In this thesis, we have modeled two major bottlenecks in airplanes and airports, which are exits and queues, by using cellular automata and queueing theory. The models are analyzed by both simulation and theoretical analysis to establish new methods to achieve smoother pedestrian flow. Their validities are also verified by experiments with real pedestrians.

In the first half of the thesis, we focus on pedestrian outflow through an exit. It is one of the most important indexes in evaluating pedestrian and evacuation dynamics. In order to study the outflow in detail, the floor field model, which is a crowd model using cellular automata, is extended by taking account of realistic behavior of pedestrians around an exit. The model is studied by both numerical simulations and cluster analysis to obtain a theoretical expression for the average pedestrian outflow through an exit. It is investigated quantitatively that the effects of exit-door width, wall, and pedestrians' mood (competition or cooperation) significantly influences the pedestrian outflow. The results show that there is appropriate pedestrians' mood to evacuate smoothly according to the width and the position of an exit.

Two important factors which affect the pedestrian outflow at a bottleneck significantly are also studied in detail to analyze the effect of an obstacle setup in front of an exit. One is a conflict at an exit when pedestrians evacuate from a room. In the floor field model, conflicts have been conventionally taken into account by the friction parameter; however, it is so far a constant and does not depend on the number of pedestrians conflicting at the same time. Thus, we have improved the friction parameter by the frictional function, which is a function of the number of pedestrians involved in a conflict. Second, we have presented the cost of turning of pedestrians at an exit. Since pedestrians have inertia, their walking speeds decrease when they turn, and the pedestrian outflow decreases. The validity of the extended model, which includes the frictional function and the turning function, is supported by the comparison of a mean-field theory and real experiments. Moreover, we have observed that the pedestrian outflow increases when we put an obstacle in front of an exit in our real experiments. The analytical results clearly explain the mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians moving to the exit and decreases the average number of pedestrians involved in the conflict. Our theoretical results also indicate that an obstacle works more effectively when we shift it from the center since pedestrians can go through an exit with less turning.

In the latter half of the thesis, queueing systems are studied in detail. We have introduced the excluded-volume effect, which is a significant factor to model a pedestrian queue in the real world, into the queueing theory. The model is exactly solved, and the probability distributions of the physical quantities such as number of waiting pedestrians, length of a queue, and waiting time, are obtained in simple form. In the normal queueing theory, the length of a queue is represented by the number of pedestrians; however, due to the excluded-volume effect, the length becomes longer by the interval distance between pedestrians in our new model. Moreover, when the ratio of the arrival probability to the service probability remains constant, the mean length of a queue increases as the two probabilities increase since pedestrians take time to close up a queue. Furthermore, the mean waiting time does not increase monotonically with the increase in service time, and the minimum could be reached instead. We have performed the queueing experiments with real pedestrians and succeeded to observe the phenomena which are expected from our theoretical study.

We have also considered queueing systems with multiple service windows. By introducing the effect of delay in walking from the head of a queue to service windows into the queueing theory, we have obtained the suitable type of queueing system under various conditions. When there are multiple service windows, the normal queueing theory indicates that a fork-type queueing system, which collects people into a single queue, is more efficient than a parallel-type queueing system, i.e., queues for each service windows. However, in our walking-distance introduced queueing model, we have discovered that the parallel-type queueing system is more efficient when sufficiently many people are waiting in a queue, and the ratio of service time to walking time is small. In the fork-type queueing system, a pedestrian at the head of a queue, which is usually set at the end of the system, starts to move when one of the service windows become vacant. Since this walking time from the head of a queue to the windows increases the waiting time, we propose to set the head of a queue at the center of a queueing system and keep one pedestrian waiting at each service window when it is occupied by other pedestrians. The validities of these methods are examined by the theoretical analysis, simulations, and experiments. The situation where there are two kinds of pedestrians, whose service time is short and long, is also studied. It turns out that dynamical transformation of a queueing system decreases the mean waiting time of each pedestrian.

Our studies in this thesis mainly focus on indexes of average values such as the pedestrian outflow and the mean waiting time. Thus, they are in the viewpoint of facility operator who wants to maximize total efficiency of the system; however, for each individual pedestrian, waiting time of him/her is much more important. Hence, further studies are needed to satisfy the demand of all pedestrians.

We would like to emphasize that one of the main characteristics of our study is the firm theoretical analysis. There are many studies on pedestrian dynamics with computer simulations, and a number of successful results have been obtained from them; however, theoretical analysis has two advantages over simulations. First, simple theoretical expressions are easy to apply since we can calculate physical quantities with little time. Second, we can understand the mechanism of models in detail by analyzing the mathematical expressions. Therefore, our study on pedestrian outflow through an exit and queueing systems is useful to analyze egress process from airplanes and many queueing systems in airports, respectively. If smoother pedestrian flow is achieved by proposed methods in this thesis, air-traffic system will become much more efficient in the future.

