论文标题

数据驱动的自私路由模型:为什么无政府状态的价格确实取决于网络拓扑

Data-Driven Models of Selfish Routing: Why Price of Anarchy Does Depend on Network Topology

论文作者

Benita, Francisco, Bilò, Vittorio, Monnot, Barnabé, Piliouras, Georgios, Vinci, Cosimo

论文摘要

我们从理论和现实世界数据的角度研究流量路线。首先,我们介绍了一种新型游戏:$θ$无流量游戏。在这里,通勤者仅在其策略集中考虑其自由流动成本(非正式的长度)的路径位于最佳自由流量的小乘以$(1+θ)$常数,连接其源和目的地,其中$θ\ geq0 $。在一般拥塞/路由游戏以及Path-Disjoint网络的特殊情况下,我们为任意类别功能的POA($θ$)的紧密界限($θ$)提供了详尽的分析。其次,通过在新加坡使用大型移动性数据集,我们检查了成千上万的通勤者的分钟决策,发现$θ= 1 $是对代理商(PER)选择机制的很好估计。相比之下,在Pigou网络中,路线的自由流成本(因此$θ$)的比例为\ textit {infinite};因此,尽管这种最坏的案例网络在数学上很简单,但它们对应于人工路由方案,与现实世界中的条件几乎没有相似之处,从而通过明确研究其对$θ$的依赖性来证明无政府状态保证的可能性更高的可能性。例如,对于标准公路局(BPR)成本模型,其中$ c_e(x)= a_e x^4+b_e $,并且对于一般而言,标准POA的限制为$θ= \ infty $是$ 2.1505 $,并且对于通用网络以及PATHS-DISEDESEDSENTS and PARTISENTESEDSENTESS既紧张又有范围。相比之下,对于$θ= 1 $,在通用网络的情况下,POA仅为$ 1.6994 $,而对于Path-dischoint/Paralleal-Edge网络的POA甚至更小($ 1.3652 $),表明,这两种路线的几何形状都是由参数$θ$以及网络拓扑对POA产生的重大影响。

We investigate traffic routing both from the perspective of theory as well as real world data. First, we introduce a new type of games: $θ$-free flow games. Here, commuters only consider, in their strategy sets, paths whose free-flow costs (informally their lengths) are within a small multiplicative $(1+θ)$ constant of the optimal free-flow cost path connecting their source and destination, where $θ\geq0$. We provide an exhaustive analysis of tight bounds on PoA($θ$) for arbitrary classes of cost functions, both in the case of general congestion/routing games as well as in the special case of path-disjoint networks. Second, by using a large mobility dataset in Singapore, we inspect minute-by-minute decision-making of thousands of commuters, and find that $θ=1$ is a good estimate of agents' route (pre)selection mechanism. In contrast, in Pigou networks, the ratio of the free-flow costs of the routes, and thus $θ$, is \textit{infinite}; so, although such worst case networks are mathematically simple, they correspond to artificial routing scenarios with little resemblance to real world conditions, opening the possibility of proving much stronger Price of Anarchy guarantees by explicitly studying their dependency on $θ$. For example, in the case of the standard Bureau of Public Roads (BPR) cost model, where$c_e(x)= a_e x^4+b_e$, and for quartic cost functions in general, the standard PoA bound for $θ=\infty$ is $2.1505$, and this is tight both for general networks as well as path-disjoint and even parallel-edge networks. In comparison, for $θ=1$, the PoA in the case of general networks is only $1.6994$, whereas for path-disjoint/parallel-edge networks is even smaller ($1.3652$), showing that both the route geometries as captured by the parameter $θ$ as well as the network topology have significant effects on PoA.

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