Costefficient Scheduling on Machines from the Cloud
Abstract
We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machinetype dependent prices and for arbitrary durations. However, a machinetype dependent setup time is required before a machine is available for processing. Jobs arrive online over time, have machinetype dependent sizes and have individual deadlines. The objective is to rent machines and schedule jobs so as to meet all deadlines while minimizing the rental cost. Since we observe the slack of jobs to have a fundamental influence on the competitiveness, we study the model when instances are parameterized by their (minimum) slack. An instance is called to have a slack of $\beta$ if, for all jobs, the difference between the job's release time and the latest point in time at which it needs to be started is at least $\beta$. While for $\beta < s$ no finite competitiveness is possible, our main result is an $O(\frac{c}{\varepsilon} + \frac{1}{\varepsilon^3})$competitive online algorithm for $\beta = (1+\varepsilon)s$ with $\frac{1}{s} \leq \varepsilon \leq 1$, where $s$ and $c$ denotes the largest setup time and the cost ratio of the machinetypes, respectively. It is complemented by a lower bound of $\Omega(\frac{c}{\varepsilon})$.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.01184
 Bibcode:
 2016arXiv160901184M
 Keywords:

 Computer Science  Data Structures and Algorithms