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Integrated Evacuation Network Optimization and Emergency Vehicle Assignment Chi Xie and Mark A. Turnquist a two-stage solution strategy is described, where the emergency vehicle assignment constrains subsequent decisions on lane reversal and intersection use. A brief description is provided of the Lagrangian relaxation and tabu search method that solves the evacuation network optimization problem. The model and solution procedure are illustrated in an evacuation case study for a nuclear power plant in Monticello, Minnesota.

Three treatments are combined in the design of evacuation network operating plans: reversing lanes, eliminating intersection crossings, and reserving lanes for use by emergency vehicles. An optimization approach is taken and casts the problem as a form of discrete network design, with constraints imposed by emergency vehicle lane assignment. What have previously been separate strands of work examining ways of configuring road networks for effective evacuation performance are integrated. A case study for a network around a nuclear power plant illustrates the usefulness of this integrated approach.

MODEL FORMULATION Evacuation is an important emergency response strategy to protect human populations from potentially catastrophic events. During the past three decades, considerable research has been conducted on developing evacuation plans. Recently, interest in lane-reversal schemes to increase available evacuation capacity has grown (1–4). Many evacuation routes are at least partially on signal-controlled arterials, and intersections usually are the capacity-limiting parts of the network. At least two studies have focused on or included intersection crossing elimination as a strategy to reduce overall delay in defining an evacuation network (5, 6). The basic rationale for eliminating crossings during an evacuation is to convert an intersection from interrupted to uninterrupted traffic flow by prohibiting some turning movements, blocking lane entries, and limiting flow directions. The first objective of the present study is to combine lane reversal with intersection crossing elimination into an integrated approach to evacuation network design. Evacuation performance (measured by network clearance time or total evacuation time, for example) is a vital characteristic of an evacuation network design, but it is also important to consider access to the evacuation area by emergency vehicles and equipment (7, 8). Furthermore, if buses are an integral part of the evacuation strategy, then they need to be able to return to the area to pick up more people. The need for inbound access to the area being evacuated may conflict with the desire to maximize outbound capacity, particularly when lane reversal strategies are used. The second objective of the work presented in this paper is to incorporate emergency vehicle route assignment into the evacuation network design process. In the following section, a model formulation of evacuation network design is presented as an explicit optimization problem. Next,

The core idea of integrating the treatment of lane reversals and crossing elimination in evacuation network design is illustrated by the examples in Figure 1, which show how controlling lane entries and turning movements at intersections can create uninterrupted flow conditions for specific evacuation paths. The intersections must be expanded into subnetworks, as shown in Figure 2, to model an evacuation network design that uses lane-reversal and crossingelimination strategies. Figure 2 also illustrates how intermediate nodes are introduced into roadway sections to serve as origins of evacuation trips. The parameters, sets, and variables used in the model are listed below. Parameters and sets nικ,ϑρ = total number of lanes of two adjacent link pairs ι → ς → κ and ϑ → τ → ρ in a roadway-section subnetwork cις(nικ) = capacity of roadway-section link ι → ς, as a function of lanes allocated to the traffic direction ι → κ uηι = dummy capacity of link η → ι, where η → ι is an intersection link t 0ις = free-flow travel time on link ι → ς, where ι → ς is a roadway-section link bς = net flow rate at node ς Sι = set of the starting nodes of links pointing to node ι Rρ = set of the ending nodes of link emanating from node ρ Variables nικ = number of lanes on link pair ι → ς → κ, where ι → ς → κ is a pair of consecutive roadway-section links n lικ = number of reserved lanes for emergency vehicle us on roadway link pair ι → ς → κ xις = evacuation flow rate on link ι → ς tις = travel time on link ι → ς, where tις is a function of xις and nις yηι = connectivity indicator of link η → ι, where η → ι is an intersection link l yηι = connectivity indicator of link η → ι used by emergency vehicles, where η → ι is an intersection link

C. Xie, Center for Transportation Research, Department of Civil, Architectural, and Environmental Engineering, University of Texas, Austin, TX 78759. M. A. Turnquist, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853. Corresponding author: M. A. Turnquist, [email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2091, Transportation Research Board of the National Academies, Washington, D.C., 2009, pp. 79–90. DOI: 10.3141/2091-09

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T krs = perceived travel time on path k between O-D pair r-s δ rsις,k = path-link incidence indicator denoting the relationship rs between link ι → ς and path k(δ ις,k = o or 1)

