國
立
交
通
大
學
網路工程研究所
碩
碩
碩
碩 士
士
士
士 論
論
論
論 文
文
文
文
利用小世界性質達成群體協調以維持車隊叢集機制
Maintaining Cohesive Fleets via Swarming with
Small-World Communications
研 究 生：蔡赫維
指導教授：陳 健 教授
中
中
中
中 華
華 民
華
華
民
民 國
民
國
國 九
國
九
九 十
九
十 八
十
十
八
八 年
八
年
年 七
年
七
七
七 月
月
月
月
利用小世界性質達成群體協調以維持車隊叢集機制
Maintaining Cohesive Fleets via Swarming with
Small-World Communications
研 究 生：蔡 赫 維
Student：Hen-Wei Tsai
指導教授：陳 健
Advisor：Chien Chen
國 立 交 通 大 學
資 訊 科 學 與 工 程 研 究 所
碩 士 論 文
A ThesisSubmitted to Institute of Network Engineering College of Computer Science
National Chiao Tung University In partial Fulfillment of the Requirements
For the Degree of Master
In
Computer Science
July 2009
Hsinchu, Taiwan, Republic of China
利用小世界性質達成群體協調以維持車隊叢集機制
研究生 : 蔡赫維 指導教授: 陳 健 國 立 交 通 大 學 網 路 工 程 研 究 所中文摘要
中文摘要
中文摘要
中文摘要
在此篇論文中，我們在VANET網路上提出一個以車隊為主的應用，其目的是 要發展一個分散式維持車隊叢集的策略。因為車隊在VANET網路常會受到路 況、交通號誌、道路的速度上限不同等因素影響，導致車隊分散成許多無法溝通 的子車隊。我們的策略就是要來解決這樣時常分散的情形。首先我們將每台車分 成 Pseudo-leader與Follower，
在每個分散的子車隊中，車輛間透過短距離的通訊 方式(V2V)彼此協調速度以及位置等資訊。另外，為了要能在分散的子車隊中交 換資訊，Pseudo-leaders 透過遠距離的通訊方式(V2I)來達成，而這樣的通訊方式 就如同小世界現象中的Shortcuts一般，建立起一個快速資訊交換的網路。因此每 個 Pseudo-leader 便可以得知本身在整體車隊中的相對位置，進而決定加速與減 速的行為。能讓車隊在出遊時每台車能夠密集而不失散並且彼此保持相同的速率 前進，如同動物界中群體協調的特性。關鍵字: 車用行動通訊網路、群、小世界現象、車隊。
Maintaining Cohesive Fleets via Swarming with
Small-World Communications
Student:Hen-Wei Tsai Advisor: Dr. Chien Chen
Institute of Network Engineering
National Chiao Tung University
Abstract
A car fleet is a group of cars that should travel close together with a common speed. Due to dynamic road conditions, traffic signals, road speed limits and other factors, a car fleet may suffer from frequent partition. This paper proposes a distributed cohesive car fleet maintenance scheme by employing a swarming model complemented by a small world phenomenon. Vehicles within a car fleet are classified into the roles of pseudo-leader and follower. Within each partition, cars form a cohesive swarm by coordinating their speed and position via short-distance V2V communications. To exchange information between partitions of a dispersed cat fleet, pseudo-leaders communicate via long-distance V2I communications, which resembles the shortcuts of the small world phenomenon. Pseudo-leaders then determine their relative positions within the car fleet, and decide to speed up or slow down so as to achieve a cohesive swarming behavior of the entire car fleet. Merits of the distributed scheme are demonstrated through simulations.
