1 Introduction

1Service continuity during a disaster is absolutely crucial in various service domains, particularly in those involving human lives. Service continuity implies far more than just disaster recovery planning, because service activities during a disaster depend on the recovery process of the infrastructure and both are heavily affected by disruptions to the infrastructure itself. Many studies have been conducted on interdependency analysis of critical infrastructures; however, most of these studies have focused on the assessment of vulnerability, reliability or functionality of the infrastructure as a whole. For the assessment of service continuity in a disaster, it is essential to consider not only aspects of the infrastructure, but also those of the service and recovery activities and the interdependencies among them. In this study, dialysis treatment service during a disaster is adopted as the case study and a model and simulation of the service system is presented. Then, we introduce a method to assess the service system in a disaster based on the concept of resilience. In the next section, we give an outline of the dialysis treatment service requirements in a disaster. In Sections 3 and 4, we explain the modeling of the service system using a multi-agent model and a simple network model, as well as the procedure to assess the resilience of the service system. We then explain the simulation of the dialysis service in a disaster and present some results of the assessment of its resilience in Section 5. Finally, we present our conclusions and directions for future work in Section 6.

2 Dialysis treatment during a disaster

2We selected dialysis treatment as an example of a critical service system. Dialysis treatment provides an artificial replacement for lost kidney function in people with renal failure. Continued dialysis treatment during a disaster is crucial for patients since they cannot stay alive without constant treatment every two to three days. In Tokyo, for example, there are about 30,000 patients with chronic renal failure. In addition, in the event of an earthquake disaster, additional crash syndrome (acute renal failure) patients will also require dialysis treatment. Dialysis treatment requires a dialyzer (equipment) and a large amount of water as well as power and operators. Most of the dialysis clinics and hospitals stock some water and are equipped with emergency power generation; however, they are still vulnerable to damage to their support lifelines. The Medical Association and the national/local government in Japan have established a web-based collaborative network for dialysis treatment during a disaster (e.g., Tokyo Metropolitan Govt., 2007). In the case of a large earthquake disaster, they can share information about patients and available facilities and give the patients and related agencies appropriate instructions for subsequent dialysis treatments.

3 Service System Modeling

3We model the dialysis treatment service from two different perspectives: service and recovery activities and the infrastructure. The service and recovery activities are represented by a multi-agent model, and the infrastructure by a multi-layered network flow model. A schematic of the service model is shown in Figure 1. Details of the model are explained below.

3.1 Multi-Agent Modeling

4We consider five major agents in a dialysis service, namely, patients, hospitals, aid-stations, restoration teams, and the headquarters of the dialysis network. Each agent has response options, one of which is selected based on its inner status and the environment in each simulation step. The details of each agent are explained next.

5Patient. Each patient agent has a time limit until the next treatment. Unless an agent receives treatment within the time limit, he/she cannot stay alive. The options for patient agents are to remain where they are, go to an aid-station, or go to the nearest or their hospital. An agent stochastically selects one of these options. The probability and travel speed are determined by the agent’s care level.

6Hospital. The daily capacity for treating patients is defined for each hospital. There is a stock of water and electricity (emergency power generator) in each hospital. Thus, it can provide dialysis treatment with the available stock even when water and electricity are unavailable from the normal reticulation supplies (lifelines). The task of a hospital is to treat patients according to their urgency and send information about the daily capacity to the headquarters if possible.

7Aid-station. Aid-stations are established immediately after the disaster. Each aid-station examines the number of dialysis patients gathered at the station and reports this to the headquarters if possible. Assuming contact can be made with the headquarters, transport is arranged for the patients to an appropriate hospital as instructed; otherwise patients are transported to the nearest hospital.

8Restoration Team. Restoration teams try to repair the damage from the disaster. There are different types of teams for different types of lifelines. Because there are interdependencies between different infrastructures, the schedule for restoration is subject to such interdependencies. For example, damage to a water line cannot be repaired if the damaged location is unreachable; it may be necessary to repair the road first to gain access to the water line.

9Headquarters. The headquarters gathers information about the total treatment capacity on a particular day, the number of patients gathered at aid-stations, and road availability. Based on this information, the headquarters creates a transportation plan using linear programming and requests patient transportation to aid-stations.

3.2 Multi-layered Network Model

10Lifeline networks are implemented as simple multi-layered networks with nodes and links. We implemented a road network, and water, electricity, and communication lines. The reachability of a node in the graph from any source node determines the availability of the lifeline at that node. There are various interdependencies between different lifelines; however, only interdependencies in the restoration process are considered in this study. That is, unless damage to the road is repaired, a restoration team cannot use the road and cannot start to restore other lifelines across the road.

