[SIAM NEWS] Smells Like a Traffic Jam

By Dana Mackenzie

November 01, 2013

[Freelance writer Dana Mackenzie writes from Santa Cruz, California. He is the author of the 2012 book The Universe in Zero Words: The Story of Mathematics as Told Through Equations.]

Next time you’re at a picnic and you discover a procession of ants marching over your meal, wait just a second before you throw your hamburger into the nearest trash can. Take a moment to admire the rapid, purposeful flow of traffic on the ant highway. Pause to appreciate what you don’t see: stopped ants.

下次你去野餐的时候，你把汉堡包扔进最近的垃圾桶，只需稍等秒秒钟，你就会发现一排蚂蚁在你的食物上行进。花点时间欣赏一下在蚂蚁公路上快速而有目的的交通流。停一下，你意识到你没看到：不动的蚂蚁。

Now compare this ant highway to an interstate highway through any large American city at rush hour. Whether it’s Route 5 in Seattle or Route 95 outside Washington, DC, the story will be the same—long lines of stopped vehicles.

现在将这条蚂蚁公路与一条高峰期横跨任何美国大城市的州际公路进行比较。无论是西雅图的5号公路还是靠近华盛顿特区的95号公路，情况都是一样的，即停止车辆排成长队。

What gives? What do ants know that we don’t know? And more importantly, is there anything we can do to make our highways a little bit more like ant highways?

到底发生了什么呢？蚂蚁知道什么我们不知道的吗？更重要的是，我们能做些什么使我们的公路更像一条蚂蚁公路呢？

Those are some of the questions studied by Katsuhiro Nishinari, a self-described “jam-ologist” at the University of Tokyo, who spoke about traffic at this year’s SIAM Annual Meeting in San Diego. “Jam-ology is a very interdisciplinary study,” says Nishinari. “It extends not only to vehicles and ants but also pedestrians, schools of fish in the water, or inventory in a warehouse.”

那些是东京大学的Katsuhiro Nishinari所研究的一些问题，他自称“拥堵学家”，并在今年San Diego举办的SIAM年会上谈到了交通。Nishinari说，“拥堵学是一门跨学科的研究，它不仅能扩展到车辆和蚂蚁，还能扩展到行人、水中的鱼群或仓库中的库存”。

Even the brain has some similarities to a traffic network, as another traffic expert points out. “They are both consensus-like systems with nearly identical equations,” says Sean Brennan of Pennsylvania State University. “I don’t think it’s a coincidence that the 1-dimensional shock-wave behavior of vehicle traffic jams is remarkably similar to the 2-dimensional neural behavior that manifests itself as seizures.”

正如另一位交通专家指出，即使是大脑也与交通网络存在某些相似性。宾夕法尼亚州立大学的Sean Brennan说：“它们都是具有几乎相同等式的近似一致系统，我认为一维车辆交通拥堵的激波行为与表现为癫痫发作的二维神经行为非常相似不是一种巧合”。

Traffic engineers, physicists, biologists, and mathematicians have been modeling different kinds of traffic for more than 75 years, and they have come up with a wide variety of mathematical models. And yet, we still don’t have an answer even to some simple questions, such as: Can one person unblock a traffic jam?

交通工程师、物理学家、生物学家以及数学家模拟不同种类的交通已经超过75年了，并且他们提出了各种各样的数学模型。然而，我们甚至对一些简单的问题仍然没有答案，比如说：人们能否疏通交通拥堵？

Let’s get back to those ants. One of the main things that makes them different from humans is a specialized sense of smell. According to Nishinari, their ability to detect pheromones excreted by other ants gives them a way to estimate the density of ants in their immediate vicinity. Unlike humans at rush hour, ants won’t let the density exceed a critical level beyond which the flux of ants would start to decrease. Another thing they won’t do is pass one another. And they always maintain a safe following distance. As a result, they tend to form large platoons that move in a synchronized fashion to their goals. If humans adopted these three simple behaviors, we would be a long way toward curing our traffic woes.

