  We consider the Online Rent Minimization problem, where online jobs with
release times, deadlines, and processing times must be scheduled on machines
that can be rented for a fixed length period of $T$. The objective is to
minimize the number of machine rents. This problem generalizes the Online
Machine Minimization problem where machines can be rented for an infinite
period, and both problems have an asymptotically optimal competitive ratio of
$O(\log(p_{\max}/p_{\min}))$ for general processing times, where $p_{\max}$ and
$p_{\min}$ are the maximum and minimum processing times respectively. However,
for small values of $p_{\max}/p_{\min}$, a better competitive ratio can be
achieved by assuming unit-size jobs. Under this assumption, Devanur et al.
(2014) gave an optimal $e$-competitive algorithm for Online Machine
Minimization, and Chen and Zhang (2022) gave a $(3e+7)\approx
15.16$-competitive algorithm for Online Rent Minimization. In this paper, we
significantly improve the competitive ratio of the Online Rent Minimization
problem under unit size to $6$, by using a clean oracle-based online algorithm
framework.
