•Investigate the congestion management issues of a bottleneck-constrained highway system with manned vehicles (MVs) and autonomous vehicles (AVs)•Incorporate the effects of in-vehicle activity utilities and activity type choices of AV commuters in the model.•Differentiated and non-differentiated (or anonymous) step tolling schemes for the mixed MV and AV traffic system are analyzed and compared.•Queuing segregation phenomenon occurs between MV and AV commuters.•Optimal AV proportion solution that minimizes total social cost of the mixed MV and AV system is derived.•Differentiated step tolling scheme outperforms non-differentiated step tolling scheme in terms of total social cost and queuing removal rate. This paper addresses the congestion management issues of a bottleneck-constrained highway system with manned vehicles (MVs) and autonomous vehicles (AVs). A novel model that incorporates the in-vehicle activity utilities and activity type choices of AV commuters is presented for analyzing the equilibrium of the bi-modal bottleneck system with MVs and AVs. Time-varying and step tolling schemes accounting for the effects of in-vehicle activity utilities are analytically explored. In particular, a differentiated and a non-differentiated (or anonymous) step tolling scheme for the mixed MV and AV traffic system are analyzed and compared. The differentiated step tolling scheme means different toll levels across MV and AV commuters, whereas the non-differentiated step tolling scheme means an identical toll level for both the MV and AV commuters. The results show that a queuing segregation phenomenon occurs between the MV and AV commuters. The optimal AV proportion solution that minimizes the total social cost of the mixed MV and AV system exists. For a pure MV or AV system, the optimal step toll scheme can eliminate exactly half of the total queuing delay with the no-toll equilibrium for each of the differentiated and non-differentiated step tolling schemes. However, for a mixed MV and AV system, the queuing removal rate of the optimal differentiated step tolling scheme would exceed a half, whereas that of the optimal non-differentiated step tolling scheme may be lower than a half. The differentiated step tolling scheme outperforms the non-differentiated step tolling scheme in terms of total social cost and queuing removal rate.