让我们回到那些蚂蚁身上。使它们不同于人类的一个主要原因是一种特殊的嗅觉。根据Nishinari的说法，它们身上所具有的检测由其它蚂蚁分泌信息素的能力使它们能够估计在其附近的蚂蚁的密度。与高峰期的人有所不同，蚂蚁不会让密度超过某个临界值，否则蚂蚁的流量就会开始下降。另一件它们不会做的事是超车。它们总是保持安全的跟随距离。结果，它们往往会形成很长一排，步调一致地达到它们的目的地。如果人们也采用这三种简单的行为，那么我们将离解决我们的交通问题非常遥远。

Technological Fixes for Selfish Humans

对自私人类的技术修正

Perhaps it’s hopeless to expect humans to behave this way—we’re just too selfish. Moreover, we have no incentive to change. If just one driver chose to obey these rules, it wouldn’t make any difference as long as other drivers continued in their normal selfish ways.

指望人类这样做大概是没用的（我们太自私了）。此外，我们没有改变的诱因。如果只有一个司机选择遵守这些规则，只要其他司机继续他们通常的自私行为，那就没有任何区别。

But technology can encourage us to behave more altruistically. Metering lights on highway entrance ramps are intended to keep the density of traffic below a critical level. High-occupancy vehicle lanes have the same purpose, along with another, less obvious benefit: They reduce the amount of lane-changing. According to Michael Cassidy, a civil and environmental engineer at the University of California at Berkeley, people often overlook this point. “Even if the special lane is underused, even if it’s only 60% filled, the net benefit to all traffic can be positive. There is less lane changing between the adjacent lanes, and that means less lane changing near the bottlenecks.”

但技术能让我们表现得更无私。公路入口匝道上的计量灯旨在使交通密度保持在临界水平以下。大容量车道有相同的目的，还有另一个不那么明显的好处：它们减少了变道的数量。据University of California at Berkeley土木与环境工程师Michael Cassidy说，人们常常忽视这一点。“即使专用车道未充分使用，即使它只有60%的填充率，交通的净收益也可能是正的。相邻车道间换道较少，这也就意味着在瓶颈附近换道较少。

Another technological innovation just starting to show up on the world’s roads is automatic cruise control. Nishinari consulted on the development of a system called CyberNavi (sold by Pioneer Electronics in Japan, but not in the U.S.), that warns drivers when they get within 40 meters of the car ahead. More ambitious systems, already under development in Europe, will enable cars to “talk” to each other and to the infrastructure of the highway. Using wireless communication and GPS devices, cars will tell the highway where they are and what the conditions are around them. In turn, the highway will warn them of traffic jams up ahead, enabling them to slow down in advance. If everybody’s car has the technology, it will keep all the cars spaced far enough apart to give the jam a chance to dissipate. It’s the next best thing to ant pheromones.

另一项刚刚开始出现在路上的技术革新是自动巡航控制。Nishinari谈到一款被称为CyberNavi的系统开发（由Pioneer Electronics在日本销售，而不是在美国），它能够在距离前车40米内对司机发出警告。正在欧洲开发的更具雄心的系统，将使汽车能够彼此“交谈”以及与公路基础设施进行“交谈”。使用无线通信和GPS设备，汽车将告诉公路它们的位置以及周边条件。反过来，公路也会警告它们前方交通堵塞，从而使它们提前减速。如果每辆车都有这项技术，它将使所有车保持足够距离，从而有机会使拥堵消失。这是蚂蚁信息素的下一个最佳选择。

You don’t have to wait, however, if a retired engineer and amateur scientist named Bill Beaty is right. In 1998, Beaty wrote the following Internet post about an impromptu experiment he had conducted on State Route 520 near Seattle:

然而，如果退休工程师和业余科学家Bill Beaty是正确的，那你无须等待。1998年，Beaty写了下面关于他在西雅图附近的520国道上进行的即兴实验的Internet文章：

“Rather than repeatedly rushing ahead with everyone else, only to come to a halt, I decided to try to move at the average speed of the traffic. I let a huge gap open up ahead of me, and timed things so I was arriving at the next ‘stop-wave’ just as the last red brakelights were turning off ahead of me.