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FIGURE 1 Examples of joint use of lane reversal and crossing elimination.

zικ = connectivity indicator of link pair ι → ς → κ, where ι → ς → κ is a pair of consecutive roadway-section links (zικ = 0 or 1) qrs = evacuation flow rate between origin–destination (O-D) pair r-s f krs = evacuation flow rate on path k between O-D pair r-s

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In an emergency evacuation, many evacuees may be uncertain about their destination and also may be using unfamiliar routes. In some cases, many people may be headed to designated shelters, but many evacuees are likely to focus on simply leaving the emergency area. Traffic conditions during an evacuation are abnormal, so the usual knowledge that people have about choosing routes probably will be irrelevant. Under these conditions, some type of stochastic traffic assignment probably will be most appropriate, because it allows for variations in perceptions of travel time and produces a predicted flow pattern that is based on much milder conditions than the usual assumptions for deterministic equilibrium. In the model formulated below, a probit-based stochastic equilibrium is assumed (9, 10). The assumption that evacuees determine destination and route choices simultaneously is implemented by connecting all shelter locations and network exit nodes to a single “super” destination node. Thus, in terms of network modeling, all travelers have the same destination but may reach it through different shelter nodes or network exits, each of which constitutes a “real” destination. By including capacities on the connection arcs from shelter nodes, for example, to the super destination, capacity limits at those shelters can be respected. The evacuation network optimization problem is formulated as a lane-based discrete network design model where the underlying traffic flow pattern follows a stochastic user equilibrium. It has a bi-level structure. Stochastic traffic assignment forms the bottom level of the model and can be specified by an equivalent mathematical program (11); the top level minimizes total network evacuation time by selecting lane reversals and crossing elimination variables. The model is described as follows; more details are presented elsewhere (12). min t ( x, n ) = ∑ ις x ις t ις ( x ις , ntκ )

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12) in the bottom-level part of the model are (nominal) capacity constraints for links in a roadway-section subnetwork and in an intersection subnetwork, respectively; the third constraint is the flow nonnegativity constraint. The next two constraints (Equations 14 and 15) denote the flow conservation relationships of source nodes and nonsource nodes. Equations 16, 17, and 18 describe the inherent relationships of traffic variables, such as traffic flow rate and travel time at the link, path, and O-D levels. Some evidence indicates that the overall capacity of links with reversed lanes is not necessarily proportional to the number of lanes (13). Accordingly, a general expression cις(nικ) is used for the capacity on link ι → ς. In the specific case study presented later, the total road capacity for one traffic direction is assumed to be simply the product of the number of lanes of this traffic direction and single-lane capacity. However, the model formulation is more general. Emergency vehicle route assignment involves reserving a specified number of lanes (typically one or two) along paths between designated origins and destinations (e.g., shelter locations, fire stations, hospitals, designated bus pick-up points for evacuees, and disaster site) for use by emergency vehicles and evacuation buses. This assignment is done by using a simple shortest-path procedure over a network that includes all links that have a sufficient number of lanes. After these lanes are reserved (i.e., setting variables nικl , n lϑρ, and y lμγ in the above model formulation), they serve as constraints on the lanereversal and crossing-elimination decisions for evacuation design (Equation 2). There is a trade-off between the amount of roadway capacity reserved for emergency vehicles and evacuation buses and the effectiveness of the network design for evacuees in private vehicles. Aspects of this trade-off are explored in the case study described later.

SOLUTION METHOD (114) (15)

where qrs = ∑ k fkrs

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The objective of the top-level part of the model (Equations 1 through 9) is to minimize total evacuation time over the evacuation network. The first two constraints (Equations 2 and 3) describe the capacity reservation relationship of any reversible roadway sections and nonnegativity and integral requirements for roadway-section design variables. The next three constraints (i.e., Equations 4, 5, and 6) represent the crossing elimination requirement. Equations 7 and 8 quantify the relationship between a roadway-link connectivity indicator and the corresponding number of lanes: if zικ = 1, then nικ ≥ 1, and vice versa; if zικ = 0, then nικ = 0, and vice versa, where M is an arbitrary, sufficiently large constant. For the validity of this set of constraints, M ≥ maxικ,ϑρ (nικ,ϑρ) must be set. The bottom-level problem (Equations 10 through 18) describes the stochastic equilibrium flow conditions, as described originally by Sheffi and Powell (11). The first two constraints (Equations 11 and

