In the emerging era of autonomous vehicles (AVs), an important question is how to integrate AVs in a multi-modal framework. Recent studies on Transportation Management Centres (TMCs) for future AVs addressed the issue of providing system optimal (SO) solution. However, none of them considered the possibility of developing a multi-modal SO-based solution. In this regard, we propose a novel multi-modal Transportation Management Centre (MMTMC) for future AVs, which controls both the routing and mode use of each traveller and distributes the AVs in such a way that SO flows are maintained for the whole network every day, while travellers on the same origin-destination (OD) have the same Multi-modal Average Travel Time (MMAVT) over a cycle or period of time (in days). That is, travellers on the same OD may encounter different travel times or costs on different days, but over the planning cycle of many days, their travel times will all average to be the same MMAVT, hence preserving the MMAVT equilibrium. Travellers will travel on single occupancy vehicles (SOVs) or high occupancy vehicles (HOVs) on different routes for different days within the planning cycle, while maintaining the same MMAVT overall for the cycle. Travellers on SOVs will experience no crowdedness while on HOVs will experience crowdedness. We model both the cases of minimum system time and minimum system cost (including crowdedness cost), and provide link-based solution first for both cases. For minimum system time, we apply the conventional Frank Wolfe algorithm to generate feasible link flows, whereas for the minimum system cost problem, we incorporate a sensitivity-based equilibrium procedure to derive the SOV, HOV link flows and demand profiles. Afterwards, we utilize the most likely path method to compute unique SOV and HOV path flows and solve the MMAVT equilibrium. Then, we investigate the case of mixed-equilibrium (ME), where some travellers are given the option not to subscribe to the MMTMC and do their own private routing, i.e. user equilibrium (UE) travellers, who are penalized by a toll. The tolls imposed on these MMTMC non-subscribers are defined by the travel time/cost difference between the MMAVT of subscribers and UE users based on their value-of-time (VOT) distribution. This study investigates the properties of this MMTMC routing pattern, the relationship between MMAVT, tolling, and SOV and HOV market penetration, which offers insights to integrate AVs in a multi-modal framework.

在自动驾驶汽车（AV）的新兴时代，一个重要的问题是如何将自动驾驶汽车集成到多模式框架中。最近对未来自动驾驶汽车运输管理中心（TMC）的研究解决了提供系统最优（SO）解决方案的问题。然而，他们都没有考虑开发基于 SO 的多模式解决方案的可能性。在这方面，我们为未来的自动驾驶汽车提出了一种新颖的多式联运运输管理中心（MMTMC），它控制每个旅行者的路线和模式使用，并以这样的方式分配自动驾驶汽车，使得整个网络的 SO 流量保持在每个时间。日，而同一出发地-目的地 (OD) 的旅行者在一个周期或一段时间（以天为单位）内具有相同的多式联运平均旅行时间 (MMAVT)。也就是说，同一 OD 上的旅行者在不同日期可能会遇到不同的旅行时间或成本，但在多天的计划周期中，他们的旅行时间将平均为相同的 MMAVT，从而保持 MMAVT 平衡。旅客将在规划周期内的不同日期乘坐单人车辆 (SOV) 或高载人车辆 (HOV) 在不同路线上出行，同时在整个周期内保持相同的 MMAVT。乘坐 SOV 的旅客不会感到拥挤，而乘坐 HOV 的旅客则会感到拥挤。我们对最小系统时间和最小系统成本（包括拥挤成本）的情况进行建模，并首先为这两种情况提供基于链路的解决方案。对于最小系统时间，我们应用传统的 Frank Wolfe 算法来生成可行的链路流，而对于最小系统成本问题，我们采用基于灵敏度的平衡程序来导出 SOV、HOV 链路流和需求概况。然后，我们利用最可能路径方法来计算唯一的 SOV 和 HOV 路径流并求解 MMAVT 平衡。然后，我们研究混合均衡（ME）的情况，其中一些旅行者可以选择不订阅 MMTMC 并进行自己的私人路由，即用户均衡（UE）旅行者，他们会受到通行费的惩罚。对这些 MMTMC 非订户征收的通行费是根据订户和 UE 用户的 MMAVT 之间的行程时间/成本差异（基于时间价值 (VOT) 分布）来定义的。本研究调查了这种 MMTMC 路线模式的属性、MMAVT、收费以及 SOV 和 HOV 市场渗透率之间的关系，为将 AV 集成到多模式框架中提供了见解。