“并不是不停地向前冲到其他人面前才停下来，我决定尝试以正常交通速度行驶。我与前面车辆保持一个很大距离，时间流逝，正当我前面的车关掉红色刹车灯时我陷入了下一个‘停车波’”。

“Finally I happened to glance at my rearview mirror. There was an interesting sight.

“最后我偶然瞥了一眼后视镜。有一个有趣的景象。

. . . In the neighboring lanes I could see maybe five of the traffic stop-waves. But in the lane behind ME, for miles, TOTALLY UNIFORM DISTRIBUTION. . . . By driving at the average speed of traffic, my car had been ‘eating’ the traffic waves.” [Emphasis present in original.]

. . .在相邻车道上，我大概可以看到五个交通停车波。但在我身后的车道上，长达数英里，都完全均匀分布. . .我的车在以正常交通速度‘吃’交通波”。

Because his article was not published in a scientific journal, Beaty’s home-brewed experiment did not attract a lot of attention. Last year, though, Nishinari and three co-authors put “jam-absorption driving” to the test. In a simple computer model of a single-lane road, they confirmed that Beaty’s strategy works. “Slow-in, fast-out” driving, even by one driver, could give an already-formed jam time to dissolve and also prevent the creation of new jams behind the jam-absorbing driver. Beyond that, Nishinari and his colleagues showed (in work not yet published) that the total fuel consumption of all the vehicles on the highway would be decreased by as much as 35%. Thus, one person can make the driving experience more pleasant for everyone and benefit the environment.

因为他的文章没有发表在科学杂志上，Beaty自制的实验没有引起太多的关注。然而去年，Nishinari和三名合作者将“消除拥堵的驾驶”放入了测试中。在一个简单的单车道计算机模型中，他们证实了Beaty的战略工作。甚至一个司机“慢进、快出”驾驶，可以使一个已经形成的拥堵有时间消失，也能防止消除拥堵的司机背后的新拥堵。除此之外，Nishinari和他的同事发现（在还未发表的工作中），公路上所有车辆的总油耗将下降35%。因此，人们可以有更愉悦的驾驶体验，并有利于环境。

Jam-absorbing Drivers

消除拥堵的司机

Before you go out and try to drive like Beaty, it’s important to be aware of certain caveats. First, the model Nishinari’s group used was extremely simplistic. The “fast-out” part of the model (which was not part of Beaty’s experiment) was actually instantaneous, which is both physically impossible and extremely unwise. Even if you could accelerate instantaneously, you would run into the car ahead of you unless it was doing the same thing. Also, the model did not take into account the likelihood that the big gap in front of a jam-absorbing driver would encourage drivers from other lanes to cut in front of him.

出去试着像Beaty一样开车前，你需要了解一些注意事项。首先，Nishinari团队使用的模型是非常简化的。模型的“快出”部分（这并不是Beaty的实验部分）实际上是瞬间发生的，这本身是不可能的也是极其轻率的。即使你能瞬间加速，你也会撞上你前面的汽车，除非它也做同样的事情。此外，该模型并没有考虑消除拥堵的司机前面的巨大空间可能会使司机从其它车道突然插到他前面。

Other jam-ologists have differing opinions. “The ‘slow into a jam’ strategy is in complete accord with our prior work,” says Brennan. He and his student Kshitij Jerath have work in progress that leads to a similar conclusion, but with a catch. There appear to be “event horizons” such that a car outside the event horizon can eat the jam, although a car inside the event horizon cannot have any effect. Brennan also thinks, based on intuition rather than study, that a gap of more than 5 MPH between your speed and your neighbors’ speeds would lead to more accidents—which certainly would not solve the jam problem.