誌謝
誌謝
誌謝
誌謝
本篇論文的完成，我要感謝這兩年來給予我協助與勉勵的人。首先要感謝 我的指導教授 陳健博士，即使這段期間遭遇了不少的挫折，陳老師對我的指導 與教誨使我都能在遇到困難時另尋突破，在研究上處處碰壁時指引明路讓我得以 順利完成本篇論文，在此表達最誠摯的感謝。同時也感謝我的論文口試委員， University of Delaware 沈建中教授幫助我完成整篇論文的推手與交大的簡榮宏 教授以及清華大學的許健平教授，他們提出了許多的寶貴意見，讓我受益良多。 感謝與我一同努力的學長陳盈羽、張哲維，由於我們不斷互相討論及在論 文上的協助，使我能突破瓶頸，研究也更為完善。另外我也要感謝實驗室的同學、 學弟們、張文馨、黃鼎峰、孫冠宇、莊敬中等人，感謝他們陪我度過這兩年辛苦 的研究生活，在我需要協助時總是不吝伸出援手，陪我度過最煩躁與不順遂的日 子。 特別感謝我的朋友，及許多大學時代的好友們，芳如、Tammy 在實質的翻譯 寫作上面給了我不少的幫助，另外也在精神上給我莫大的鼓勵，傾聽我內心 的 聲音並帶給我無比的溫暖，指導我做出了許多正確的抉擇，而不致迷失了自我。 這些好朋友們就像是明燈般照亮了昏暗的旅程，並陪伴我度過枯燥的研究生涯。 最後，我要感謝家人對我的關懷及支持，他們含辛茹苦的栽培，使我得以 無後顧之憂的專心於研究所課業與研究，我要向他們致上最高的感謝。
Table of Content
中文摘要 中文摘要 中文摘要 中文摘要... iii Abstract ... iv 誌謝 誌謝 誌謝 誌謝... v Table of Content ... viList of Figure ... vii
List of Equation ... viii
Chapter 1: Introduction ... 1
Chapter 2: Related work ... 4
2.1 Swarming Model ... 4
2.2 Small World Phenomenon ... 5
Chapter 3: Distributed Cohesive Car Fleet Scheme ... 6
3.1 Dynamic clustering mechanism ... 7
3.2 Small-world information exchange via V2I communications ... 10
3.3 Calculation of center of gravity ... 11
3.4 Calculation of speed difference between neighbors ... 12
3.5 Collision avoidance ... 13
3.6 Establishing region and acceleration formula ... 14
Chapter 4: Simulation ... 17
4.1 Simulation environment ... 17
4.2 Metrics ... 18
4.3 Simulation result and study ... 19
4.3.1 Without DCFS ... 19
4.3.2 Evaluation of different minimum speed of road: ... 20
4.3.3 Evaluation of the impact of collision avoidance: ... 21
4.3.4 Evaluation of two specific scenarios: ... 23
4.3.5 Evaluation of different length of LG ... 25
4.3.6 Evaluation of the number of vehicles ... 27
4.3.7 Evaluation of the expected speed ... 29
4.3.8 Evaluation of the impact of traffic lights (TL) ... 31
Chapter 5: Conclusion ... 34
List of Figure
Figure 1: System architecture and cohesive car fleet. ... 2
Figure 2 : Three basic flocking rules. ... 4
Figure 3(a): Regular Graph Figure 3(b): Small World Graph ... 5
Figure 4: Dynamic Clustering Flow Chart... 8
Figure 5: Dynamic Clustering Flow Example. ... 9
Figure 6: Communication scenario and mapping position sketch of car fleet. ... 10
Figure 7: Calculation center of gravity. ... 11
Figure 8: Establishing three different region. ... 14
Figure 9: The length of GR Trend chart. ... 15
Figure 10: Without DCFS. ... 19
Figure 11: Comparison of cohesion performance in different minimum speed of road. ... 20
Figure 12: Comparison of cohesion performance with collision avoidance and without collision avoidance... 21
Figure 13: Comparison of formation performance in with collision avoidance and without collision avoidance. ... 22
Figure 14: Comparison of Average speed in with collision avoidance and without collision avoidance... 22
Figure 15: Comparison of cohesion performance in DCFS and ALL scenarios. ... 24
Figure 16: Comparison of formation performance in DCFS and ALL scenarios. ... 24
Figure 17: Comparison of average speed in DCFS and ALL scenarios. ... 25
Figure 18: Comparison of cohesion performance in different length of LR. ... 26
Figure 19: Comparison of formation performance in different length of LR. ... 26
Figure 20: Comparison of average speed in different length of LR. ... 27
Figure 21: Comparison of cohesion performance in different number of vehicles. .... 28
Figure 22: Comparison of formation performance in different number of vehicles. ... 28
Figure 23: Comparison of average speed in different number of vehicles. ... 29
Figure 24: Comparison of cohesion performance in different expected speed of entire car fleet containing 15, 20 and 25 MPS. ... 30
Figure 25: Comparison of formation performance in different expected speed of entire car fleet containing 15, 20 and 25 MPS. ... 30
Figure 26: Comparison of average velocity in different expected speed of entire car fleet containing 15, 20 and 25 MPS. ... 31
Figure 27: Cohesion performance in with traffic light and without traffic light. ... 32
Figure 28: Formation performance in with traffic light and without traffic light. ... 33
List of Equation
∑
∈ = A i i A P(t) A ) t ( G 1 (1) ... 11( )
∑
∈ = SG j j group G t SG ) t ( G 1 (2) ... 12( )
∑
( )
∈ = i N j ij i Neighbors , i V t N t V 1 (3) ... 13 ion Aeccelerat V Vt × − = 2 ) ( ) ( S 2 0 2 (4) ... 13 ion Deccelerat _ Max ) V ( current × − = 2 0 Distance Braked 2 2 (5) ... 13 1 5 . 0 , Distance Reaction =γ
⋅Vcurrent ≤γ
≤ (6) ... 13( )
t
V
( )
t
MAX
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Accelerati
on
V
i+
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=
i+
(7) ... 15( )
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(9) ... 16 For( )
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Leader , i Neighbors , i Leader , i Neighbors , i≤
≤
. (10) ... 16( )
∑
(
( )
)
∈ − = SG j group j p G t G (t) SG t 1 2σ
(11) ... 18( )
∑
(
( )
)
∈ − = SG j group j v AvgV t AvgV (t) SG t 1 2 σ (12) ... 18Chapter 1: Introduction
The Intelligent Transportation System (ITS) integrates information and communication technologies to transport infrastructure and vehicles to improve their safety and efficiency. In general, the wireless communication technologies used by ITS can be classified into three types: Vehicle-to-Infrastructure (V2I), Vehicle-to-Roadside (V2R), and Vehicle-to-Vehicle (V2V). For instance, both V2V and V2R employ short-range communication such as Dedicated Short Range Communications (DSRC). V2I uses long-range communication such as WiMAX (IEEE 802.16), Global System for Mobile Communications (GSM), or 3G.
