hypothetical transportation networks (Sullivan et al., 2009b) where scaling problems were avoided. To test the scalability of the NTR it will be necessary to obtain NRI and NTR outputs for a range of networks spanning three orders of magnitude in population to conduct statistical analyses of scaling relationships. The road networks generated using the TDPM procedure will be used. The relevant variables for scaling of the NTR are variables used to determine the “size” of a network (population) – the total travel-demand in the network, Dn , and the NRI values. Two tests will be used to determine the scaling relationship of the NTR: 1) a test of the distribution function, and 2) a regression analysis. First, the cumulative distribution function of the actual NRI values will be evaluated to see if and how the function changes across networks of varying sizes. The complementary cumulative distribution function (CCDF) of the NRI values will be calculated for various networks across a wide range of sizes and will identify differences and similarities in the distributional forms. Significant differences in the CCDFs of the NRIs for networks of different sizes indicate that the NTR is not scalable as formulated. Alternative formulations which bring the CCDFs closer together will be explored. Second, the NTR will be tested directly for scalability using regression analysis. Since the NTR uses the total demand in the network, Dn, the relationship between Dn and the value we use to indicate the size of the region (population) can be tested. If total demand relates isometrically to population, then the scalability of the NTR will depend entirely on the test of the NRI distributions. The presence of scaling relationships in the NTR will require that either (1) the formulation of the NTR be altered to reflect the new scaling relationships discovered, or (2) the NTR be discarded as a useful measure of network robustness.

UNIVERSITY OF VERMONT TRANSPORTATION RESEARCH CENTER BURLINGTON, VERMONT www.uvm.edu/trc