4 Assessment of Resilience

11In recent years, systems’ resilience has been the focus of attention in the field of safety engineering and disaster research (Hollnagel et al., 2008). To date, many resilience definitions have been provided from different professional disciplines, however, one of the common concepts of resilience is related to the capacity of physical and human systems to respond to and recover from extreme events. Falasca et al. (2008), for example, summarized resilience as: 1) the ability to minimize the possibility of damage, 2) the ability to mitigate damage, and 3) the ability to reduce the time for recovery. Vugrin et al. (2010) also suggested that the duration of system recovery depends on the efforts or recovery strategy. In this study, we focused on the third aspect of Falasca’s definition and evaluated the resilience of a service system as the capacity for recovery under an optimized recovery plan. We optimized a recovery plan using Genetic Algorithms (GAs) and assessed the resilience of the dialysis service system by drawing a resilience triangle or resilience loss (Bruneau et al., 2007). An overview of the process for assessing resilience in this study is illustrated in Figure 2.

4.1 Disaster Recovery Planning with GAs

12A recovery plan is coded into a gene, which consists of a sequence of restoration operations and the restoration teams in charge of each operation (Furuta et al., 2008). We used three criteria for optimizing the recovery plan in the following simulation: restoration rate, the number of surviving patients, and a hybrid of these two criteria. The restoration rate is defined by Equation (1), where n and t denote the simulation period and step, respectively. Jt represents the set of repaired links of lifelines at simulation step t. The GA parameters for the optimization are: population 300, generation 700, selection 50 %, crossover 60 %, and mutation 60 %.

5 Simulation

13We used 6×6 lattice networks to represent each infrastructure network. Hospitals, aid­stations, patients, the headquarters, restoration teams, and resources were placed at nodes in the network based on the actual distribution of these objects in Setagaya ward, Tokyo. Patients were homogeneously distributed in the initial setting. The location of hospitals was based on their actual locations. The capacity and stock was assigned according to the actual number of hospital beds. The location of aid-stations was determined according to the location of the designated elementary schools in the emergency plan. The simulation settings are shown in Table 1.

Table 1. Simulation Settings

5.1 Assessment of Resilience

14We assessed the resilience of the dialysis service system by drawing a resilience triangle (Bruneau et al., 2007). The resilience triangle is obtained by plotting the functionality or performance of the system over the recovery process. It is a loss triangle as shown in Figure 3. The vertical axis corresponds to the ability to mitigate damage, while the horizontal axis corresponds to the ability to reduce the recovery time. We define the performance of the dialysis service system by the following equations. The resilience triangle is obtained from the time series behaviors of the service performance after the first impact of the disaster. Capacitymax in Equation (2) denotes the sum of the capacity of all the hospitals under normal conditions (with no damage).

15Figure 3 depicts the resilience triangles under two different restoration plans. The dotted line represents the recovery process under the plan optimized by restoration rate (infra), while the solid line represents the recovery process under the optimized plan using the hybrid criteria. This graph shows that the area of the resilience triangle in the latter case is smaller than that in the former, which suggests that the resilience of the dialysis service can be enhanced by considering human activities as well as restoration of the infrastructure. In other words, there is interdependency between service activities and infrastructure and it is useless to restore lifelines blindly without considering the impact of human activities on the infrastructure.

16Figure 4 shows the results with different patient behavior. The dotted line represents the resilience triangle under the condition that patients go to the nearest aid-station or hospital, while the solid line represents the resilience triangle where each patient first tries to go to his/her hospital, which corresponds to the emergency plan of Hiratsuka City in which patients are instructed to go to their own hospitals in case of an emergency. As shown in Figure 4, the resilience under the latter condition is slightly better. This result suggests that patient behavior or instructions to the patients could influence the resilience of the dialysis treatment service, and thus, it is possible to improve service resilience not only by infrastructure reinforcement, but also by redesigning service activities.

6 Conclusion

17We have developed a model and simulation of a service system in a disaster that considers both human activities and critical infrastructures and have proposed a method for assessing the resilience of a service system. We used dialysis treatment during a disaster as an example and applied our method to it. The simulation results suggest a simple outcome: it is important to consider service activities when creating a restoration plan for infrastructures to maintain higher service performance during a disaster. The results also imply that system resilience could be enhanced by redesigning human behavior by, for example, instructions and guidelines to service recipients. This could be true of all service activities in a large city because critical service facilities such as hospitals for medical services are not uniformly-distributed geographically in a city and the criticality of these facilities would change during the recovery process. Both the multi-agent and network models in this study are fairly simple and more detailed modeling and simulation are necessary for further analysis. On the other hand, it is difficult to comprehend and predict all the aspects that should be considered in a detailed assessment of service resilience in a disaster. Future possible directions of this research include: 1) narrowing the target area of the service system and enhancing the integrity of the model, and/or 2) utilizing the simulation as a tool for intensive discussions and making it contribute to improving human ability to anticipate disruptions, pressures, and their consequences.