The solution procedure follows a two-stage process. First, the emergency vehicle routing problem is solved, resulting in one or more reserved emergency vehicle routes; then, the evacuation network optimization problem is solved over the remaining network capacity and connectivity. In this section, the main elements of the evacuation network solution procedure are described. The algorithmic description is somewhat abbreviated because of length considerations; Xie presents a more complete discussion of the algorithm elsewhere (12). The evacuation network optimization problem is a form of the discrete network design model. The computational complexity comes from its combinatorial characteristics and bi-level structure, which imply that in general the problem is nonconvex. A metaheuristic method is proposed to address this problem. It takes advantage of Lagrangian relaxation for problem decomposition and complexity reduction and uses an algorithmic design based on tabu search principles. In this Lagrangian relaxation framework, the set of crossingelimination constraints (i.e., Equations 4, 5, and 6) are relaxed and compensated for by a penalty term in the objective function. The relaxed Lagrangian problem becomes a pure lane-reversal optimization problem plus a penalty term. Evaluation of the penalty term collapses to a set of optimization problems for reducing intersection-level crossings. The Lagrangian relaxation problem can be written as min ∑ ις x ις t ις ( x ις , ηις ) + ∑ I ∑ ηι ,ρσ Pηι ,ρσ ( yηι + yρσ − 1)

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where (yηι + yρσ − 1)+ equals max(0, yηι + yρσ − 1) subject to Equations 2, 3, and 7 through 18.

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The rationale behind the application of Lagrangian relaxation should be emphasized. First, note that in the network optimization model, all travel costs are associated with the links in roadwaysection subnetworks, whereas intersection subnetworks are used only for specifying intersection turning movements. In this regard, the intersection crossing-elimination constraints may be treated as side constraints, and the objective function value (of the original problem) is determined only by the lane-reversal configuration. Second, with the relaxation of crossing-elimination constraints, the traffic assignment can be performed in a reduced version of the network, in which any intersection subnetwork collapses to a node. This relaxation greatly reduces the problem size and computational burden. Third, the pure lane-reversal optimization problem may result in an optimal solution with full lane reversals on many roadway links. If

Equation Box 1

this is the outcome, then the resulting flow pattern can be accommodated locally at many intersection subnetworks without causing any crossing points. Ultimately, as long as an optimal solution to the Lagrangian problem is found with the penalty term value equal to zero, this optimal solution also is optimal to the original network optimization problem. Thus, the Lagrangian relaxation strategy offers a convenient approach to reduce the problem size and complexity so that the original problem can be addressed by solving a series of traffic assignment subproblems and crossing optimization subproblems sequentially. The major algorithmic steps of this integrated Lagrangian relaxation and tabu search (LR-TS) method are summarized using the pseudo code in Equation Box 1. The term “integrated” is used to mean that the updating of Lagrangian multipliers is integrated into the iter-

Algorithmic Procedure of LR-TS Method

algorithm LR-TS heuristic; begin define elite_size, tabu_tenure, freq_threshold, max_iteration_num, max_diversification_num; define roadway subnetwork set R={r}, intersection subnetwork set T={t }, crossing-elimination constraint C(t ) = {c} for each t ∈T; initialize i:=0, best_solution, unit_penalty(c):=0, for each c ∈C(t ), t ∈T; while i < max_diversification_num do begin create tabu_list, residence_freq; j:=0; while j < max_iteration_num do begin create elite_list; for each r ∈R do begin if residence_freq < freq_threshold begin identify a candidate move, move(r); evaluate the objective function of move(r ), obj(move(r )); if move(r ) belongs to tabu_list then begin cancel the candidacy of move(r ); if obj(move(r )) < obj(move(best_solution)) then begin retrieve the candidacy of move(r ); end; end; update elite_list; end; end; for each move(e) ∈elite_list do begin conduct a local move, move(e), and evaluate obj(move(e)); update unit_penalty(c) for each c ∈C(t ), t ∈T; update tabu_list; update residence_freq; update best_solution; k:=k+1; if obj(move(e))≥obj(best_solution) then j:=j+1 else j:=0; end; end; conduct a diversification move; i:=i+1; end; end;