Many researchers have studied different approaches of employing these technologies to facilitate information exchange between vehicles: (i) Using V2I or V2R, vehicles can obtain the necessary information by accessing the access points of V2R or the base stations of V2I [1, 2, 3]. (ii) Using V2V, vehicles use short-range communications to communicate with each other [4, 5]. (iii) Hybrid approaches integrate V2V, V2I, and V2R [6], where vehicles can directly exchange information when within proximity, or utilize infrastructure or roadside units to exchange information.
Vehicular Ad hoc Network (VANET), formed by vehicles with wireless communication capability, is one realization of ITS which provides crucial functions such as road safety and reduction of traffic congestions. VANET, which is a subclass of Mobile Ad hoc Networks (MANET), has evolved as a practical application of MANET. However, VANET exhibit very different characteristics from MANET, and one main difference is the frequent partition of the network which may significantly degrade the performance of information dissemination. In general cases, the moving
may even be higher, especially when moving in opposite directions. Depending on the traffic patterns, the density of vehicles varies significantly over different areas.
Figure 1:System architecture and cohesive car fleet.
The goal of this paper is to develop a communication solution to deal with a car fleet of the partition issues faced by the VANET. A car fleet is a group of cars, sharing a common starting point and a destination, which should travel close together at best. Due to higher speed, dynamic road conditions, traffic signals, road speed limits and other factors. A car fleet may suffer from frequent partition. This paper proposes a distributed scheme to maintain a cohesive car fleet autonomously by employing a
swarming model complemented by a small world phenomenon.
Fig. 1(a) depicts the system architecture. Specifically, a dynamic clustering protocol classifies vehicles into the roles of pseudo-leader (red car) and follower (yellow car),
which allow them to use different communication capabilities. Within each partition, cars form a cohesive swarm by coordinating their speed and position via short-distance V2V communications (e.g., DSRC). To exchange information between partitions of a dispersed cat fleet, pseudo-leaders communicate via long-distance V2I communications (e.g., WiMAX and 3G), which resembles the shortcuts of the small world phenomenon. By communicating with all the other pseudo-leaders, each pseudo-leader then determines its relative position within the car fleet by referring to the center of gravity of the entire car fleet. Each pseudo-leader then speeds up (and direct its followers to speed up) when it falls behind, or slows down (and direct its followers to slow down) when it is ahead, so as to achieve a cohesive swarming behavior of the entire car fleet. For instance, in Fig. 1(b) without proper maintenance, a car fleet may be dispread into three partitions. Our goal is to maintain a cohesive car fleet as shown in Fig. 1(c) where cars travel close together at the same speed. Notice that the system proposed was not intended to substitute human drivers, but to provide helpful information to the drivers.
The remainder of this paper is organized as follows. Section II introduces related works on swarming model and small-world phenomenon. Section III presents our Distributed Cohesive Car Fleet Scheme. Subsequently, Section IV presents the simulation results, and Section V concludes the paper.
Chapter 2: Related work
2.1 Swarming Model
In recent years, people have been inspired by the swarming behaviors of animal groups, such as the flocking of birds, to design coordination protocols to control the collective motion of groups of autonomous agents. Our goal is to adapt such swarming principles to develop effective protocols to maintain cohesive car fleets in the context of VANET. The basic swarming principles rely on the internal
communications among individuals of swarm to influence individuals’
decision-making for their next movements to achieve a common goal. In Fig. 2, such swarming strategy can be attributed to the Reynolds Model [7] which consists of the following three basic flocking rules: (i) Collision Avoidance: avoid collisions with nearby flockmates; (ii) Velocity Matching: attempt to match the velocity with nearby flockmates; (iii) Cohesion: attempt to stay close to nearby flockmates.
(i) (ii) (iii) Figure 2 : Three basic flocking rules.
There have been many applications of Reynolds Model to the control of robotic
swarms and the autonomous navigation of cars. For instance,the work of [8] assumed
assumed that the flocking agents are steered using information from nearest neighbors within a dynamic but connected topology. The work of [10] employed a fixed leader to navigate the entire swarm, and the work of [11] assumed constant speed. In contrast, our work takes into account the road traffic where cars will need to adjust their velocity to form cohesive fleets.
