Network Robustness Index: A new method for identifying critical links and evaluating the performance of transportation networks

Abstract

Highway planning efforts, especially those involving capacity expansions, have traditionally relied on the volume/capacity (V/C) ratio to identify “highly congested” or critical links, resulting in localized solutions that do not consider system-wide impacts. This paper presents a new, comprehensive, system-wide approach to identifying critical links and evaluating network performance. The approach considers network flows, link capacity and network topology. Moreover, it relies on readily available sources of data. Using three hypothetical networks, we demonstrate that the approach, known as the Network Robustness Index, yields different highway planning solutions than the traditional V/C ratio. Moreover, these solutions yield far greater system-wide benefits, as measured by travel-time savings, than solutions identified by the V/C ratio.

Introduction

In the United States, the interstate highway system is undoubtedly one of the most critical components of the transportation system due to its role in facilitating economic growth, providing timely access for travelers and contributing to the nation’s defense. In recent years, the country has witnessed incredible growth in vehicle travel on the interstate system. Between 1991 and 2001, for example, overall vehicle travel increased by 38% and commercial truck travel increased by 42% (TRIP, 2003). Consequently, in many urban and suburban locations, the interstate system has become highly congested (Schrank and Lomax, 2005)—an unfortunate situation that is not remedied easily (Scott, 2002). Simply stated, it is impossible to expand all such sections and to meet all travel demand with a high level of service given the current fiscal environment. In a world of limited resources, where funds do not necessarily keep pace with the growing demand for infrastructure improvements, not to mention the increasingly costly maintenance of aging infrastructure, it is essential to make well-informed public policy choices when selecting specific segments for improvement (USDOT FHWA, 1996).

Certain regions of the country may rely on the interstate highway system more than others if their economic specializations and trading relationships with the rest of the nation and other countries are contingent upon truck transport. While not necessarily as congested as urban interstate sections, the economic consequences of even a relatively short-term disruption in travel on rural interstate links may be extremely serious for these regions, effectively cutting or severely curtailing access to other regions of the country, and even isolating the affected region from particular inputs or markets. For example, the 1994 Northridge, CA earthquake is estimated to have resulted in nearly $1.5 billion in economic losses attributed to transportation interruptions (Davis, 1998). In 2004, a tanker truck accident along I-95 closed a mile-long section of interstate near Bridgeport, CT. The economic consequences of the closure were severe, with construction costs alone amounting to $4 million and another $11 million in emergency federal aid required to reopen the interstate (Scarponi, 2004). Connecticut declared a state of emergency and heavily traveled portions of I-95 were completely closed to commercial truck traffic for several weeks (Associated Press, 2004). Commercial trucks were required to completely by-pass large portions of Connecticut and reroute through New York and Massachusetts while repairs to the interstate were made. The impact of this closure on the network was not only a function of the demand on the closed section itself, but also on the availability of alternative detour routes, their capacity and level of usage.

The removal or blockage of one or more network links, particularly those that are heavily traveled or those containing bridges, could have direct and serious economic consequences in terms of overall system travel-time increases, but also with respect to freight logistics/supply-chain management (Bell, 2000, Chen et al., 2002, Smith et al., 2003). Not only could supply routes and delivery schedules be disrupted, but also the costs associated with rescheduling and rerouting could be prohibitive for both suppliers and resellers. Rerouting traffic could also result in additional safety risks and congestion on alternate interstate segments, particularly if a large volume of commercial vehicle traffic were routed to links that were already operating at or close to capacity. Depending on the spatial layout of the network (i.e., network topology) and on specific origins and destinations, different types of traffic could have very difficult times rerouting in the event of a link failure (Bell, 2000).

Network “flexibility” addresses spatial organization in various infrastructure (e.g., communications and transportation) planning and engineering practices. Feitelson and Salomon (2000) identify network flexibility as a network attribute that relates to a network’s physical characteristics and to the level-of-service it provides users. The authors suggest that differences in network flexibility have important ramifications for spatial organization, particularly at the macro level. Morlok and Chang define “system capacity flexibility” as “the ability of a transport system to accommodate variations or changes in traffic demand while maintaining a satisfactory level of performance” (Morlok and Chang, 2004, pp. 405–406). A flexible highway network must therefore be able to adapt to changes in the quantity of traffic, freight commodity mix and spatial flows from one geographic area to another. Capacity flexibility is an important issue for two reasons. First, the seemingly endless growth in US road traffic coupled with a relatively stagnant highway infrastructure requires flexibility in terms of serving increasingly high levels of travel demand with a relatively constant supply of infrastructure capacity. Second, dramatic changes in trade patterns, the types of goods carried and the nature of transportation services needed require a flexible transportation infrastructure (Morlok and Chang, 2004).

