Jams on road traffic cause huge financial losses, e.g., 11 trillion yen in 2005 year in Japan, therefore in this thesis we aim to reduce them. The characteristic of this thesis is to utilize microscopic interactions of cars for easing jams. In the field of traffic engineering, traffic dynamics has been developed by observations and making traffic models. Moreover, various methods to ease jams, for instance, ramp metering, variable speed limits and route guidance have been studied and applied in real traffic. Great efforts have been made for these methods. However, it is important to seek other methods for further improvement of traffic flow. On the other hand, in the field of physics, traffic flow has been studied as a dynamics of the self-driven particles (SDPs). SDP is the general term of particles which move by themselves, e.g., cars, pedestrians, ants and animals. SDPs move and stop by themselves and the interactions among them are not always symmetric so that the law of action-reaction is not satisfied in SDP-systems. The systems contain rich collective phenomena such as phase transitions from free flow to jams and self-clustering. The relationships between microscopic interactions among SDPs and the collective phenomena have been studied and clarified. For instance, in traffic flow from 90's, the three phase traffic flow theory was proposed by Kerner, spontaneous traffic jams were observed in circuit experiments by Sugiyama et al. and metastable branches have been studied in simple models such as Cellular Automata (CA). As a next step, we use microscopic interactions, e.g., car-following behaviors and lateral interactions, for improving the efficiency of the collective flow. There are related fields to utilize microscopic behaviors such as the driver-assistance systems (e.g., adaptive cruise control). In this thesis, we aim to improve the flow with least devises since the rate of propagation of the assistance systems is low, e.g., ACC is spread only 1 percent for the total cars and large-sized cars made for the use in Japan in 2010. As to the jams to be eased, we choose the two jams, jams due to merging behaviors and spontaneous jams. We choose them since they are the major jams in the three Japanese highways. Besides, jamming formations of the two jams are closely related to the microscopic behavior of each car so that they are expected to be eased by tuning microscopic behaviors. As to the methods, we utilize the microscopic behaviors as follows. We study to improve the merging flow by stirring emergent zipper configuration before merging since this configuration realizes smooth merging. We study to realize the zipper merging by only drawing orange compartment lines on the roads without any additional devices equipped with cars. On the other hand, we study to remove spontaneous jams by tuning a single car's car-following behavior such as taking large headways before entering a jam and absorbing it. This method was firstly demonstrated by Beaty. Beaty's study lacks theoretical studies so that we make the methodology of this driving. This thesis covers mainly the construction of methodology and the study of basic phenomena with simple models since fundamental studies are the basis of more extended studies such as numerical simulations with the latest traffic models. Regarding the zipper merging, firstly we have covered the emergent zipper configurations before merging as an arrangement of our previous results. We have prepared a plan to induce zipper merging such that we draw a compartment line between the two lanes in a merging area. We have used a simple cellular automaton model with a lateral interaction such that cars tend to decelerate in responding to the existence of other cars on the neighboring lane. Moreover, we have defined the degree of zipper configurations as a measurement value. Numerical simulations have shown that emergent zipper configurations are achieved before merging by only this local hesitation. Furthermore, we have constructed how to obtain analytical results of spatial change of the configurations and intensions (corresponding to velocities) with mean field analysis. The analytical results agree with the results of numerical simulations. Then, we have studied the effect of zipper merging by using flux and travel time as measurement values. We have used as dynamics a multiple-lane CA model with a slow-to-start (SlS) rule where SlS rules represent the delay of action of cars after the blocked state. We have used an open system such as a two-lane lattice connected with a cell to investigate the flux. From numerical simulations we have observed that the flux in case zipper merging is higher than that in case non-zipper merging when the slow-to-start rule is relatively strong. Moreover, we have depicted how the achievement of zipper merging depends on the length of interaction-area, the parameter of hesitation and the injection probability. Furthermore, we have constructed the analytical flux with mean field analysis. This analytical result agrees with the results obtained by numerical simulations. For investigating the travel time, we have used a semi-open system such that a two-lane lattice connected with three cells. Cars are initially placed and we set two kinds of cars such as cars determined to go out of the system with or without merging behaviors. Cars without merging behaviors go straight through the system. We have investigated the travel time by changing the ratio of the two kinds of cars. We have found that the improvement of travel time by zipper merging needs not only the relatively strong SlS rule, relatively small hesitation, sufficient length of the interaction area and relatively high initial density but also relatively high ratio of merging cars. Furthermore, we have investigated the cases of the existence of cars which do not interact with other cars on the neighboring lane. In the system for investigating flux, we have set the case that cars on the one lane do not have hesitations. In the system for investigating the travel time, we have set the ratio of cars in both lanes which have no hesitations. Numerical simulations show that in the presence of these ignoring cars, the efficiency of merging is not improved well. This result suggests that each car should interact with other cars for improving the efficiency of merging. Regarding the driving for jam-absorptions, we have made the framework of this driving. We have used a simple kinematic model for representing the movement of cars. We have calculated the propagation of perturbations caused by the car performing this driving and analyzed in detail the point where the perturbations disappear. We have also calculated the driving for jam-absorption in two steps. This two-step absorption leads to multiple patterns of collisions among perturbations and we have divided the patterns clearly. As pointed above, from the results of the zipper merging, we have obtained the possibility to improve the efficiency of merging behaviors. From the results of the driving for jam-absorption, we have obtained the whole image of this driving helpful to perform this driving. Therefore, our results show the possibility to reduce the two major jams in highways and their related roads so that we conclude that our methods contribute to reduce traffic jams.

