Risk Minimizing Evacuation Strategies under Uncertainty

This paper presents results on the simulation of the evacuation of the city of Padang with approximately 1,000,000 inhabitants. The model used is MATSim (www.matsim.org). Three different strategies were applied: shortest path solution, user optimum, system optimum, together with a constraint that moves should reduce risk whenever possible. The introduction of the risk minimization increases the overall required safe egress time (RSET). The differences between the RSET for the three risk minimizing strategies are small. Further quantities used for the assessment of the evacuation are the formation of congestion and the individual RSETs (in comparison with the available SET). Introduction: Safety, Risk, and the Need for Simulation Safety is a basic need for individuals and societies. Safety can be roughly defined by: existing risk < acceptable risk. It can also be discriminated from security by dealing with non-intentional threats. In this paper, the potential threat is a natural hazard: a submarine earthquake in the Indian Ocean causing a Tsunami wave hitting the coast of Sumatra, Indonesia and the city of Padang. The risk, and consequently also the safety if the acceptable risk is specified can be quantified based on the following formula:    dt t P C D = R     1 (1) The damage is denoted by D, the coping capability by C, and P(t) is the probability of the wave reaching the coast. The criterion usually applied to assess a risk is: R < acceptable risk. Please note that there is always a residual risk (RR>0), which cannot be reduced by technical or management means. In case of a tsunami, the physical safety or lives of people are at risk. Evacuation is one means in ensuring the safety, especially to avoid the risk and threat to human life. Evacuation reduces the damage. Another strategy would be to build tsunami safe buildings which would increase C. This is beyond the scope of this paper. We focus on the evacuation. The condition for a safe egress is RSET < ASET, where ASET is the available safe egress time and RSET is the required safe egress time. In this paper, we R.D. Peacock et al. (eds.), Pedestrian and Evacuation Dynamics, DOI 10.1007/978-1-4419-9725-8_26, © Springer Science+Business Media, LLC 2011 present the calculation of RSET (based on a microscopic multi-agent simulation). ASET is provided by inundation simulations that show the consequences of an earthquake off-shore the island of Sumatra (Indonesia) for the coastal city of Padang. The overall egress time is one major criterion for assessing an evacuation plan. Such a plan addresses – among many other issues – evacuation routes for the endangered population. There are many models that find optimal routing strategies (i.e. minimizing RSET) for a given road and walkway network. In the case of large-scale inundation, the network changes with time. Links or edges (i.e. roads or lanes) become impassable due to flooding. The evacuation simulation based on a dynamic network works only as long the advance warning time is known beforehand, though. When this is not the case, the optimal routing strategy might increase the risk for some persons on some stretch of way. This issue is addressed in the next section on utilities of evacuation strategies. Implementation details are given in section 3, experimental results discussed in section 4. The paper concludes with a discussion of the simulation results (section 5) and a conclusion and recommendations (section 6). Utility of an Evacuation Strategy The utility of an evacuation path often depends on uncertain aspects. One uncertain aspect is the advance warning time warn τ . We assume that warn τ follows an unknown probability distribution with, for this section,   1 0 = > τ P warn , i.e. there is always a warning before the event. Let us consider a situation with two different evacuation paths 0 p and 1 p ; 0 p does not depend on the advance warning time warn τ but has considerably longer travel time than 1 p . The path 1 p first leads “towards danger” for a time period T before it leads to safety, i.e. when the warning time is too short one cannot take it. An example is a bridge close to the shore heading to a safe area. If an evacuee takes 1 p , she moves towards the shore (danger) in order to reach the bridge. As a result the utility of 1 p depends on warn τ . The utility for 0 p and 1 p can be formulated as follows:  