Bell (2000) offers the following definition of “network reliability”. “A network is reliable if the expected trip costs are acceptable even when users are extremely pessimistic about the state of the network” (Bell, 2000, p. 534). According to Bell, reliability pertains directly to instances of natural disaster when parts of the transportation network may fail and also to road space reallocation among competing transportation modes such as transit, pedestrians and cars. He points out that reliability has two dimensions: network connectivity and performance reliability. In the case of network connectivity, the more sparsely connected the network, the more difficult it may be for travelers to arrive at their destinations on schedule if there are segment blockages or failures. Measuring reliability is difficult as it includes both the physical infrastructure and the behavioral responses of travelers. Chen et al. (1999) consider capacity reliability as a network performance index that builds upon the network reliability concepts introduced by Bell and Iida (1997). Chen et al. (2002) define capacity reliability as “the probability that the network can accommodate certain traffic demand at a required service level, while accounting for drivers’ route choice behavior” (Chen et al., 2002, p. 227).

In this paper, we draw on both the flexibility and reliability concepts introduced by other researchers. Each offers important insights into the spatial layout of the physical highway network, the need to address capacity planning and, more generally, transportation planning from a system-wide perspective taking into account network topology. Current infrastructure management practices typically address the complex decision-making required just to manage demand on individual congested portions of the highway network by identifying critical highway segments using localized level-of-service (LOS) measures such as the volume/capacity (V/C) ratio (Bremmer et al., 2004, Dheenadayalu et al., 2004). A V/C ratio greater than one is indicative of congestion. When a high ratio is identified, improvements are implemented at the segment or corridor level to alleviate or reduce congestion on that particular segment. Often the solution to congestion planning problems is to simply add more capacity along existing highway segments. In effect, this is a localized solution. Performance improvements are measured via a decrease in travel times on specific segments in the local area of the improvement.

The localized V/C approach, however, may not enable traffic engineers and planners to identify the most critical highway segments or corridors in terms of maximizing system-wide, travel-time benefits associated with a highway improvement project. Bremmer et al. (2004) point out that traditional congestion measurements are based on volume and capacity information, but are often inadequate in many cases. Potential problems associated with the V/C ratio are illustrated in the hypothetical and greatly simplified network shown in Fig. 1.

A comparison of V/C ratios suggests Link 2 is the more critical link—that is, the ratio on Link 2 is equal to 1, while the ratio on Link 1 is equal to 0.3. However, Link 1 carries three times the traffic volume of Link 2. If Link 1 were eliminated, or even partially blocked, rerouted traffic from Link 1 cannot be accommodated on Link 2 as it does not have the capacity to handle the additional traffic. On the other hand, if Link 2 were blocked, rerouted traffic can be accommodated easily on Link 1. Link 1 is actually the more critical link, although the V/C ratio does not adequately reflect its importance to the highway network.

We believe the current, localized planning approach should be improved upon, as it does not consider system-wide impacts resulting from improvement projects. While implementing local solutions may result in localized benefits, these solutions may have limited, negligible or even adverse system-wide effects. Recent studies of induced travel in North America offer strong evidence that this is indeed the case (see Scott, 2002 for a review of such studies). An equal level of investment in another location or locations may provide more benefit to the network. We argue that it is time to reconsider the existing localized V/C-based planning approach and focus on a comprehensive system-wide approach to identifying critical infrastructure and evaluating network performance. Improvements should thus be evaluated in terms of maximizing the performance of the highway system from a system-wide perspective. This approach should complement existing local planning to prevent the spread of localized problems to other parts of the highway network.

Our research is based on the premise that a fundamental change in highway network design philosophy is needed. We believe that a transportation network should not only meet origin-destination (OD) demand, but should provide ample connectivity so as to not be overly vulnerable to disruptions on individual segments within the system. This directly supports the importance of the concepts of transportation flexibility and reliability. The underlying goal of the planning and management process should encourage the development of well connected highway networks that focus on spatial relationships between different segments, as well as using the traditional V/C measure. In this paper, we introduce a new measure for identifying critical network links and evaluating network performance that considers not only traffic flows and capacity, but also network connectivity. We test how well the proposed measure performs compared to the traditional V/C ratio by using three hypothetical networks, each of which is characterized by a different level of connectivity. We demonstrate that our approach, known as the Network Robustness Index, yields different highway planning solutions than the traditional V/C ratio. Moreover, these solutions yield far greater system-wide benefits, as measured by travel-time savings, than solutions identified by the V/C ratio.

The remainder of this paper is organized as follows. The next section presents a brief review of related literature. A discussion of key transportation indices, namely the gamma index and the V/C ratio, follows in Section 3. Derivation and implementation of our new approach, the Network Robustness Index, is discussed in Section 4. The data employed in our study are described in detail in Section 5. Results are found in Section 6, followed by the conclusions in Section 7.