## 2 Literature Review
Nevertheless, owing to the absence of supplementary travel costs, TRS garners superior public endorsement compared to alternative \"push\" strategies. Using [PERSON] and [PERSON]'s study as an example, they surveyed the public acceptance of a reservation system implemented on highways during holidays [27]. The results showed that over 80% of respondents were willing to adjust their departure times to reduce highway congestion during holidays. This reflects that TRS is more likely to gain public support and participation. Despite the promising outcomes of these studies, the cost and economic viability of TRS mechanisms remain largely underexplored. Implementing TRS requires substantial investments in infrastructure, data collection, and system management. Moreover, there are costs related to incentives and penalties, which must be balanced against the benefits of reduced congestion and improved travel time reliability. Some studies have begun to address this gap, considering factors such as public transportation fare revenues, penalties for non-compliance, and subsidies for system participants. A cost-benefit analysis of TRS would be valuable for understanding its economic feasibility, particularly when evaluating the long-term sustainability of such systems in urban settings. In the establishment of the TRS model, [PERSON] and [PERSON] laid the foundation for research in this domain by introducing a reservation policy to manage urban traffic demand, examining the potential benefits of adjusting departure times during holiday peak travel periods [28]. Building upon this foundational study, subsequent inquiries have broadened the application of TRS across diverse urban scenarios, enriching the conceptual framework of the domain. The urban road reservation system is further stratified into regional reservation, road reservation, and lane reservation based on the scope of the reserved space. [PERSON] et al. developed a downtown space reservation system that mitigates congestion in cordon-based central areas by requiring driver reservations [29]. [PERSON] et al. postulated that a heterogeneous urban area is segmented into multiple homogeneous regions, with vehicle entry permitted only when the anticipated traffic volume remains below the critical capacity during the time interval required to traverse the urban area [30]. [PERSON] et al. demonstrated, utilizing real-world traffic data, that a lane reservation strategy could significantly reduce travel time and air pollution for the lanes in question [9]. [PERSON] et al. proposed a time-dependent route reservation method to alleviate traffic congestion [31]. Some studies have increased the flexibility of travelers' choice of reservation time by introducing evolutionary [32] or pricing mechanisms [33] that combine a dynamic auction with capacity control rules. Improving travel time reliability could be a huge benefit of the reservation system. However, there remains a lacuna in the extant literature regarding the explicit consideration of the impact that departure time modifications yield on TRS's efficacy and intrinsic value. Addressing this gap, the present study formulates a multi-objective optimization model to examine the influence of disparate subsidy strategies on the modulation of travelers' departure times and the consequent shift in travel modes. Moreover, existing research involving TRS has primarily focused on the scheduling models for reserved vehicles [10], the allocation of travel rights [34; 35], and evaluating the effects of TRS implementation [8]. These studies often rely on completely known information for traffic assignment and tend to overlook the actual behavior of heterogeneous travelers. Due to technical and informational limitations, travelers cannot always obtain complete information.