修士 柳澤大地提出の論文は「Modeling and Analysis on Bottlenecks in Airplanes and Airports towards Achievement of Smoother Pedestrian Flow (和文題目:航空機と空港におけるスムーズな歩行者流実現に向けたボトルネックのモデル化と解析)」と題し,本文7章から成っている.

近年の国際交流の活性化に伴い,世界全体での航空機の需要は高まってきているが,それによる航空機や空港内の混雑や長蛇の待ち行列の形成といった問題に対する有効な解決策は未だ十分には得られていない.また航空機は90秒以内に全員が避難できるような設計である必要があるため,総避難時間の短縮方法が分かれば航空機の安全設計に貢献することができる.そこで本研究では,航空機や空港での人の流れを滞留させるボトルネックをモデル化して,それをシミュレーションと理論を用いて解析することにより人の流れをスムーズにする方法を考案し,その妥当性を実際の人を用いた実験により確認した.モデルは汎用性の高い一般的な数理モデルであるため,航空機や空港のボトルネックだけでなく建物からの避難やテーマパーク、鉄道の駅などの混雑解消に応用することもできる.

第一章は序論であり,混雑や待ち行列が航空機の離陸時間に及ぼす影響や人に与えるストレスについて述べ,航空機や空港におけるボトルネックの中でも,「出口」,「待ち行列」の二種類が重要であることを考察している.そして渋滞学と群集運動という本研究の基礎となる二つの学問について説明している.

第二章では,群集運動のセルオートマトンモデルであるフロアフィールドモデルについて簡単に解説している.

第三章及び第四章は,出口における流動係数の増加方法について書かれている.流動係数は,単位時間当たりに単位幅の出口を通過する人数を表し,建築分野における避難安全検証法でも用いられている重要な指標である.

第三章では,避難時の出口付近での人の振る舞いの効果をフロアフィールドモデルに導入し,クラスター近似により流動係数の理論式を導いた.この式を解析することにより,出口の幅が広い場合は競争状態にある群集の方が早く避難できるが,幅が狭い場合は協力状態の群集の方が早く避難できることが分かった.さらに出口が部屋の角にある場合,壁の効果により競争状態の流動係数が大きくなることも調べられた.

第四章では,退出過程で重要な現象である「複数人の同時衝突」と「出口手前での方向転換」の効果を第三章のモデルに導入し,そのモデルの妥当性を実験により検証した.さらに障害物を出口前の適切な位置に置くと流動係数が大きくなることを実験により発見した.本論文のモデルを用いることで,この現象は障害物で人の自由な動きが制限され,大人数での衝突頻度が減少することが原因であると説明することができる.

第五章は,窓口が一つの場合の人の待ち行列について書かれている.現在通信の分野などで応用されている待ち行列理論は,人の排除体積効果が考慮されていないという点で人の待ち行列の設計に対しては必ずしも有効な理論とは言えない.そこで待ち行列理論に排除体積効果を導入し,待ち人数や待ち時間,人と人の間の間隔も考慮した行列の長さの確率分布や平均値を厳密に求め,それらが列を詰める時間のために増加してしまうことを数学的に示した.さらに論文では実際の人による実験も行い,上記の現象を確認することにも成功した.

第六章は,窓口が複数ある待ち行列における平均待ち時間の減少方法ついて書かれている.待ち行列理論に行列の先頭から窓口までの歩行距離の効果を導入しシミュレーションと理論解析を行うと,非常に混雑している場合や歩行時間に対してサービス時間が短い場合は,窓口ごとに待ち行列を形成する「並列型」の方が待ち行列を一つにまとめる「フォーク型」より平均待ち時間が短くなるという今までの待ち行列理論ではなかった結果を導出した.また待ち行列の先頭を待ち行列システムの中心に設置したり,窓口の手前で一人だけ待たせるようにしたりしたフォーク型は,平均待ち時間を短くできることも見出された.さらに人の精神的なストレスに関係のあるサービス順序についても考察が加えられ,トーナメント表のような形状の待ち行列システムを形成することにより,平均待ち時間と順序の入れ替わりが共に小さい待ち行列システムを実現できることも分かった.空港の入国審査会場のような審査時間が長い外国人と短い日本人が混在したケースを研究し,その流れの改善方法の提案をしている.

以上要するに,本論文は,航空機や空港内などのボトルネックである出口と待ち行列をモデル化し,そこにおける流動係数の増加方法と平均待ち時間の短縮方法,つまりは人の流れをスムーズにするための具体的な方法を提案している.これらの結果は,航空機や建物からの総避難時間や空港や駅などの待ち時間短縮や、航空機の定時運行などに応用することが可能であり,航空工学上貢献するところが大きい.

よって本論文は博士(工学)の学位請求論文として合格と認められる.