2.2 Small World Phenomenon
The small world phenomenon came from the observation that individuals are often linked via a small group of acquaintances. The same phenomenon has also existed on today’s Internet and popular social networks. By conducting a set of re-wiring experiments on regular graphs, Watts and Strogatz [12] observed that by rewiring a few random links, termed shortcuts in a regular graph, such as Fig. 3, the average path length in the resulting small-world graph was reduced significantly (approaching that of the random graphs) while still maintaining a high degree of clustering among the neighboring nodes (since the neighboring nodes are also neighbors of each other, and hence forming a cluster). This class of graphs was termed small world graphs, which emphasizes the importance of random links acting as shortcuts to reduce the average path length.
Wireless networks, such as VANET, can be represented as spatial graphs where links are determined by radio connectivity. Such networks usually do not have long-length connection (shortcuts) due to the limitation of radio transmission range. Hence, typical wireless networks do not possess the small world phenomenon, even though such networks have high clustering. Helmy [13] first investigated the small world phenomenon in wireless networks by adding a few wired links between random nodes to construct the shortcuts in wireless networks and calculating the average path length. The experimental results resembled those of the small world model: the degree of clustering remains almost constant and the average path length is reduced significantly. In the context of wireless networks, (long path) shortcut connections facilitate faster information exchange between nodes.
The work of [11] improved the motion protocol for self-driven flocks via small-world connections by randomly adding long-range interactions from the only global leader to a few distant agents, namely pseudo-leaders to achieve coherent flocking with more stable formation. Our approach is different from [11] in the following ways. First, there exists no single global leader. Second, pseudo-leaders are adaptively selected via a dynamic clustering mechanism to accommodate the changing road condition and traffic. Third, pseudo-leaders communicate via small-world long-range (V2I) connections to collectively maintain the cohesion of the entire car fleet.
Chapter 3: Distributed Cohesive Car Fleet Scheme
Due to the dynamic and heterogeneous nature of VANETs, we design a distributed cohesive car fleet maintenance scheme termed DCFS by integrating the communication technologies of V2V and V2I. DCFS consists of two main
components to facilitate small-world communications (Subsections 3.1 and 3.2) and to support swarming model (Subsections 3.3, 3.4, 3.5 and 3.6), respectively.
3.1 Dynamic clustering mechanism
To make the clustering mechanism work, initially we lineup all the cars in a car fleet and assign an increasing sequence of unique IDs from the head of the car fleet to its tail. Throughout the clustering operations, each vehicle is assumed not to overtake (or pass) its front vehicle. The clustering mechanism classifies the vehicles into two different roles, pseudo-leader and follower, where each follower is associated with only one pseudo-leader at any time. Hence a car fleet will be clustered into several one-hop sub-groups. During the process of dynamic clustering, each vehicle will reside in one of the following three states and will change states in response to different conditions. Figure 4 depicts the state transition diagram of the dynamic clustering scheme. Initially, all the vehicles are in the CH state to broadcast their IDs to one-hop neighbors, and at the same time, also collect the IDs from one-hop neighbors.
Cluster-head (CH): While residing in this state, a vehicle keeps broadcasting its
own ID, and collects and records its neighbors’ IDs. Upon knowing the existence of a neighbor with a lower ID (a potential pseudo-leader), the vehicle changes to the QCM state.
Quasi-cluster-member (QCM): While residing in this state, a vehicle waits for a
fixed time interval to receive a second confirmation message from its potential pseudo-leader. If the vehicle doesn’t receive the second confirmation, it will move back to the CH state. Otherwise, the vehicle changes to the CM state.
pseudo-leader’s broadcast ID, and also collects and records IDs broadcast from its neighbors who are still in the CH state. If the vehicle doesn’t receive a broadcasting ID from its pseudo-leader, it will change to CH state. In addition, if the vehicle receives a lower ID from another neighbor than its current pseudo-leader’s ID, it will change to the QCM state waiting to receive a second confirmation from the neighbor with lower ID.
Figure 4: Dynamic Clustering Flow Chart.
First of all, each point of the initial state is the CH, and they all have ability to broadcasting their ID to their one-hop neighbors and also collect the same ID information from neighbors in this state. Second, after comparing the ID from their list of neighbor nodes, each node can find out which one node is pseudo-leader with the smallest ID. If the smallest ID node is itself, the status unchanged. On the contrary, it has to change state from CH to QCM and wait for receive the second information from the smallest ID of the car (pseudo-leader) in its neighbor list. If it received the second information, it can change the state to CM. On the contrary, its status will be changed back to CH, and indicated that it did not belong to any cluster, return to the beginning of flow chart. In Figure 5, we can more clearly understand the dynamic
clustering mechanism. Since there is a state of QCM, this approach can be avoided when Node3 at Step2 soon become a member of Node2, and the error is happening. Different from the Lowest-ID mechanism, a cluster member can’t have the two cluster-head in the same time.
Figure 5: Dynamic Clustering Flow Example.
Notice that whether the entire car fleet is connected or partitioned into several dispersed groups, the dynamic clustering protocol always runs within each connected group to elect pseudo-leaders which use long-range ability to communicate with other pseudo-leaders (as described in the next subsection), and followers which only use short-range ability to communicate with neighboring cars.
