Two-sided platforms rely on their recommendation algorithms to help visitors successfully find a match. However, on platforms such as VolunteerMatch, which has facilitated millions of connections between volunteers and nonprofits, a sizable fraction of website traffic arrives directly to a nonprofit's volunteering page via an external link, thus bypassing the platform's recommendation algorithm. We study how such platforms should account for this external traffic in the design of their recommendation algorithms, given the goal of maximizing successful matches. We model the platform's problem as a special case of online matching, where (using VolunteerMatch terminology) volunteers arrive sequentially and probabilistically match with one opportunity, each of which has a finite need for volunteers. In our framework, external traffic is interested only in their targeted opportunity; by contrast, internal traffic may be interested in many opportunities, and the platform's online algorithm selects which opportunity to recommend. In evaluating the performance of different algorithms, we refine the notion of competitive ratio by parameterizing it based on the amount of external traffic. After demonstrating the shortcomings of a commonly used algorithm that is optimal in the absence of external traffic, we propose a new algorithm, adaptive capacity (AC), which accounts for matches differently based on whether they originate from internal or external traffic. We provide a lower bound on AC's competitive ratio that is increasing in the amount of external traffic and that is close to (and, in some regimes, exactly matches) the parameterized upper bound we establish on the competitive ratio of any online algorithm. We complement our theoretical results with a numerical study motivated by Volunteer Match data where we demonstrate the strong performance of AC relative to current practice and further our understanding of the difference between AC and other commonly used algorithms.
