\section{Conclusion}\label{sec:7}

In this paper, we study GMPMW and consider the complicated trade-off between reward accumulation and resource consumption imposed by multiple workers. We propose the OWA algorithm to tackle the new challenges. OWA balances the resource consumption across workers through a set of assignment guarantees and tracks the virtual resource consumption to capture the long-term resource availability.
The competitive ratio of OWA, $\alpha=\mathtt{P}_1(\{\gamma_l^*\})$, which is lower bounded by $\alpha'=\max\{{1}/{L},c\}\cdot(1-K^{-\frac{1}{2}})$, is tight and approaches the maximum competitive ratio. When there is only one worker, this lower bound (thus the competitive ratio $\alpha$) matches the best existing result for the original GMP. We perform trace-driven experiments to demonstrate the excellent capability of the OWA algorithm to accommodate multiple workers in GMPMW.