Modeling pedestrian evacuation movement in a swaying ship

In the past decades, cruise travel has been a rapid expanding field around the world. A worldwide annual growth rate of 6.55% for passage by sea from 1990 to 2019 has been recorded which is expected to grow continuously. The transportation of passengers in water has also made a rapid development. It is expected that ships will be more and more widely used in transporting passengers. Unfortunately, several ship disasters occurred in these years which caused serious losses to people’s lives and properties. It raised the concern on the effectiveness of large crowd passenger evacuation on ships.

To mitigate the ill effect of an emergency, evacuating passengers from the ships will be necessary. The International Maritime Organization (IMO) has already developed guidelines for passenger ship evacuation. However, these guidelines and regulations, like most building codes, only enforces capacity limit of individual components such as exits, passenger way width, etc., thus can barely provide efficient setting and management strategies. Computer simulation, on the contrary, can be helpful by performing simulations even at the ship design stage. The International Conventions for the Safety of Life at Sea (SOLAS) now requires evacuation analysis at the early stage of ship design (IMO MSC.1/Circ.1238, 2007). Thus some simulation models have been built to perform computer simulation based evacuation analysis.

When compared with building evacuation, passenger ship evacuation is still a new research topic and only limited publications can be found. Existing works were more or less inspired by the IMO guidelines. The two full scale drill exercise projects, i.e., ”FIRE-EXIT” and ”SAFEGUARD” have provided valuable information for model validation, especially for ”maritime-Exodus” Galea2013 . Some other models have also been established including, AENEAS Valanto2006 , EVI Azzi and VELOS Ginnis2010 . The former two models are grid-based models, and thus have great advantage in computing efficiency, yet the discretization may affect their ability to model environmental space and detailed pedestrian motion when compared with the last two continuous space models. The influences of ship motion on pedestrian movement in these models are almost mimicked by speed reduction considering different inclination angle rather than considering the coupled-forced pedestrian movement features.

Thus, in the present paper we establish an evacuation model taking into account forced pedestrian movement pattern. The rest of the present paper is organized as follows. In section 2, we introduce the model which takes into account ship swaying effect. In section 3, we firstly compare several single pedestrian movement features under different conditions and then analyze a ship evacuation process. In the last section, conclusions are made.

Basically, the design layout of the cruise ships is same as that of hotels on the ground, which includes separated accommodation cabins, restaurants, sports facilities, etc., so that cruise ships can be regarded as mobile hotels. However, one of the important differences between them is that the deck of cruise ship has a complex motion pattern as a result of periodical water movement. Thus pedestrian on board would be affected by the inertial force, which further makes pedestrian movement characteristic different from when walking on a static horizontal floor. Taking into consideration of this special feature, an agent-based pedestrian model is formulized, and the effect of ship swaying on pedestrian evacuation efficiency is investigated.

The Equations (1) to (6) in Section 2 together describes forced movement pattern for a pedestrian on a swaying ship. It should be noticed that in reality, the ship swaying induced force component $F_{s}$ for a pedestrian might be very complex. So in the present section, we explore its effects by performing two simple case studies.

Firstly, we place a pedestrian $5m$ away from his target, as shown in Fig. 2a. The pedestrian has a free movement speed of $1.2m*s^{-1}$. Three scenarios were considered. I) We assume the pedestrian is moving on a horizontal ground, and there is no ship swaying. II) The ship was swaying along the direction perpendicular to the pedestrian’s movement direction. III) The ship is swaying along the direction which parallels to the pedestrian movement direction. Simulation snapshots for these three different scenarios can be found in Fig. 2b, 2c and 2d, respectively. As can be found in these figures, when there is no swaying, the pedestrian can move freely towards his target. When the ship was swaying perpendicular to the pedestrian movement direction, we can see as a result of the swaying, the pedestrian makes lateral movement when approaching his target. That is due to the ship swaying induced inertial force exerted on that pedestrian and changed his gait. We can also find although the pedestrian made lateral movement, the movement towards his direction has barely been influenced, as can be found in Fig. 3a. When the ship is swaying along the direction paralleling to the pedestrian movement direction, as shown in Fig. 2d, his trajectory seems like the one when there was no ship swaying, as in Fig. 2a. We further compared the spatiotemporal feature of these trajectories shown in Fig. 2a and 2d, and found as shown in Fig. 3a, the pedestrian accelerate at first and then decelerate, meaning he keeps changing his speed during the process when he moves towards his target in the case when the ship is swaying along the direction paralleling to his movement direction. We can see that the ship swaying affected pedestrian microscopic features even in these simple conditions.

Secondly, scenarios of a ship evacuation with/without swaying were simulated. Considering that in case of emergency, prior to any decision to actually abandon the ship, passengers on a ship have to be evacuated to the assembling site. That is because if abandoning is unavoidable, these passengers can be evacuated immediately, and if there is no need to abandon ship, dealing with emergency would be much easier with no passengers around for those crew members. So, passengers were ordered to evacuate to the assembling area on the right side, i.e., front of ship in the present case, as shown in Fig. 4. There were in total 60 passengers on the ship. In Fig. 4a and 4b we show the trajectories of those passengers on the ship when there was no sway and there was sway, respectively. Comparing these figures we can easily find that due to ship swaying, passengers made lateral movements during evacuation. The lateral movement slowed down the evacuation process, as shown in Fig. 3a. We can also find that for those passengers initially located in the relatively open area, as shown in the left part of Fig. 4, their trajectories show clear curved features when the ship was swaying. When there was no sway, these trajectories were almost linear, representing these passengers can move freely towards their targets. For those who were located in the long channel, as can be found in the right part of Fig. 4, they were barely influenced by the swaying ship. The reason is that the channel is so narrow that passengers’ lateral movements were hindered by those chairs and walls.

When we compare the evacuation process, as can be found in Fig. 3b, when there was no ship swaying, the total assembling time for 60 passengers is only slightly shorter than when there was ship swaying. That is because the evacuation processes were mainly performed in the long channel section, as shown in Fig. 4. But the assembling efficiency when there was no sway is always higher, as indicated by the number of assembled people shown in Fig. 3b. That is because, passengers located on the back and front sections had to make movement along the ship swaying direction, which would slower them down, as shown in Fig. 3a.

An agent-based passenger evacuation model was built. Each agent in the model can sense the ship swaying feature and adjust its own gait, in this way, forced pedestrian movement feature as a result of ship swaying was mathematically quantified. Simulations of single pedestrian movement show that the angle between pedestrian movement direction and ship swaying direction may influence spatiotemporal features of a pedestrian. Thus under the situation of total evacuation, the passenger assembling efficiency would be affected. The simulated assembling time provides a very important criterion to evaluate the total evacuation time needed for a completed orderly evacuation. It should also be noticed that the computed evacuation time gives an estimate of the time the passengers need to get out of the ship interior and reach a boarding site, thus the influence of the ship interior can be evaluated to find out bottlenecks and make improvement accordingly.