3.2 Small-world information exchange via V2I
communications
In order to address partition in VANETs, we use small-world information exchange via V2I communication. As shows as Figure 6, when a car fleet is dispersed, we use the dynamic clustering mechanism to identify a pseudo-leader in each sub-group. Pseudo-leader uses the long-range communications such as 3G or WiMAX, etc. to exchange location and speed information with other pseudo-leaders. The few long-range links among pseudo-leaders like the shortcuts in the small-world phenomenon. In addition, pseudo-leaders direct their respective followers by the short-distance communications to reduce communication costs so that the entire car fleet is directed by few pseudo-leaders.
3.3 Calculation of center of gravity
For a car fleet to achieve its desired cohesive moving behavior, only pseudo-leaders of different (dispersed) clusters need to compute the relative positions among each other. To facilitate such computation, we compute the center of gravity of each cluster and of the entire fleet as follows. In this paper, each car is assumed to be equipped with GPS to report its current position. Because the definition of car fleet is assumed that each car has common initial starting point and destination hence we can make mobile path planning. To simplify the computation, we map the two-dimensional position of a car into a one-dimensional coordinate system as exemplified in Figure 6.
Figure 7: Calculation center of gravity.
At time t, the pseudo-leader of cluster A collects the position information of its cluster members and computes its center of gravity as follows.
∑
∈ = A i i A P(t) A ) t ( G 1 (1)where |A| denotes the number of elements in sub-group A. Therefore, after exchanging information, each pseudo-leader can calculate the center of gravity of the entire car fleet as follows.
( )
∑
∈ = SG j j group G t SG ) t ( G 1 (2)where the |SG| denotes the number of clusters. After a pseudo-leader obtains Ggroup (t),
the pseudo-leader can use this information as a reference to determine its relative position within the entire vehicle fleet. When a pseudo-leader determines that it is
ahead of the center of gravity over a certain threshold, the pseudo-leader directs the
cluster to slow down. When a pseudo-leader determines that it is behind the center of gravity over a certain threshold, the pseudo-leader directs the cluster to speed up. How to specify a proper threshold will be discussed later. In this way, a dispersed car fleet is able to stay closer to achieve the desired cohesive swarming behavior.
3.4 Calculation of speed difference between neighbors
For a car fleet to abide by the flocking rule of Velocity Matching (as described in Section II.A), each car has to be aware of the speed differences between itself and its neighbors. Figure 3 illustrates how each vehicle calculates the speed difference. Each car collects the speed information from its one-hop neighbors, and computes the
speed differences. For instance, Vij = Vj － Vj is a speed difference between cars i and j.
Also, let Ni denote a set of neighbors of car i. Each car i computes the average of
( )
∑
( )
∈ = i N j ij i Neighbors , i V t N t V 1 (3)If the value of Vi,Neighbors is negative, car i is faster than its neighbors on average so
that it has to brake to slow down.
3.5 Collision avoidance
Before each vehicle finalizing its speed, the mechanism of collision avoidance must be enforced. Here, we have made use of the laws of physics. Equation 4 computes the moving- distance S from time 0 to time t with a constant acceleration. We therefore adapt this equation to calculate the brake distance. To avoid collision, a safe distance needs to be maintained which is equal to a brake distance plus a reaction distance, both of which depend on the current speed of the vehicle. A brake distance is the distance that a car starts braking to a complete stop using a given maximum deceleration Max_Deceleration. ion Aeccelerat V Vt × − = 2 ) ( ) ( S 2 0 2 (4) ion Deccelerat _ Max ) V ( current × − = 2 0 Distance Braked 2 2 (5) 1 5 . 0 , Distance Reaction =
γ
⋅Vcurrent ≤γ
≤ (6) A reaction distance is the distance a vehicle will travel during a given reaction time between when a driver sees the brake lights and when the driver starts braking. InEquation 6, the parameter γ is a given reaction time. Hence, in order to avoid collision, after computing the speed for the next step (to be described in Section 3.6), each car must first check the safe distance with the current speed. If the (required) safe distance is longer than the real distance between two vehicles, the rear vehicle must brake.
3.6 Establishing region and acceleration formula
To support cohesive swarming behavior, three regions, Gravity Region (GR), Linear Region (LR) and Outside Region (OR), are defined around the center of gravity of the entire car fleet, as shown in Figure 8. Depending on which region a pseudo-leader resides, each pseudo-leader will decide to accelerate or decelerate.
Figure 8: Establishing three different region.
The range of GR depends on two factors, (1) the initial maximum number of cars (on a lane) among all the lanes occupied by the entire car fleet, and (2) a given expected speed which is the speed of the entire car fleet in a cohesive situation. With collision avoidance, the expected speed of the entire car fleet will affect the length of the safe distance. In Figure.9, hence the length of GR is equal to the initial maximum number of cars (on a lane) among all the lanes occupied by the entire car fleet multiplied by the safe distance of the expected speed of the entire car fleet. Our aim is
to achieve a cohesive situation where the length of GR is equal to the length of entire car fleet. The length of LR is set to be the same as the length of GR. The area outside of LR is OR.
