A Generalized Queuing Model and its Solution Properties
A Generalized Queuing Model and its Solution Properties
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DOI：
10.1016/j.trb.2015.05.008
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
Jia Li;H. M. Zhang
中科院分区：
文献类型：
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作者：
Jia Li;H. M. Zhang
排队行为建模是交通和其他服务系统分析的核心。到目前为止，已经开发了几个排队模型，但很难获得其全局特性的分析见解。这是因为在大多数情况下，排队动力学被公式化为微分或差分方程，其解中可能存在不连续性，使得大多数传统的分析工具不足。因此，经常使用模拟来研究这些模型，如果处理不当，在某些间断附近的模拟可能会产生负流。在本文中，我们提出了一个连续时间排队模型，捕捉广义排队动态，瓶颈放电能力和需求可以同时变化。我们提供的见解，这个模型的全局特性，推导其封闭形式的变分解。而不是诉诸通常的哈密顿-雅可比理论，我们的推导是建立在一个内在的周期性属性的一般排队动力学结合测量理论分析。这种处理方法使我们能够得到更复杂边界条件下的结果，并作进一步的推广。我们展示了它的应用程序，并显示其解决方案的性能在排队模拟和性能边界。特别是，我们提供了图形，迭代和线性化的解决方案，这都是没有众所周知的负流问题与数值解的点队列模型。
Modeling queuing behavior is central to the analysis of transportation and other service systems. To date, several queuing models been developed, but analytical insights on their global properties are hard to obtain. This is because in most cases, queuing dynamics are formulated as differential or difference equations, with possible discontinuities in their solutions, making most conventional analytical tools inadequate. As a result, simulations are often used to study these models, and if not properly treated, negative flows could arise from the simulation near certain discontinuities. In this paper, we propose a continuous-time queuing model that captures generalized queuing dynamics, where bottleneck discharging capacity and demand can vary simultaneously. We provide insights on the global properties of this model, upon deriving its closed-form variational solutions. Rather than resorting to the usual Hamilton–Jacobi theory, our derivations are built on an intrinsic periodicity property of the general queuing dynamics combined with measure-theoretic analysis. This treatment allows us to obtain results with more complex boundary conditions and make further extensions. We demonstrate its applications and show its solution properties in queuing simulation and performance bounding. In particular, we provide graphical, iterative and linearized solution schemes, which are all devoid of the well-known negative flow issue associated with numerical solutions to the point queue model.