{"abstract":[{"lang":"eng","text":"We consider a scheduling problem where machines need to be rented from the\r\ncloud in order to process jobs. There are two types of machines available which\r\ncan be rented for machine-type dependent prices and for arbitrary durations.\r\nHowever, a machine-type dependent setup time is required before a machine is\r\navailable for processing. Jobs arrive online over time, have machine-type\r\ndependent sizes and have individual deadlines. The objective is to rent\r\nmachines and schedule jobs so as to meet all deadlines while minimizing the\r\nrental cost.\r\n  Since we observe the slack of jobs to have a fundamental influence on the\r\ncompetitiveness, we study the model when instances are parameterized by their\r\n(minimum) slack. An instance is called to have a slack of $\\beta$ if, for all\r\njobs, the difference between the job's release time and the latest point in\r\ntime at which it needs to be started is at least $\\beta$. While for $\\beta < s$\r\nno finite competitiveness is possible, our main result is an\r\n$O(\\frac{c}{\\varepsilon} + \\frac{1}{\\varepsilon^3})$-competitive online\r\nalgorithm for $\\beta = (1+\\varepsilon)s$ with $\\frac{1}{s} \\leq \\varepsilon\r\n\\leq 1$, where $s$ and $c$ denotes the largest setup time and the cost ratio of\r\nthe machine-types, respectively. It is complemented by a lower bound of\r\n$\\Omega(\\frac{c}{\\varepsilon})$."}],"department":[{"_id":"63"}],"user_id":"15415","citation":{"bibtex":"@article{Mäcker_Malatyali_Meyer auf der Heide_Riechers_2016, title={Cost-efficient Scheduling on Machines from the Cloud}, journal={arXiv:1609.01184}, author={Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Riechers, Sören}, year={2016} }","chicago":"Mäcker, Alexander, Manuel Malatyali, Friedhelm Meyer auf der Heide, and Sören Riechers. “Cost-Efficient Scheduling on Machines from the Cloud.” <i>ArXiv:1609.01184</i>, 2016.","ama":"Mäcker A, Malatyali M, Meyer auf der Heide F, Riechers S. Cost-efficient Scheduling on Machines from the Cloud. <i>arXiv:160901184</i>. 2016.","short":"A. Mäcker, M. Malatyali, F. Meyer auf der Heide, S. Riechers, ArXiv:1609.01184 (2016).","ieee":"A. Mäcker, M. Malatyali, F. Meyer auf der Heide, and S. Riechers, “Cost-efficient Scheduling on Machines from the Cloud,” <i>arXiv:1609.01184</i>. 2016.","apa":"Mäcker, A., Malatyali, M., Meyer auf der Heide, F., &#38; Riechers, S. (2016). Cost-efficient Scheduling on Machines from the Cloud. <i>ArXiv:1609.01184</i>.","mla":"Mäcker, Alexander, et al. “Cost-Efficient Scheduling on Machines from the Cloud.” <i>ArXiv:1609.01184</i>, 2016."},"type":"preprint","title":"Cost-efficient Scheduling on Machines from the Cloud","date_created":"2020-04-03T09:24:28Z","external_id":{"arxiv":["1609.01184"]},"publication":"arXiv:1609.01184","date_updated":"2022-01-06T06:52:50Z","status":"public","author":[{"full_name":"Mäcker, Alexander","last_name":"Mäcker","first_name":"Alexander","id":"13536"},{"full_name":"Malatyali, Manuel","last_name":"Malatyali","first_name":"Manuel"},{"last_name":"Meyer auf der Heide","full_name":"Meyer auf der Heide, Friedhelm","first_name":"Friedhelm","id":"15523"},{"first_name":"Sören","last_name":"Riechers","full_name":"Riechers, Sören"}],"year":"2016","language":[{"iso":"eng"}],"_id":"16396"}