In our scheme, since only the pseudo-leaders have the information of the center of gravity to decide which region they reside, pseudo-leaders decide acceleration formula as follows.
Figure 9: The length of GR Trend chart.
In Gravity Region: Make every effort to speed up with MAX_Acceleration
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In Linear Region: Linear relations with center of gravity degree and take account of
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(9)When a pseudo-leader residing in LR, the pseudo-leader computes the distance between itself and the center of gravity, and uses the distance to decide acceleration or deceleration. We use value α to adjust two factors: the distance between the pseudo-leader and the center of gravity, as well as the impact of speed difference between the pseudo-leader and its neighbors. When a pseudo-leader residing in OR, the pseudo-leader is too far away from the entire car fleet. It should speed up when it falls behind or slowdown when it is ahead. From the perspective of the followers:
From perspective of the Follower:
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. (10)Since followers do not have the overall information of the entire fleet, each follower decides its own speed based on both its relative speed with its pseudo-leader and its relative speed with other neighbors, where the relative importance of these two factors is adjusted by a value β.
swarming rules of collision avoidance, velocity matching and cohesion to maintain a cohesive car fleet.
Chapter 4: Simulation
4.1 Simulation environment
In our simulation, we use C language to architecture model of the entire traffic environment to perform actual simulation. Table I summarizes the default values of simulation parameters. In our simulation, we configure the entire car fleet on one single lane and vehicles are initially deployed 250 meters apart. Each result is an average of 50 trials.
Number of vehicles 15
Simulation time (seconds) 1000
Topology x (meters) 1
Topology y (meters) 40000
Parameter α 0.5
Parameter β 0.5
Parameter γ (seconds) 0.6
Transmission range of a node (meters) 100
Maximum speed of road (MPS: meters / second) 30
Minimum speed of road (MPS: meters / second) 0
Acceleration interval of a node (meters / second2) -8 ~ +3
Expected speed (MPS: meters / second) 20
Initial speed of a node (MPS: meters / second) Random[0,30]
4.2 Metrics
We conducted extensive simulation using ns-2 to evaluate the performance of DCFS using two metrics. The metric of cohesion performance is defined as follows.
( )
∑
(
( )
)
∈ − = SG j group j p G t G (t) SG t 1 2 σ (11)In statistics, standard deviation is a simple measure of the variability or dispersion of a data set. Low standard deviation indicates that all of the data points are very close to the average value while high standard deviation indicates that the data are spread out
over a large range of average values. Thus, when σp large to represent the various
sub-groups away from the center of gravity and vice versa close. In addition, we also can use the same process to measure the formation performance of car fleet. After exchanging speed information, we can obtain the speed standard deviation for entire car fleet. Therefore, we can understand the difference of speed in the overall fleet and use it as a measure of indicator. If the value is bigger that it represents the topology of entire car fleet changes in larger. Here is a list of the definition of equation:
( )
∑
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∈ − = SG j group j v AvgV t AvgV (t) SG t 1 2 σ (12)4.3 Simulation result and study
4.3.1 Without DCFS
In the first set of simulation, each car moves with a random acceleration chosen
within [-8, +3] meters/second2 every second without employing DCFS. In Fig. 10, we
can observe that σp increases from the initial value of 1000 to 3000 over a period of
1000 seconds, clearly indicating that the cohesion performance of the entire car fleet deteriorates.
4.3.2 Evaluation of different minimum speed of road:
In Figure 11,we compare the cohesion performance in three different minimum
speeds imposed on the road, 0 MPS, 10 MPS and 20 MPS. Although all three configurations converge to the same cohesion performance, the convergence time differs. When the minimum speed of road is 0 MPS, vehicles located in the front of the car fleet may stop and wait for the vehicles on the back. Hence the entire car fleet takes the least amount of time to achieve cohesion. In comparison, it takes 30*5 seconds and 60*5 seconds, respectively, for the configurations of the minimum speed 10 MPS and the minimum speed 20 MPS. The observation implies that the lower the minimum speed imposed on road the faster it takes for a car fleet to achieve cohesion.
4.3.3 Evaluation of the impact of collision avoidance:
We set the expected speed of a car fleet of 15 vehicles to be 20 MPS. In Fig. 11, the cohesion performance of the scenario with collision avoidance is only slightly worse than the scenario without collision avoidance, indicating that collision avoidance did not significantly degrade the cohesion performance. However, in Figs. 12 and 13, the formation performances and the average speeds of the two scenarios are much different. In the scenario without collision avoidance, since each car does not have to take the safe distance into account, the formation performance becomes zero after the entire car fleet achieves cohesion. Furthermore, without being constrained by collision avoidance, the speed of each car and the entire car fleet may keep accelerating up to the maximum speed 30 MPS. In contrast, with collision avoidance, vehicles will need to maintain a safety distance, which prevents vehicles from accelerating and decelerating.
Figure 13: Comparison of formation performance in with collision avoidance and without collision avoidance.
Figure 14: Comparison of Average speed in with collision avoidance and without collision avoidance.