其他拥堵学家们也有不同的看法。Brennan说：“‘慢慢进入拥堵’的策略与我们以前的工作是完全一致的”。他和他的学生Kshitij Jerath有一些正在进行的工作，得出了一个类似的结论，但也有些意想不到的发现。似乎存在这样的“视界”使得视界外的汽车可以吞噬拥堵，而视界内的汽车没有任何作用。Brennan还基于直觉而非研究，认为你的速度与相邻速度间超过5英里/小时就会导致更多事故，这当然并没有解决拥堵问题。

Cassidy, by contrast, is very skeptical of one car’s ability to affect a traffic jam. “The name of the game should be one thing and one thing only, maximizing discharge rate from your bottleneck,” he says. Because the “slow-in” phase doesn’t affect anything downstream of the bottleneck, he thinks that it cannot address the root of the problem.

相比之下，Cassidy非常怀疑一辆汽车对交通堵塞的影响能力。他说，“这个名字应该只是一件最大化瓶颈退出率的东西”。因为“慢进”阶段并不会影响瓶颈下游处的任何东西，他认为这不能解决问题的根源。

Adaptive cruise control (ACC) should, in principle, be even better than manual “jam-absorption,” and it’s based on a similar principle—slowing down long in advance of the “event horizon.” But Brennan and Jerath have shown that a little bit of a good thing can actually turn out badly. They studied a traffic model with two populations of cars. The cars in one group, with a “sensitivity” of 0.3 to the actions of the car in front of them, would correspond to cars not equipped with automatic cruise control. The other group, with a sensitivity of 0.7, would be cars with ACC systems that could detect when the car in front was slowing down, and react accordingly.

原则上来说，自适应巡航控制（Adaptive cruise control，ACC）要比人工“消除拥堵”更好，这是基于一个类似的原理，即提前在“视界”前很长一段距离减速。但Brennan和Jerath表示这有点好心办坏事了。他们研究了一个有两种汽车的交通模型。一种汽车对它们前面的汽车动作的灵敏度为0.3，这就相当于没有自动巡航控制系统的汽车。另一种灵敏度为0.7，就是装有ACC系统的汽车，它们可以检测前方车辆减速，并相应地作出反应。

When almost all the vehicles on the road had ACC, Brennan and Jerath showed that the highway could accommodate twice as much traffic before starting to jam. But the increased capacity came with a cost: The flow of traffic became highly vulnerable to the introduction of just a few non-ACC vehicles. If the number of ACC-equipped vehicles decreased from 95% to 90%, for instance, the road’s capacity would decrease significantly. If the density was already close to capacity when the non-ACC vehicles joined the flow, traffic would almost certainly jam. The result suggests that ACC-equipped vehicles should get a separate lane, if and when these systems become popular. But the lane restriction would need to be enforced very strictly.

当几乎所有车辆都有ACC时，Brennan和Jerath发现，公路可容纳拥堵前两倍的交通。但增加的容量是有代价的：交通流量变得极易受到少数非ACC车辆引入的影响。例如，如果装有ACC的车辆数量从95%减少到90%，那么道路的容量将大大下降。如果密度已经接近非ACC车辆加入车流时的容量，那么交通几乎肯定会堵塞。结果表明，当这些系统流行时，装有ACC的车辆应该有单独的车道。但需要严格执行车道限制。

Heterogeneous traffic (made up, say, of vehicles with and without ACC) is a headache not only for traffic but also for traffic modelers. A team led by Saskia Ossen of the Delft University of Technology recently showed that none of the seven leading traffic models predicted the behavior of heterogeneous traffic accurately, when compared to real data extracted from high-speed videos taken from a helicopter. The models include lots of parameters that describe the average behavior of drivers. But a highway where half the vehicles have sensitivity 1 and half have sensitivity 0 will behave very differently from a highway where all the vehicles have sensitivity 0.5. Now imagine a highway with buses, trucks, ACC-equipped vehicles, non-ACC-equipped vehicles . . . Or even worse, go to India, where pedicabs, motorcycles, and elephants are added to the mix.

