  Two-sided platforms rely on their recommendation algorithms to help visitors
successfully find a match. However, on platforms such as VolunteerMatch (VM) --
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 VM terminology) volunteers arrive
sequentially and probabilistically match with one opportunity, each of which
has 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 different algorithms, we
parameterize the competitive ratio 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 VM data that demonstrates the strong performance of AC and
furthers our understanding of the difference between AC and other commonly-used
algorithms.