4.3.4 Evaluation of two specific scenarios:
To evaluate the performance of the proposed cohesive car fleet maintenance scheme, we evaluated two scenarios:
ALL: Every car is a pseudo-leader and the value of α is set to 1.
DCFS: Cars are classified into different roles. The value of α is 0.5 and the value of β is 0.5. We use 15 vehicles and the expected speed is 20 MPS. As observed in Fig. 15, ALL and DCFS show almost the same, good results, due to the fact that status of the entire car fleet is known to all the pseudo-leaders in the two scenarios. However, in ALL, since each car does not take its neighbor’s information into account (α is set to 1), its cohesion performance varies around 150. In contrast, the cohesion performance
of DCFS is stable around 150. As shown in Fig. 16, ALL exhibits higher values of σv
than DCFS for the reason that ALL does not take the speed of nearby cars into account so that car speeds are inconsistent. Although ALL also has high cohesive performance, to avoid collision, cars brake more often in ALL than in DCFS.
Therefore, in DCFS, the smooth and small value of σv implies that the entire car fleet
almost travels at the same speed. As shown in Fig. 17, due to frequent braking, ALL exhibits smaller speed than DCFS on average.
Figure 15: Comparison of cohesion performance in DCFS and ALL scenarios.
Figure 17: Comparison of average speed in DCFS and ALL scenarios.
4.3.5 Evaluation of different length of LG
In the chapter 3.6, we set the default radius length of linear region is the same with the radius length of gravity region. But the radius length of linear region is certainly an important parameter in our distributed cohesive car fleet scheme. In the set of simulations, we set the 15 vehicles and expected speed to be 20 MPS and calculated the radius length of gravity region is 277.5 meters. We then evaluate the radius length of linear region in different length using 100% (277.5 meters), 50% (138.75 meters) and 0% (0 meter). Figs. 18, 19 and 20 show the comparison of performance and average speed in different length of linear region. As we can see, when the radius length of linear region is 0 meter, the cohesion performance and average speed are smaller and formation performance is larger than 50% and 100% radius length of linear region. Because the radius length of linear region is 0 meter means that there is no linear region and pseudo-leaders don’t take account of nearby speed. We also
notice that both the 50% and 100% radius length of linear region have the same results. It means that the radius length of linear region isn’t too long. However, if there is no linear region, our scheme will lose some part of swarm characteristic.
Figure 18: Comparison of cohesion performance in different length of linear region.
Figure 20: Comparison of average speed in different length of linear region.
4.3.6 Evaluation of the number of vehicles
We now evaluate the impact of the number of vehicles in a car fleet on DCFS. Fig. 21, Fig. 22 and Fig. 23 compares the performance and the average speed with different number of vehicles in a car fleet. In Fig. 21, we observe that the more
vehicles in a car fleet, the higher the initial value of σp and the higher the converged
value of σp. We also observe that higher vehicle numbers of in a car fleet prolong
convergence time. For the formation performance and the average speed, similar results are observed in Figs. 22 and 23, with different convergence time.
Figure 21: Comparison of cohesion performance in different number of vehicles.
Figure 23: Comparison of average speed in different number of vehicles.
4.3.7 Evaluation of the expected speed
We evaluate DCFS by comparing the performance and the average speed using expected speed of 15 MPS, 20 MPS, and 25 MPS, respectively. In Fig. 24, the higher
expected speed results in higher σp value. In Fig. 25, the formation performance is not
affected the expected speed. In Fig. 26, a car fleet achieves the expected speed when the car fleet becomes cohesive.
Figure 24: Comparison of cohesion performance indifferent expected speed of entire car fleet containing 15, 20 and 25 MPS.
Figure 25: Comparison of formation performance in different expected speed of entire car fleet containing 15, 20 and 25 MPS.
Figure 26: Comparison of average velocity in different expected speed of entire car fleet containing 15, 20 and 25 MPS.
4.3.8 Evaluation of the impact of traffic lights (TL)
Finally, we evaluate the impact of traffic-light on DCFS with a car fleet of 15 vehicles and the expected speed of 20 MPS. A traffic light is established every 250 meters, and each traffic light changes its signal once every 30 seconds. Within 50 meters from a traffic-light, if a car observes a change to red light, the car will
decelerate with-8 m/s2. We observe from Fig. 27 that although a car fleet achieved the
same cohesion (from σp = 1000 to σp = 400) within the first 60 seconds, with or
without traffic lights, the existence of traffic lights does have a negative impact on the cohesion performance. For instance, without traffic lights, it took the car fleet 150
seconds to stabilize at σp = 150. In contrast, with traffic lights, it took the car fleet 250
seconds to reach σp = 150, but the cohesion performance varies over time. In Fig. 28,
value σv varies over time. Without traffic lights, our scheme achieved good formation
performance with stable σv values. In Fig. 29, it is clear that the existence of traffic
lights slows down the car fleet where the average both fell below the expected average speed of 20 MPS, and varies greatly.
Figure 28: Formation performance in with traffic light and without traffic light.