修士(工学)西遼佑提出の論文は「Methods for easing traffic jams by microscopic behaviors (和文題目:ミクロな相互作用による渋滞改善方法)」と題し,5章から成っている。

本論文は、自動車交通の渋滞改善の方法を流体力学的手法を用いて新しく提案したものである。渋滞を改善する研究の意義として、日本における交通渋滞による経済損失は約11兆円程度にものぼり、その軽減は社会的にも大きな意義がある。そして本論文の特徴は、その解決手法として車同士の流れの中でのミクロな相互作用を積極的に活用している点である。まず1章において、この着想に至るまでの背景として、交通工学と数理物理学における交通流研究の発展が下記のように述べられている。交通工学では、観測や交通流モデルによる交通流メカニズムの解明が長足の進歩を遂げてきた。この知見に基づいた渋滞対策として、ランプ流入を制御したり、道路ネットワークでの経路選択を補助するなど、いくつかの方法が考案され、実用化されてきた。しかしながら、根本的な渋滞解消には至らず、新規の渋滞改善策が望まれているのが現状である。一方で、近年、数理物理学の分野では、自動車を含めた歩行者・アリなどを自己駆動粒子と総称し、その多体問題が盛んに研究されてきた。特に、近接する自己駆動粒子同士にはたらくミクロな相互作用と、発現されるマクロな集団現象の関連性が解明されてきた。本論文は、この結果をいち早く取り入れ、ミクロな相互作用を活用することで、マクロな交通流を改善することを主張している。従来よりミクロな相互作用を利用するための車車間通信などのドライバー補助装置の研究があるが、本論文はできるだけこのような補助装置に頼らず、数理物理学と流体力学の理論を活用した各々の車の運転方法を提案している。また、本論文の範囲としては、基礎研究として、簡易なモデルを用いた方法論の構築と基礎現象の解明に焦点を当てている。そして、改善を試みる具体的対象として、実高速道路で主要な渋滞を占める自然渋滞と合流による渋滞を取り上げている。

続いて2章において、合流による渋滞の改善方法として、ジッパー合流の励起方法を述べている。これは修士論文での結果のまとめであり、合流部に車線変更を禁止するオレンジ色の区画線を引くと、その線に沿って走行する車同士に排斥力が働き、お互いに位置を調整してスムーズな合流が実現されることを説明している。これはこの区間を二車線格子系で記述し、車の動きをセルオートマトンでモデル化することで得られた成果である。そこでは車線間相互作用として、隣近傍に車がいる場合に車の前進確率が減少するというルールを付加し、そしてジッパー配置の程度を表す指標が定義されている。また、シミュレーションと平均場近似によって、ミクロな相互作用のみでジッパー配置に近づいて流量が改善できる様子がまとめられている。

3章では、簡素な合流系を考察し、ジッパー合流の発生と合流効率の関連性が調べられている。理論モデルとしては、発進遅れの効果を付加したセルオートマトンを用いて、この発進遅れが大きい場合に、あらかじめジッパー合流する方が流量が増加すること、ならびに合流を行う車の割合が高い場合に旅行時間が改善することを見出している。また、シミュレーション結果とよく一致する流量の平均場近似計算が導出されている。

次に、自然渋滞の解消方法として、4章で圧縮性流体力学を応用した渋滞吸収運転の理論的枠組みが構築されている。渋滞吸収運転とは、渋滞に入る前に車間距離を空けて渋滞波を吸収する運転方法である。この吸収運転に関する理論はこれまでなく、本論文において初めてその枠組みが示されている。理論モデルとしてキネマティックモデルを利用し、吸収運転が成功する条件、吸収運転実行車が起こす衝撃波の後方車への伝播、そしてその衝撃波が膨張波と出会って消失する位置と時刻などが理論計算されている。特に、モデルのパラメータと衝撃波消失点の軌跡の関連性が解明されている。さらに、より現実的な吸収運転として、2段階で減速する吸収運転の提案がなされており、この2段階吸収運転で発生する複数の衝撃波と膨張波の干渉の様子が理論的に分類されている。

そして最後の5章で研究成果を総括し、まず本論文が扱ったジッパー合流の励起は、ミクロな相互作用が合流効率を改善する可能性について新たな知見をもたらしたことを述べている。また、渋滞吸収運転に関する基礎理論は、吸収運転の適用範囲と限界を明確に示したものであり、実際に実行する上で大いに役立つものである。

以上要するに,本論文は,ジッパー合流の励起と渋滞吸収運転の2つの方法を通して、高速道路上での主要な渋滞要因である合流渋滞と自然渋滞の改善に対して新たな知見をもたらしており、またその成果のもとになった圧縮性流体力学の新分野への応用を切り開いた点で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。