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ative tabu search process. Lagrangian multiplier values are reviewed and updated at each iteration in terms of the historical and current network solutions. The search starts with a feasible lane-reversal network solution, then proceeds with a sequence of local searches and diversification phases based on typical tabu-powered algorithmic steps until a predetermined stopping criterion is met. Each local search scans all the candidate lane-reversal network solutions in the neighborhood, evaluating the objective function of the Lagrangian problem for each solution. The total evacuation time over the network is evaluated by solving a traffic assignment subproblem; the evaluation of the penalty term consists of a set of crossing optimization subproblems. An iteration is finished by accepting a best network solution from the neighborhood as the new current solution. The algorithmic choices and LR-TS steps are described in detail elsewhere (12). To compute the value of the penalty term in the objective of the Lagrangian problem, a series of optimization problems for intersection crossings must be solved. For each intersection, the objective of the problem is to find the minimum number of crossing points in the intersection subnetwork. This problem can be formulated as the following mixed-integer programming model, given a typical four-leg intersection such as the one shown in Figure 2: min c ( y ) = ∑ ηι ,ρσ ( yηι + yρσ − 1)

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where Sι is the set of the starting modes of all links pointing to node ι (e.g., Sι = {η, ϕ, μ} in Figure 2) and xις is an input parameter, which is the result of the traffic assignment process. The objective function of this crossing optimization program serves as a surrogate for the crossing-elimination constraints and counts the number of crossing points. If the optimal objective function value is greater than zero— that is, if one or more traffic crossing points exist—then the traffic flow pattern violates the crossing-elimination constraint at this intersection. The optimal solution of this problem independently determines the local traffic flow pattern in each intersection subnetwork and gives the most desirable traffic-crossing condition subject to the overall traffic flow pattern; it does not change the traffic flow pattern over the whole network. Although solving the crossing-minimization problem is indeed a problem of local network design and a traffic reassignment process in the intersection subnetwork, this local network change will not change the network traffic flow pattern. The intersection crossing–optimization problem can be efficiently solved by the branch-and-bound method or a simplex-based pivot method because of its relatively small solution space. Xie has described the latter method in detail (12). The computational cost depends on algorithmic parameters such as neighborhood structure, tabu list, and elite list as well as maximum iteration and diversification criteria, which jointly determine the number of objective function evaluations in a search process. The neighborhood structure and maximum iteration and diversification numbers depend on the problem size. For example, the number of candidate

solutions in a neighborhood is linear in the number of reversible roadway sections and the number of lanes in each reversible section. Thus, larger problems imply an increasing number of objective function evaluations. The objective function evaluation is dominated by the stochastic user equilibrium traffic assignment. In this study, an efficient approach—the approximate solution algorithm of Maher and Hughes, which has a similar algorithmic structure to the Frank– Wolfe algorithm—is implemented for solving the stochastic traffic assignment problem (14). The LR-TS method is a heuristic and cannot guarantee an optimal solution. Infeasibilities (i.e., violations of the crossing elimination constraints) are conceptually possible, but solution feasibility can be checked easily. In the authors’ extended calibration and evaluation experiments, no infeasible solution was found. Solution optimality is more difficult to access because in problems of realistic size, determining a provably optimal solution is computationally prohibitive. As an empirical evaluation effort, the solution quality of the LR-TS method was compared with two heuristics in the literature that can be adapted to solve the integrated lane-reversal and crossing elimination problem: the Flip-High-Flow-Edge (FHFE) method (3) and the Shortest-Path Tree (SPT) method (15). Across various test problems, the total evacuation time of the best solution obtained by the LR-TS method averaged 8% lower than that obtained by the FHFE method and 29% lower than that obtained by the SPT method. This result provides evidence that the LR-TS method is likely to provide solutions superior to existing heuristics. More discussions about the solution quality are available elsewhere (12).

CASE STUDY To illustrate the model and solution method, evacuation planning is considered for the nuclear power plant in Monticello, Minnesota. Monticello is in northern Wright County, along the Mississippi River about 30 mi northwest of Minneapolis. The Monticello nuclear plant is owned by Northern States Power, a subsidiary of Xcel Energy, and operated by Nuclear Management Company. The plant began operation in 1971 and is currently licensed until 2030. As enacted by the Nuclear Regulatory Commission (NRC) and Federal Emergency Management Agency (FEMA), an emergency planning zone (EPZ) with a 10-mile radius must be delimited, centered at the site of any nuclear power plant in the United States. Because the Monticello plant is situated along a river that forms a county boundary, this EPZ covers areas in Wright and Sherburne Counties. If a nuclear accident alarm is triggered, all inhabitants in the EPZ are required to leave the area so as to avoid potential exposure to a released radioactive plume. For evacuation planning, an evacuation network was extracted from the regional highway and street network. The resulting network (Figure 3) was originally constructed by Shekhar and Kim (3). The evacuation demand generation is estimated on the basis of the demographic data of the region from the U.S. Census 2000 survey. The total number of evacuees from the network is about 42,000. The surge demand rates are approximated by using the historical diurnal curves of evacuation demand generation, such as those presented by Goldblatt and Weinisch (16). Four potential evacuation destinations are identified for the Monticello network, at Nodes 40, 28, 23, and 2 (Figure 3). The first three destinations are designated emergency reception centers located at local high schools: Osseo Junior High School (Node 40), Rogers High School (Node 28), and Princeton High School (Node 23). These centers can provide evacuees with basic accommodations and