Chapter 5: Conclusion
In this paper, by incorporating the small world phenomenon into a swarming model, we described a cohesive car fleet maintenance scheme which takes the traffic and road conditions into consideration. A dynamic clustering protocol classifies vehicles into the roles of pseudo-leader and follower. Within each partition, cars form a cohesive swarm by coordinating their speed and position via short-distance V2V communications. To exchange information between partitions of a dispersed cat fleet, the pseudo-leaders communicate via long-distance V2I communications, which resembles the shortcuts of the small world phenomenon. By communicating with all the other pseudo-leaders, each pseudo-leader then determines its relative position within the car fleet by referring to the center of gravity of the entire car fleet. Each pseudo-leader then speeds up (and direct its followers to speed up) when it falls behind, or slows down (and direct its followers to slow down) when it is ahead, so as to achieve a cohesive swarming behavior of the entire car fleet. Simulation results show that the proposed mechanism achieve excellent cohesion and formation performance under different fleet and road conditions. Our future work will improve DCFS to consider more realistic traffic environment. For instance, we will introduce other vehicles onto the road to interfere the car fleet, similar to the work [14] which adds obstacles to flocking. To do so, we have to make all the vehicles to have the ability to switch lanes and overtake (pass) the front vehicles when they are approaching the front vehicles.
References:
[1]. B. Petit, M. Ammar, and R. Fujimoto, “Protocols for roadside-to-roadside data
relaying over vehicular networks,” in proceedings of the IEEE Wireless Communications and Networking Conference, pp. 294-299, Las Vegas, USA, April 2006.
[2]. M. Bechler, L. Wolf, O. Storz, and W.J. Franz, “Efficient discovery of Internet
gateways in future vehicular communication systems,” in proceedings of the 57th
IEEE Semiannual Vehicular Technology Conference, Jeju, South Korea, April 2003.
[3]. M. Bechler, and L. Wolf, “Mobility management for vehicular ad hoc
networks,“ in proceedings of the 61th IEEE Semiannual Vehicular Technology
Conference, Vol. 4, pp.2294- 2298, Stockholm, Sweden, June 2005.
[4]. T.D.C. Little, and A. Agarwal, “An information propagation scheme for
VANETs” in proceedings of the 8th Intelligent Transportation Systems, pp.13-15,
Vienna, Austria, Sept 2005.
[5]. Q. Xu, T. Mak, J. Ko, and R. Sengupta, “Vehicle-to-Vehicle Safety Messaging in
DSRC,＂in proceedings of the 1st ACM international workshop on Vehicular ad
hoc networks, pp. 19-28, Philadelphia, PA, USA, October 2004.
[6]. T, Taleb, M. Ochi, A. Jamalipour, N. Kato, and Y. Nemoto, ”An efficient
vehicle-heading based routing protocol for VANET networks,“ in proceedings of the IEEE Wireless Communications and Networking Conference, vol. 4, pp. 2199-2204, Las Vegas, USA, April 2006.
[7]. Craig W. Reynolds, and Symbolics Graphics Division, “Flocks, Herds, and
Schools: A Distributed Behavioral Model” in ACM SIGGRAPH Computer Graphics21, pp.25-34, 1987.
[8]. H.G. Tanner, A. Jadbabaie, and G.J. Pappas, “Stable flocking of mobile agents,
part i: Fixed topology,” in Proc. IEEE Conf. Decision Control, Maui, Hawaii, pp. 2010–2015, 2003.
[9]. H.G. Tanner, A. Jadbabaie, and G.J. Pappas, “Stable flocking of mobile agents,
part ii: Dynamic topology,” in Proc. IEEE Conf. Decision Control, Maui, Hawaii, pp. 2016–2021, 2003.
[10].Bo Liu, Tianguang Chu, and Long Wang, “Flocking of Multi-Vehicle Systems
with a Leader” in proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, October 9-15, 2006.
[11].Hai-Tao Zhang1, et al.” Predictive protocol of flocks with small-world
connection pattern” in PhysCom, arXiv0709.0184, Germany, 2008.
[12].D. Watts, and S. Strogatz, “Collective dynamics of ‘small-world’ networks,”
Nature Volum.393, pp. 440-442, 1998.
[13].A. Helmy "Contact Based Architecture for Resource Discovery (CARD) in Large
Scale MANets," in Proc. IPDPS, April. 2003.
[14].R. O. Saber, and R. M. Murray, “Flocking with obstacle avoidance: Cooperation
with limited communication in mobile networks,” in Proceedings of the IEEE
Conference on Decision and Control, Maui, Hawaii, pp.2022–2028, December
9-12 2003.
[15].T.C. Hou, and T.-J. Tsai, “Adaptive clustering in a hierarchical ad hoc network,
Multimedia, pp.171-176, Dec. 1998.
[16].X. Zhang, H. Su, and H. Chen, “Cluster-based multi-channel communications
protocols in vehicle ad-hoc networks,” in proceedings of IEEE Wireless
Communications Magazine 13 (5), pp. 44–51, 2007.
[17].H. Levine, and W. J. Rappel, “Self-organization in systems of self propelled
