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 nonsubscribers 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.
