The surge in online shopping has dramatically increased the demand for short-term curb access for package pickups and deliveries, leading to heightened competition for limited curb space. This paper addresses the problem of how the unique parking demand of deliverers, particularly their parking duration for delivery attempts linked to parking space availability, affects the dynamics of urban curb parking systems. We develop continuum models of a curb parking system and perform analytical analyses to understand the dynamics and steady-state properties of the system under the influence of increased urban deliveries. We conduct comparative statics to examine how various curb management measures, such as pricing, parking duration caps, and dedicated delivery bays, influence the equilibrium conditions, followed by comparisons of the theoretical capacity of these measures. We further demonstrate the working mechanism of delivery bays and their role in forestalling specific failures within a hybrid system with both general parkers and deliverers. Finally, we investigate curb management strategies in nonstationary operational contexts and prescribe the optimal strategies therein. Our findings offer valuable insights into the unique properties that deliverers introduce to curb parking dynamics, highlighting the need for a strategic reevaluation of current management practices. We find that pricing strategies for metered parking to general parkers prove to be more efficient and flexible compared with other interventions. Notably, our analysis suggests that when curb parking pricing is optimally calibrated, the necessity for dedicated delivery bays diminishes. Furthermore, we reveal that optimal curb management strategies could diverge in response to surges in demand, depending on whether the increase sources from general parkers or deliverers. To be effective, the sizing of delivery bays must align with the underlying causes of parking scarcity. History: This paper has been accepted for the Transportation Science Special Section on ISTTT25 Conference. Funding: This work was supported by the George Washington University [University Facilitating Fund]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2024.0569 .
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