# Transportation Network Design Following a Large Metropolitan Earthquake - 2502005a

Project Title—ID Number | Transportation Network Design Following a Large Metropolitan Earthquake - 2502005a |

Start/End Dates | 10/1/05 – 9/30/06 |

Funding Source | PEER-CA State Transp. Fund |

Project Leader (boldface) and Other Team Members | Yueyue Fan (UCD/F), Changzheng Liu (UCD/GS), P.N. Raghavender (UCD/GS) |

## Project goals and objectives

The highway system is one of the most important lifeline systems subject to natural and manmade hazards. The main objective of this research is to ensure a high level of reliability for continued operation of the system following an earthquake through more efficient transportation operation and resource allocation.

## Role of this project in supporting PEER's mission (vision)

These results build closely on what has already been done, and will be relevant to both MAE and MCEER researchers pursuing related research. The proposed models would fit usefully into the FHWA/MCEER REDARS Project. REDARS does not currently include decision support components, and there are no plans to extend research at MCEER to address this problem. Therefore, it would greatly add to the tri-center initiative to provide the basis for implementing a network reliability analysis model and post-earthquake emergency vehicle routing and network reconstruction decision support models into REDARS. Once implemented, such a model would make REDARS a more attractive tool for investigating other issues of interest to PEER, for e.g.., evaluating the economic impact of improved bridge performance and/or the ability to more accurately predict performance through improved fragility models, and more importantly how limited resource might be more efficiently spent in disaster mitigation.

## Methodology employed

### Routing through damaged networks

Consider the stochastic network shown in the figure below with nodes numbered as 1, 2, ..., N. Given estimated link travel times (given as mean and deviation, or probability density function) on any link ij, a network routing problem findnode to the desired destination.

In this project, we focus on the movement of emergency vehicle immediately following earthquakes, and therefore do not consider the effect of traffic congestion. This is a reasonable modeling assumption since emergency vehicles usually do not need to compete with normal traffic. It reduces the computational complexity of the problem and avoids having to approximate the travel demand following disasters, which itself is a challenging socio-economic question due to too many uncertain aspects involved. The uncertainty of travel time mainly comes from the physical damage to the transportation facilities caused by the earthquake, rather than congestion and demand fluctuation. For example, a highway bridge of minor damage may still function at full capacity and speed level, whereas a highway bridge above some major damage level may be closed entirely. The probabilistic estimation on physical damage in a given earthquake scenario will be acquired from other PEER researchers or by using the risk assessment package REDARS. The decision criteria for routing are set to be (1) to choose a route that minimizes expected total time delay, and (2) to choose a route that maximizes the reliability of travel time between the given origin-destination pair.

### Task 2: Network repairing strategy

Task (2) is newly added to our Years 9 and 10 research to address an equally important problem in disaster management, post-disaster recovery problem. Our previous work on the economic loss assessment (Years 6&7) provides the basic information need to complete standard cost benefit analyses with respect to allocating resources for disaster mitigation. Our long term goal is to determine which mitigation and repair projects should be undertaken. By retrofitting or repairing some subset of existing facilities, or by adding new components to a transportation network, system planners can change the post-earthquake network configuration. This changes network performance, and travelers' behavior. Broadly stated, our research goal is to find, subject to certain resource constraints, which components should be retrofitted (in pre-disaster scenario) or repaired (in post-disaster scenario) so that the overall performance of any metropolitan transportation system is most greatly improved. This well-defined network design problem is important in the transportation network literature [2]. We start investigating a post-earthquake network design problem, which is deterministic since we are given a deterministic initial network condition to start with. The standard objective function is aggregate network delay. Most studies set the performance measure as the total expected travel delay of all users in the network. In the conventional equilibrium model, the definition of the best route is a path between the specified origin-destination pair that is of the minimum travel time. Since the travel time over a certain link depends on how congested the link is, each individual's routing decision will affect others' choices. Therefore, routing decisions of all travelers in the transportation network must be studied simultaneously. Since individual users and network planners usually do not have the same objective, this kind of network design problem often involves multiple levels of optimization. At the upper level, the system planner makes decision on resource allocation in order to achieve the best system performance. At the lower level, the network users make their travel decision based on their individual travel preferences. For a large network such as the San Francisco Bay Area network, this kind of network design problem is computationally challenging. At present, we are developing effective approximation mechanism based on artificial intelligence techniques for solving large scale problems.

In contrast, in a pre-event network design problem, the occurrence and the scale of the damage and capacity loss resulting from seismic events in the planning period are uncertain. Therefore, the initial network configuration faced in the pre-event case is stochastic, and the optimal design problem becomes stochastic. This extra uncertainty makes the pre-event network design problem even more challenging. In this project, we will focus on the post-disaster recovery problem. Starting with a problem that is more tractable reflects the PEER spirit: first to make it work, then to make it work better. The major part of this research is to develop an optimization model with evolving modeling objectives. At the early stage of system recovery process, the primary recovery objective is to ensure timely and smooth movement of emergency activities. As the recovery process continues, we will gradually give more weights to public traffic, where the primary goal becomes to satisfy more travel demand from the public at an acceptable congestion level.

## Brief Description of previous year's achievements, with emphasis on accomplishments during last year (Year 8)

Task 1 is a continued effort from our Year 8 research. Currently, we are in the process of completing mathematical modeling and numerical implementation of the proposed path-finding models. In addition to development of various network routing methods addressing different risk attitudes and different level of environment uncertainty, we are coordinating with Prof. Ann Kiremidjian and her students regarding the study area and earthquake scenarios. The Stanford team is providing estimation of seismic damages of individual bridges and the correlations of damages among neighboring bridges. This information is being input to our shortest path model to compute the best routing strategy, where correlation and real-time feedback control are taken into account. Our current agreement is to start with a relatively small network (including about 50 bridges) in the northeastern San Francisco Bay area, then expand the study area to a county once the methods from the two teams are integrated and validated.

### Results from Year 8 are:

- - Computer module for computing the expected and reliability of travel time from point A to point B. The maximum probability of not exceeding a desired time threshold indicates whether emergency tasks between the two locations A and B can be carried out effectively. This information, together with other network performance measures, such as throughput and connectivity, can also be used as performance measures to guide decision making on network recovery planning.
- - Routing strategy to be followed to achieve above-mentioned maximum probability. The routing strategy can guide the emergency vehicles through the damaged network via the in-vehicle guidance system.

## Other similar work being conducted within and outside PEER and how this project differs

As noted in the Objectives, this work will produce results that can be incorporated into the MCEER/FHWA REDARS model. This work plan has been constructed in consultation with ImageCat, Inc. and Seismic Systems personnel with the intent of complimenting and supporting development of the MCEER/FHWA REDARS (Risks from Earthquake Damage to Roadway Systems) tool and its deployment in the Caltrans demonstration project. The work done by Prof. Moore and Prof. Fan in previous PEER fiscal years on variable demand and the economic cost of trips forgone following an earthquake has been partially incorporated into REDARS, and ultimately will be in its entirety.

## Expected milestones & deliverables

In Year 9, we expect to complete the development of mathematical model for the network recovery problem. In Year 10, we plan to test the optimization model(s) in several representative earthquake scenarios, and to integrate these models into geographic information systems, so that the projects results can be better understood and utilized by a broad audience. We will also coordinate with Stu Werner to integrate the optimization model to the current version of REDARS model, so that the entire procedure from risk analysis to optimal decision making on disaster mitigation and emergency response can be automated.

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