Some studies consider variable speed limit (VSL) control as a viable option to prevent traffic breakdown at bottlenecks by limiting the mainline flow with reduced speed limits. However, few studies consider the location of the application area as a design variable of the problem. This paper explains why the location of a VSL control area is crucial to prevent the capacity drop phenomenon at lane drop bottlenecks. We first define two types of stationary states, congested and uncongested, inside a lane drop bottleneck assuming the Lighthill-Whitham Richards model with bounded acceleration. In particular, the characteristics of these stationary states and their admissible conditions are discussed thoroughly. If the speed limit imposed is low enough, the location of the VSL application area is irrelevant to ensure an uncongested stationary state inside the bottleneck. However, for a given range of speed limits, the location of the VSL application area should be designed carefully to allow for uncongested stationary states and prevent the occurrence of the capacity drop. We formulate an optimization problem and show that, contrary to the general belief, the larger the speed limit, the farther the VSL application area should be from the bottleneck. Finally, the results are extended to other types of bottlenecks, such as sag or tunnel bottlenecks. To the best of our knowledge, this is the first study to analytically identify, formulate, and solve the optimal location problem for variable speed limit application areas. It makes fundamental contributions to both traffic flow theory (by analyzing the stationary states for VSL-controlled bottlenecks) and traffic control (by determining the optimal location of a VSL application area). Moreover, the results presented are of practical relevance because they can help to establish some guidelines for practitioners to implement VSL control strategies.

一些研究认为可变速度限制（VSL）控制是可行的选择，可通过以降低的速度限制限制干线流量来防止瓶颈处的交通中断。但是，很少有研究将应用程序区域的位置视为问题的设计变量。本文解释了为什么VSL控制区域的位置对于防止在车道下降瓶颈处的容量下降现象至关重要。我们首先在假定车道加速瓶颈为Lighthill-Whitham Richards模型的车道下降瓶颈内定义两种状态，即拥塞状态和非拥塞状态。特别是，对这些稳态的特性及其允许条件进行了详尽的讨论。如果施加的速度限制足够低，VSL应用程序区域的位置无关紧要，以确保瓶颈内部没有拥挤的固定状态。但是，对于给定的速度限制范围，应仔细设计VSL应用区域的位置，以允许不拥挤的固定状态并防止容量下降的发生。我们提出了一个优化问题，并表明，与通常的看法相反，速度限制越大，VSL应用程序领域应该离瓶颈越远。最后，结果扩展到其他类型的瓶颈，例如下陷或隧道瓶颈。据我们所知，这是第一个分析确定，制定和解决变速极限应用领域的最佳位置问题的研究。它对交通流理论（通过分析VSL控制的瓶颈的稳态）和交通控制（通过确定VSL应用程序区域的最佳位置）做出了根本贡献。此外，提出的结果具有实际意义，因为它们可以帮助为从业人员实施VSL控制策略建立一些指南。