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medical services. All three reception centers are located in the eastern part of the area and may not attract inhabitants residing in the western part. The last destination node is an additional egress at the western endpoint of I-94 in the network (Node 2). The primary focus point for emergency vehicles within the evacuation area is the power plant itself. One or more routes in the evacuation network must be reserved between access nodes at the edges of the EPZ and the plant to ensure access to the plant for first responders and egress for the transport of casualties to area hospitals outside the EPZ. Three candidate routes were identified for emergency vehicle use in terms of the distribution of hospital locations and other emergency management requirements (Figure 4a). Routes 1 and 2 were established on I-94, connecting three hospitals in the east and seven hospitals in the west, respectively; Route 3 is on US-169, serving one hospital in the northeast corner of the network. The selection of emergency vehicle routes represents a trade-off between available hospital capacity for casualty treatment and the emergency route travel time to a hospital from the accident site. Figure 4b illustrates the relationship between the number of hospitals accessible within specified travel time limits and the set of designated emergency routes. Route 1 cannot provide four or more hospitals. If

four hospitals are required, then one of the following emergency routing schemes should be used: Route 2; Routes 1 and 2; Routes 1 and 3; Routes 2 and 3; or Routes 1, 2, and 3. The optimized evacuation network solutions corresponding to the six routing schemes for emergency vehicles are generated by the LR-TS search method and are presented in Figures 5 through 10. In all six evacuation network solutions, all roadway sections are fully reversed to be one-way streets, which guarantees no traffic crossing point at any intersection in the network. In extensive experiments with other network scenarios, few two-way roadway sections appear in optimal solutions. It suggests that an evacuation network optimization model with the full lane-reversal requirement might be a good approximation to solve the evacuation network optimization problem with lane-reversal and crossing elimination constraints. The lanereversal directions in each of the network solutions constitute a destination-oriented pattern. Emanating from the heart area of the network (which is far from any egress node), most roadway segments are reversed in such a way that the traffic is distributed over the network, moving outbound and merging at the egress nodes. Although the spatial patterns of these evacuation network solutions under different emergency vehicle routing schemes look similar, sev-

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FIGURE 9

Optimized network: Emergency Vehicle Routes 2 and 3. 7

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FIGURE 10

Optimized network: Emergency Vehicle Routes 1, 2, and 3.

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Xie and Turnquist

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eral roadway sections (as well as their associated intersections) are configured differently. In the central part of the network (e.g., 12-18, 18-24, 13-19, 19-25, 14-19, and 20-21), roadway sections show different lane-reversal directions over the solutions because of the capacity reduction or the connectivity prohibition imposed by the assigned emergency vehicle route(s) on the first stage. To further evaluate the different emergency vehicle routing schemes and the resulting evacuation network solutions, the trade-offs between access to hospital capacity (by reserving more emergency vehicle routes) and evacuation time for the population as a whole are assessed. These results are summarized in Figure 11. The selection of reserved emergency routes limits the potential effectiveness of the evacuation strategy that can be designed. In Figure 11, this is represented by the series of vertical dashed lines at various points along the x-axis (total evacuation time). If only Route 1 or Route 2 is reserved for emergency vehicle use, then the remainder of the population is able to evacuate reasonably effectively. If both Routes 1 and 2 are reserved for emergency vehicles, then the total evacuation time of the population increases by approximately 50%, because the use of both emergency Routes 1 and 2 precludes any lane reversal on I-94, which is a principal evacuation route. Adding Route 3 to the possible emergency routes creates further delays in evacuation for the population as a whole. If the event is small and only one hospital is required to treat casualties, then the best overall strategy is to designate Route 2 as emergency vehicle access, and the travel time to the hospital used is 38 min. (In this case, St. Cloud Hospital in St. Cloud, Minnesota, about 30 mi northwest of Monticello, was chosen; it is designated as Point 1 in Figure 11.) However, if more hospital capacity is required and only Route 2 is available for emergency access, then the average emergency route travel time increases rapidly (moving up the dashed line labeled Route 2, to get to additional hospitals). If an event is anticipated to require access to three hospitals, it might be much better to designate Route 1 as an emergency route because with only a small increase in population evacuation time, Route 1 provides access to more hospital capacity within a reasonable travel time (about 39 min, in this case). (In Figure 11, this is