异构交通（也就是说由装有ACC的车辆和无ACC的车辆组成）对交通和交通模型创作者来说都是一件头痛的事情。由Delft University of Technology Saskia Ossen领导的研究小组最近发现，相比于从直升机拍摄的高速视频中抽取的实际数据，七大交通模型没有一个能精确预测异构交通的行为。模型中包含了许多描述驾驶员通常行为的参数。但一条一半车辆灵敏度为1、一半车辆灵敏度为0的公路与一条所有车辆灵敏度都为0.5的公路表现非常不同。现在想象一条公路，上面有公共汽车、卡车、装有ACC的车辆非ACC配备的车辆. . . 或更糟的，去印度，路上甚至还有三轮车、摩托车以及大象。

Investing in Pedestrian Traffic

致力于行人交通

The elephants bring up a final interesting point. Though we usually think of traffic as a problem involving vehicles, some of the least-understood traffic problems involve pedestrians (of the two-legged variety). According to Tobias Kretz, a project manager for Viswalk, a pedestrian simulation developed by PTV in Karlsruhe, Germany, it’s partly a matter of cost. When you build a road, you’ll do a traffic simulation because the relative cost is small. That’s not true when you build a sidewalk. However, pedestrian flow becomes very important during major events like the Olympic Games. PTV has consulted with the organizers of the Vancouver, London, and Rio de Janeiro Olympics to get fans to their desired events faster.

大象带来了最后一个有趣的问题。虽然我们通常认为交通是一个涉及车辆的问题，有点最不把它当作涉及行人（包含两条腿的）的交通问题。据Viswalk（一款由德国卡尔斯鲁厄PTV开发的行人仿真系统）项目经理Tobias Kretz说，部分原因是成本问题。当你修建一条公路时，因为相对成本较小，你会做一个交通模拟。但当你修一条人行道时并不是这样的。然而，在奥运会这样的大型赛事中，行人流变得非常重要。PTV为温哥华、伦敦以及里约热内卢奥运会主办方提供咨询，使粉丝能更快地去到他们想要的赛事中。

Because the behavior of pedestrians has been studied much less than that of vehicles, Kretz had to develop his own simulations from the ground up. This year, though, a group of researchers led by Frank Fiedrich of Wuppertal University conducted experiments with 1000 pedestrians to see how they behaved when forced to go around corners or when funneled through a narrow entrance. Kretz looks forward to comparing his models to the group’s field data.

因为对行人行为的研究比对车辆行为的研究少得多，Kretz不得不从零开始开发自己的仿真系统。不过今年，一组由Wuppertal University Frank Fiedrich领导的研究人员进行了有1000个行人的实验来看看他们不得不转弯或流经一个狭窄的入口时如何表现。Kretz期待将他的模型与该团队的现场数据进行比对。

In this experiment conducted in 2013 in Dusseldorf, pedestrians in encoded hats round a corner. The experiments were intended to provide data on how traffic jams form in pedestrian traffic. The first few pedestrians travel unimpeded around a corner (left). Later, a wave of congested traffic forms in advance of the corner and the velocity of the pedestrians through the corner decreases. Photos courtesy of Forschungszentrum Jülich/Ralf Eisenbach.

It may not be obvious, but research on pedestrian traffic is important for automobile traffic, too. According to the Downs–Thompson paradox, travel times in a big city tend to an equilibrium at which all methods of transportation will get you to your destination in the same time. Therefore, the transportation system is only as strong as its weakest link. If societies invest more in road traffic but neglect public transportation or pedestrian traffic, the result may be increased travel times. “We will just blow up the area extent of our cities, implying longer trip length, implying more people choosing the car instead of cycling or walking,” Kretz says. “If we invest in pedestrian traffic, cycle paths, and comfortable walking routes, the spiral will go the other direction.” For this reason, Kretz is skeptical of technological improvements like adaptive cruise control, special lanes, or adaptive speed limits. “I doubt that road jams can be prevented with measures for road traffic only. What we need is innovation in walking, cycling, and public transport.”

