  In the Online-Dial-a-Ride Problem (OLDARP) a server travels through a metric
space to serve requests for rides. We consider a variant where each request
specifies a source, destination, release time, and revenue that is earned for
serving the request. The goal is to maximize the total revenue earned within a
given time limit. We prove that no non-preemptive deterministic online
algorithm for OLDARP can be guaranteed to earn more than twice the revenue
earned by an optimal offline solution. We then investigate the
\textsc{segmented best path} ($SBP$) algorithm of~\cite{atmos17} for the
general case of weighted graphs. The previously-established lower and upper
bounds for the competitive ratio of $SBP$ are 4 and 6, respectively, under
reasonable assumptions about the input instance. We eliminate the gap by
proving that the competitive ratio is 5 (under the same reasonable
assumptions). We also prove that when revenues are uniform, $SBP$ has
competitive ratio 4. Finally, we provide a competitive analysis of $SBP$ on
complete bipartite graphs.