Point 3 on the solid line, labeled “3” for the number of hospitals and on the dashed line labeled Route 1 for the emergency route and corresponding achievable total evacuation time.) For larger events, it is likely that both emergency Routes 1 and 2 would be used, moving the solutions to the vertical dashed line at a total evacuation time of approximately 1.4 × 106 vehicle hours. Use of emergency Route 3 in conjunction with either Route 1 or Route 2 creates substantial additional delays in the evacuation and provides relatively little advantage in terms of reducing emergency vehicle travel time, so it probably is not a good strategy.

SUMMARY AND CONCLUSIONS Evacuation planning is complex because it comprises many stakeholders with different perspectives, not to mention multiple requirements, and evacuations are nearly always surrounded by uncertainty and confusion. Past evacuation experiences have had mixed success, and significantly better analytic tools are needed to create effective evacuation plans and mitigation strategies. The focus of this paper is on finding the most effective ways to use existing network capacity for satisfying multiple objectives for emergency management. An optimization method was developed to identify an evacuation network reconfiguration when specific routes have to be reserved for emergency vehicles to access the evacuation area (usually running counterflow to the evacuation traffic). This problem is addressed by first identifying the candidate emergency vehicle routes, then constraining the reconfiguration of the network for evacuees. In the case study presented in this paper, a series of solutions were generated with other emergency mitigation factors (i.e., the medical facility capacity and the emergency route travel time) for decision makers to evaluate this trade-off. The proposed model considers two evacuation planning components: lane reversal on roadway sections and crossing elimination at intersections. These strategies complement one another by increasing capacity in specific directions through the network. The network solutions from the study experiments show that most links are fully

6 5

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FIGURE 11 Pareto–optimal sets of evacuation network configuration and emergency vehicle routing solution.

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reversed rather than some lanes partially reversed. The ability of the model and algorithm to consider partial reversals is one of the elements that contribute to its computational complexity, and limiting the search to only full reversals may be a useful simplification. The crossing elimination strategy offers a practical advantage to evacuation planning. In this and other studies, evacuation performance is measured as total evacuation time over the network, typically taking into account travel costs that occur along roadway sections. If crossing is not eliminated at an intersection, then traffic control delays at the intersection may not be neglected and should be incorporated into the system performance evaluation; an evacuation network is typically congested, and thus traffic delays at intersections take up a significant amount of total evacuation time. Most evacuation traffic delays occur at intersections (17). The crossing elimination strategy eliminates the intersection control delay to its maximum and makes the network performance evaluation easier and more reliable. The work presented in this paper is only one part of a much larger effort in planning for emergency preparedness and management. A network reconfiguration plan must be integrated with other elements of the emergency response plan, and responsibilities for implementing the various parts of the overall plan must be clear. The integration of the needs for emergency vehicle routing within an evacuation plan that is included in this paper is one piece of this larger issue, but many other pieces also should be addressed. ACKNOWLEDGMENT The assistance of Shashi Shekhar of the University of Minnesota is gratefully acknowledged for providing the data set on which the case study is based. REFERENCES 1. Urbina, E., and B. Wolshon. National Review of Hurricane Evacuation Plans and Policies: A Comparison and Contrast of State Practices. Transportation Research, Part A, Vol. 37, No. 3, 2003, pp. 257–275. 2. Tuydes, H., and A. Ziliaskopoulos. Tabu-Based Heuristic Approach for Optimization of Network Evacuation Contraflow. In Transportation Research Record: Journal of the Transportation Research Board, No. 1964, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 157–168. 3. Shekhar, S., and S. Kim. Contraflow Transportation Network Reconfiguration for Evacuation Route Planning. CTS Project Report, Minnesota Department of Transportation, St. Paul, Minn., 2006.

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