这可能并不明显，但行人交通的研究对汽车交通也很重要。根据Downs–Thompson paradox，在一个大城市的出行时间会趋向于一种平衡，此时所有的交通运输方式都能使你同时到达目的地。因此，交通运输系统的能力只与其最弱环节有关。如果社会更多地置身于公路交通而忽视公共运输系统或行人交通，结果可能会增加出行时间。Kretz说，“我们只是放大我们的城市面积，这意味着更长的行程，意味着更多的人选择汽车而非骑自行车或步行。如果我们致力于行人交通、自行车道以及舒适的步行路线，那么螺旋会走向另一方向”。正因如此，Kretz对自适应巡航控制、专用车道或自适应限速等技术改进是持怀疑态度的。“只通过道路交通的测量就能阻止道路堵塞，我对此很怀疑。我们需要的是步行、骑行以及公共交通运输方面的革新”。

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What’s in a Model?

模型中有什么呢？

The earliest traffic models described traffic as a fluid with no individual cars. Such models are called macroscopic, because they depend only on large-scale variables, such as the average density and velocity of traffic. One valuable insight provided by these models is the fundamental diagram, which conveys the important information that on any road the flux of traffic (i.e., the velocity times the density) increases only up to a certain density, and then it starts to decrease. This is, in a nutshell, why jams occur.

最早的交通模型把交通描述为没有单独汽车的流体。这种模型被称为宏观模型，因为它们只依赖于大尺度变量，如平均密度和交通速度。这些模型提供的一个有价值的见解是基本图，它传达了重要的信息，即在任何道路上，交通流量（即速度乘以密度）只能上涨到某一密度，然后开始下降。简单地说，这就是拥堵发生的原因。

Unfortunately, fluid models have certain undesirable features. They predict that traffic jams should travel in either direction from a bottleneck; in practice, though, jams travel in only one direction: upstream. Fluid models also tend to have a rather unrealistic fundamental diagram. Empirical data show that at high densities, traffic enters a synchronized state in which all the cars travel at almost the same velocity. As soon as a disturbance happens (for example, one driver hits the brakes), the synchrony is broken and the flux drops, creating a “phantom traffic jam,” i.e., one with no visible cause, such as an accident or bottleneck. The very existence of two equilibrium states—one stable and the other metastable—violates a central tenet of the basic fluid models.

不幸的是，流体模型存在某些令人讨厌的特性。他们预测，交通拥堵应该从两个方向中任一个通过瓶颈；然而，实践中拥堵只从一个方向通过：往上游。流体模型也往往有一个相当不实际的基本图。经验数据表明，在高密度处，交通进入一个同步状态，此时所有车辆几乎以相同速度行驶。一旦发生干扰（例如，一个司机踩刹车），同步性就会被打破，流量下降，从而产生“幽灵交通堵塞”，即一个没有明显原因（如事故或瓶颈）的拥堵。两个平衡态（一个稳定态和另一个亚稳态）的存在违反了基本流体模型的一个中心原理。

In recent years, traffic modelers have turned more toward microscopic models, which simulate every single car. Cellular automaton models are discrete in both time and space, representing the road as a row of cells that cars move into and out of at each time step. The most realistic class of models attempts to describe drivers’ actual behavior—representing the rate at which they accelerate as a function of the headway (distance between cars) or any other variables the modeler deems relevant. These models lead to huge systems of differential equations, either deterministic or stochastic, with as many variables as vehicles on the road. Another drawback of microscopic models is that the difficulty of acquiring experimental data on individual drivers makes all such models somewhat speculative.

近年来，交通模型制作者日益转向微观模型，它模拟每一辆车。元胞自动机模型在时间和空间上都是离散的，它把道路表示成一行细胞，每次车辆移进移出。最实际的一类模型试图描述司机的真实行为，即将他们加速的概率表示成一个运行间隔（车辆间的距离）或任何建模者认为有关的其它变量的函数。这些模型产生了巨大的变量数如路上的车辆一般多的确定或随机微分方程组。微观模型的另一个缺点是，获取单个驾驶员的实验数据的难度使得所有这些模型都有点投机。

Written on March 2nd , 2014 by 李军